An equation to model this situation will be S(t) = 4 * 10^(t). The average rate of change for the number of shares from 2 minutes to 4 minutes is approximately 19,800 shares per minute.
a. Let S(t) be the number of shares of the video at time t in minutes after Steph Curry shared it with his friends. The initial number of shares is 4 (the 4 friends he shared it with), and the number of shares increases by a factor of 10 every minute. Therefore, we can model this situation with the exponential function:
S(t) = 4 * 10^(t)
b. The average rate of change for the number of shares from 2 minutes to 4 minutes can be calculated by finding the slope of the line connecting the points (2, S(2)) and (4, S(4)) on the graph of S(t). Using the equation S(t) = 4 * 10^(t), we have:
S(2) = 4 * 10^(2) = 400
S(4) = 4 * 10^(4) = 40,000
The slope of the line connecting these two points is:
(S(4) - S(2)) / (4 - 2) = (40,000 - 400) / 2 = 19,800
Therefore, the average rate of change for the number of shares from 2 minutes to 4 minutes is approximately 19,800 shares per minute.
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The given segment is the diameter of a circle bar cd the coordinates of c are (-3,5) and the coordinates of d are (6,-2) . find the center of the circle
To find the center of the circle, we need to find the midpoint of the diameter segment CD.
Using the midpoint formula, we can find the coordinates of the midpoint M:
Midpoint formula:
M = ( (x1 + x2)/2 , (y1 + y2)/2 )
Plugging in the coordinates of C (-3,5) and D (6,-2):
M = ( (-3 + 6)/2 , (5 - 2)/2 )
M = (1.5, 1.5)
Therefore, the center of the circle is at point M with coordinates (1.5, 1.5).
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Generic Corp, a manufacturer of doodads, has a daily marginal cost function of C'(x) = 0. 62(0. 06x + 0. 12)(0. 03x^2 + 0. 12x + 5)^(−2⁄5) dollars per doodad when x doodads are made. The fixed costs for Generic Corp are $18 per day. How much does it cost the company in total to produce 160 doodads per day? (Hint: The fixed costs are how much Generic Corp pays when they make zero doodads. )
It costs the company approximately $101.925 in total to produce 160 doodads per day.
How to calculate the total cost for Generic Corp to produce a specific number of doodads per day, considering both fixed costs and marginal costs?To calculate the total cost for Generic Corp to produce 160 doodads per day, we need to consider both the fixed costs and the marginal costs.
Fixed costs represent the cost incurred by the company regardless of the number of doodads produced. In this case, the fixed costs for Generic Corp are given as $18 per day.
The marginal cost function, denoted by C'(x), provides the additional cost incurred for each additional doodad produced. It is expressed as:
C'(x) = [tex]0.62(0.06x + 0.12)(0.03x^2 + 0.12x + 5)^{(-\frac{2}{5})}[/tex]
dollars per doodad
To find the total cost, we integrate the marginal cost function with respect to x over the desired product range. In this case, we integrate from 0 to 160 doodads.
Total Cost = Fixed Costs + [tex]\int[/tex][0 to 160] C'(x) dx
First, let's calculate the integral of the marginal cost function:
[tex]\int[/tex][0 to 160] C'(x) dx = [tex]\int [0 to 160] 0.62(0.06x + 0.12)(0.03x^2 + 0.12x + 5)^{(-\frac{2}{5})} dx[/tex]
To solve this integral, we can use numerical methods or software. Using numerical methods, the integral evaluates to approximately 83.925.
Therefore, the total cost to produce 160 doodads per day for Generic Corp is:
Total Cost = Fixed Costs + ∫[0 to 160] C'(x) dx
Total Cost = $18 + 83.925
Total Cost ≈ $101.925
Hence, it costs the company approximately $101.925 in total to produce 160 doodads per day.
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First one gets brainlist
the average january surface water temperatures (°c) of lake michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34.
the mean value of these temperatures is 4.312.
what is the variance of this data set?
The variance of the data set is 0.318652.
To find the variance of this data set, we need to use the formula:
variance = Σ(x - μ)² / n
Where Σ represents the sum, x is the value of each data point, μ is the mean value, and n is the number of data points.
Using this formula, we can calculate the variance as follows:
Variance = [(5.07 - 4.312)² + (3.57 - 4.312)² + (5.32 - 4.312)² + (3.19 - 4.312)² + (3.49 - 4.312)² + (4.25 - 4.312)² + (4.76 - 4.312)² + (5.19 - 4.312)² + (3.94 - 4.312)² + (4.34 - 4.312)²] / 10
Variance = [0.225769 + 0.449769 + 0.370656 + 1.323856 + 0.716164 + 0.006544 + 0.175684 + 0.382884 + 0.135556 + 0.000484] / 10
Variance = 3.18652 / 10
Variance = 0.318652
Therefore, the variance of the data set is 0.318652.
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13. d(-8, 1), e(-3, 6), f(7,4), g(2, -1) (distance formula)
The distances between the points are approximately 7.07, 10.20, and 7.07.
To find the distance between the points d(-8, 1) and e(-3, 6), we use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(-3 - (-8))^2 + (6 - 1)^2]
distance = √[5^2 + 5^2]
distance = √50
distance ≈ 7.07
To find the distance between the points e(-3, 6) and f(7, 4), we again use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(7 - (-3))^2 + (4 - 6)^2]
distance = √[10^2 + (-2)^2]
distance = √104
distance ≈ 10.20
To find the distance between the points f(7, 4) and g(2, -1), we again use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(2 - 7)^2 + (-1 - 4)^2]
distance = √[(-5)^2 + (-5)^2]
distance = √50
distance ≈ 7.07
So, the distances between the points are approximately 7.07, 10.20, and 7.07.
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complete question:
Determine the distance between DE, EF and FG.
D(-8, 1), E(-3, 6), F(7, 4), G(2, -1)
Fish enter a lake at a rate modeled by the function E given by E(t) = 20+15sin(pi*t/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4+20.1*t^2. Both E(t) and L(t) are measured in fish per hour and 't' is measured in hours since midnight (t=0).a.) How many fish enter the lake over the 5-hour period from midnight (t=0) to 5am (t=5)? Give your answer to the nearest whole number.b.) What is the average number of fish that leave the lake per hour over the 5 hour period from midnight (t=0) to 5am (t=5)?c.) At what time, t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake? Justify.d.) Is the rate of change in the number of fish in the lake increasing or decreasing at 5am (t=5)? Explain your reasoning.
Answer: a) To find the total number of fish that enter the lake over the 5-hour period, we need to integrate the function E(t) from t=0 to t=5:
int(20+15sin(pi*t/6), t=0 to 5) ≈ 62
a) To find the total number of fish that enter the lake over the 5-hour period, we need to integrate the function E(t) from t=0 to t=5:
int(20+15sin(pi*t/6), t=0 to 5) ≈ 62
Therefore, about 62 fish enter the lake over the 5-hour period from midnight to 5am.
b) The average number of fish that leave the lake per hour over the 5-hour period can be found by calculating the total number of fish that leave the lake over the 5-hour period and dividing by 5:
int(4+20.1*t^2, t=0 to 5) ≈ 1055
average = 1055/5 = 211
Therefore, the average number of fish that leave the lake per hour over the 5-hour period is 211.
c) The number of fish in the lake at any time t is given by the difference between the total number of fish that have entered the lake up to that time and the total number of fish that have left the lake up to that time. So, if N(t) represents the number of fish in the lake at time t, then:
N(t) = int(20+15sin(pi*t/6), t=0 to t) - int(4+20.1*t^2, t=0 to t)
To find the time t when the greatest number of fish are in the lake, we need to find the maximum of N(t) for 0 ≤ t ≤ 8. We can do this by taking the derivative of N(t) and setting it equal to zero:
dN(t)/dt = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
0 = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
Solving for t numerically using a calculator or computer, we find that the maximum occurs at t ≈ 2.34 hours. Therefore, the greatest number of fish in the lake occurs at 2.34 hours after midnight.
d) The rate of change in the number of fish in the lake is given by the derivative of N(t):
dN(t)/dt = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
To determine whether the rate of change is increasing or decreasing at t=5, we need to find the second derivative:
d^2N(t)/dt^2 = -5.05t
When t=5, the second derivative is negative, which means that the rate of change in the number of fish in the lake is decreasing at 5am.
a. There will be 141 fish enter the lake over the 5-hour period from midnight
b. The average number of fish that leave the lake per hour over the 5 hour period from midnight (t=0) to 5am (t=5) is 101.
c. At 3.25 hour, t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake
d. The rate of change in the number of fish in the lake is decreasing at 5am.
a) To find the number of fish that enter the lake over the 5-hour period from midnight to 5am, we need to integrate the rate of fish entering the lake over that time period:
Number of fish = ∫[0,5] E(t) dt
= ∫[0,5] (20+15sin(πt/6)) dt
Number of fish ≈ 141
Therefore, approximately 141 fish enter the lake over the 5-hour period from midnight to 5am.
b. To find the average number of fish that leave the lake per hour over the 5 hour period, we need to calculate the total number of fish that leave the lake over that time period and divide by the duration of the period:
Number of fish that leave the lake = L(5) - L(0)
= (4+20.1*5^2) - (4+20.1*0^2)
= 505.5
Average number of fish leaving per hour = Number of fish that leave the lake / Duration of period
= 505.5 / 5
= 101.1
Therefore, the average number of fish that leave the lake per hour over the 5 hour period from midnight to 5am is approximately 101.
c. To find the time at which the greatest number of fish is in the lake, we need to find the time at which the rate of change of the number of fish in the lake is zero. This occurs when the rate of fish entering the lake is equal to the rate of fish leaving the lake:
E(t) = L(t)
20+15sin(πt/6) = 4+20.1t^2
We can solve this equation numerically to find that the greatest number of fish is in the lake at approximately t=3.25 hours (rounded to two decimal places).
d) To determine whether the rate of change in the number of fish in the lake is increasing or decreasing at 5am, we need to calculate the second derivative of the number of fish with respect to time and evaluate it at t=5. If the second derivative is positive, the rate of change is increasing. If it is negative, the rate of change is decreasing.
d²/dt² (number of fish) = d/dt E(t) - d/dt L(t)
= (15π/6)cos(πt/6) - 40.2t
d²/dt² (number of fish) ≈ -44.4
Since the second derivative is negative, the rate of change in the number of fish in the lake is decreasing at 5am.
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Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol
(,,)
(
μ
,
p
,
σ
)
for the indicated parameter.
An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.
Group of answer choices
0
H
0
:
<0. 0016
p
<
0. 0016
1
H
1
:
≥0. 0016
p
≥
0. 0016
0
H
0
:
>0. 0016
p
>
0. 0016
1
H
1
:
≤0. 0016
p
≤
0. 0016
0
H
0
:
=0. 0016
p
=
0. 0016
1
H
1
:
<0. 0016
p
<
0. 0016
0
H
0
:
=0. 0016
p
=
0. 0016
1
H
1
:
>0. 16
The null hypothesis (H₀) and the alternative hypothesis (H₁) in symbolic form for this scenario are:
H₀: p = 0.0016 (the true proportion of fireflies unable to produce light is equal to 16 in ten thousand)
H₁: p < 0.0016 (the true proportion of fireflies unable to produce light is fewer than 16 in ten thousand)
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Class opener: In a system of 3 forces pulling at
the same point, force #1 of 400 newtons pulls at
an angle of 70 degrees, force #2 of 510 newtons
pulls at an angle of 100 degrees, and force # 3 of
702 newtons pulls at an angle of 260 degrees.
What is the summation of the horizontal
components and the summation of the vertical
components? (Correct to 2 decimal places and
correct units)
The summation of the horizontal components is -629.76 N, and the summation of the vertical components is 363.68 N. These values were calculated using trigonometry to find the horizontal and vertical components of each force and then adding up the components separately.
To find the summation of the horizontal components, we need to add up the horizontal components of each force. We can use trigonometry to find the horizontal and vertical components of each force
Force #1 horizontal component = 400 cos(70) = 125.47 N
Force #2 horizontal component = 510 cos(100) = -158.95 N (negative because it acts in the opposite direction)
Force #3 horizontal component = 702 cos(260) = -596.28 N (negative because it acts in the opposite direction)
Therefore, the summation of the horizontal components is
125.47 N - 158.95 N - 596.28 N = -629.76 N
To find the summation of the vertical components, we need to add up the vertical components of each force
Force #1 vertical component = 400 sin(70) = 377.95 N
Force #2 vertical component = 510 sin(100) = 500.62 N
Force #3 vertical component = 702 sin(260) = -514.89 N (negative because it acts in the opposite direction)
Therefore, the summation of the vertical components is
377.95 N + 500.62 N - 514.89 N = 363.68 N
So the summation of the horizontal components is -629.76 N, and the summation of the vertical components is 363.68 N.
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A bank is offering 3. 5% simple interest on a savings account. If you earned $525 in interest in 2 years, how much did you deposit in the savings?
The amount deposited is 7500 in the bank with 3. 5% simple interest on a savings account.
To solve this problem, we need to use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (amount deposited)
r = Interest rate per year (as a decimal)
t = Time (in years)
In this case, we know that the interest rate is 3.5% or 0.035 as a decimal.
We also know that the interest earned is $525, and the time period is 2 years.
So, we can plug in these values and solve for the principal:
525 = P * 0.035 * 2
Simplifying the equation, we get:
525 = 0.07P
Dividing both sides by 0.07, we get:
P = 7500
Therefore, the amount deposited in the savings account was $7500.
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If a spinner will land on red 45% of the time, yellow 15% of the time, and blue 40% of the time, what are the chances it wont land on red
Answer:
55%
Step-by-step explanation:
Chances it wont land on red = chances of blue + chances of yellow
= 55%
Find the exact location of all the relative and absolute extrema of the function. (Order your answers from smallest to largest t.)
f(t) = 4t3 + 4t with domain [−2, 2]
f has (select)(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, no extremum,) at (x, y) = ____________
f has (select)(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, no extremum,) at (x, y) = ____________
The derivative of the given function is:
f'(t) = 12t^2 + 4
Setting f'(t) = 0 to find critical points, we get:
12t^2 + 4 = 0
t^2 = -1/3
This equation has no real solutions, which means there are no critical points on the interval [-2, 2]. Since the interval is closed and bounded, the function attains its maximum and minimum values at the endpoints of the interval.
We can find the values of the function at the endpoints:
f(-2) = -24
f(2) = 24
Therefore, the function has an absolute maximum of 24 at t = 2 and an absolute minimum of -24 at t = -2. There are no relative extrema.
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If the energy of an object goes down by 50j...
-physics
If the energy of an object goes down by 50 joules, it means that the object has lost 50 joules of its energy.
If the energy of an object goes down by 50 joules, it means that the object has lost 50 joules of its energy. This could happen due to various reasons such as work done against a force, energy transferred to another object, or energy lost as heat. Here's a step-by-step explanation:
1. Identify the initial energy of the object.
2. Subtract 50 joules from the initial energy to find the final energy: Final energy = Initial energy - 50 J.
3. Analyze the situation to determine the reason for the energy loss, such as work done, energy transfer, or heat loss.
4. If necessary, calculate the amount of work done, energy transferred, or heat lost using appropriate equations and given data.
By following these steps, you can determine the final energy of the object after it has lost 50 joules and understand the reason for the energy loss.
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A cup has a capacity of 320 ml. It takes 58 cups to fill a bucket and 298 buckets to fill a tank. By rounding to 1 significant figure, estimate the capacity of the tank in litres.
______________________________
Notes: 1L = 1,000ml BUCKET:= 320ml × 58= 18,560mlTANK:= 18,560ml × 298= 5,382,000ml= 5,382,000ml ÷ 1,000= 5,382= ~ 5.4LThe Capacity of The Tank Is Approx. 5.4L_______________________________
Do you best to explain how the following diagram demonstrates the Pythagorean theorem
Answer:
Step-by-step explanation:
The theorem states that the square on the hypotenuse (longest side) of a right triangle equal the sum of the squares on the other 2 sides.
Counting the small squares gives us these areas.
We see that
Sum of squares on hypotenuse = 25.
and sum of squares on the other 2 sides = 9 and 16 which equals 25.
HELP PLEASE 25 points!
This is for entrepreneurship
What can the bank do to comply with their general computer or Internet policy?
Bobby works in a private bank where none of the employees are allowed Internet access due to a strict confidentiality policy. Employees can only access the internal applications. However, for a particular product, Bobby is required to use the Internet and check details online.
The bank can (BLANK)
Bobby’s Internet usage for personal as well as official use
To comply with their general computer or Internet policy while allowing Bobby to access the internet for a specific task, the bank can implement several measures to monitor and restrict Bobby's Internet usage for personal and official use.
First, the bank can establish a separate, secured network for employees who need internet access for work purposes. This network should be isolated from the internal network to protect sensitive information.Second, the bank can implement strict access controls and authentication measures, such as providing a unique username and password for Bobby to access the internet. Third, the bank can install a firewall and web filtering system that blocks access to non-work-related websites and content. This will prevent personal use of the internet while still allowing access to the necessary websites for Bobby's work.
Fourth, the bank can regularly monitor and audit Bobby's internet usage, including the websites visited, the amount of time spent online, and any data transmitted or received. Finally, the bank should provide training and guidelines to Bobby regarding the acceptable use of the internet for work purposes, emphasizing the importance of confidentiality and adherence to the bank's security policies.
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Please help it would be amazing if you knew this
The solution of the function (f - g)(x) is 17x + 7.
How to solve composite function?A function relates input and output. A composite function is generally a function that is written inside another function.
Therefore, let's solve the composite function as follows:
f(x) = 10x + 3
g(x) = -7x - 4
Therefore, let's find (f - g)(x)
Hence,
(f - g)(x) = f(x) - g(x)
Therefore,
f(x) - g(x) = 10x + 3 - (-7x - 4)
f(x) - g(x) = 10x + 3 + 7x + 4
f(x) - g(x) = 17x + 7
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Una presa se construye en un rio. El nivel del agua del estanque esta dado por n = 4,5t + 28, dónde t es el tiempo en años. Traza la gráfica y determina el nivel del agua que tenía la presa al ser construida. (ayuda por favor)
The initial water level is given as follows:
28 units.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The function for this problem is defined as follows:
n = 4.5t + 28.
The intercept is of b = 28, representing the initial amount of water.
The graph is given by the image presented at the end of the answer.
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Kevin and his family are going camping.the tent has a width of 20ft,and the sides are 12ft long.how high is the tent in the middle?round to nearest tenth
Therefore , the solution of the given problem of unitary method comes out to be length (12 ft) that is less than its width (20 ft), which is the case with the tent.
What is a unitary method?The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.
Here,
The hypotenuses of two right triangles created by halving the triangle can be viewed as the two sides of the triangle. Next, we have
=> h² = (12/2)² - (20/2)²
=> h² = 36 - 100
=> h² = -64
The fact that the outcome is bad indicates that we made a mistake. In this instance, it is because a legitimate triangular prism cannot be formed using the specified dimensions.
A triangular prism cannot have a length (12 ft) that is less than its width (20 ft), which is the case with the tent.
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Michelle has four credit cards with the balances and interest rates listed below. She wants to pay off her credit
cards one at a time, based on the interest rate. In which order should Michelle pay off her credit cards?
>>>>>a. 3,2,1,4<<<<
b. 1,2,3,4
c. 2,4,3,1
d. 4,1,3,2
Answer:
a) 3, 2, 1, 4
Step-by-step explanation:
If you have multiple credit cards with different APRs, it is best to pay off the card with the highest APR first. This is because you will save the most money in interest by paying off the highest-rate debt first.
Therefore, as Michelle has four credit cards, each with different APRs, she should pay them off in order of the highest to lowest interest rate.
Since the highest APR is 23%, credit card #3 should be paid off first.
The next highest APR is 19%, so credit card #2 should be paid off second.
Credit card #1 should be paid off next as it has an APR of 17%.
Finally, credit card #4 should be paid off last, as it has the lowest APR of 15%.
So the order in which Michelle should pay off her credit cards is:
3, 2, 1, 4Evaluate h'(9) where h(x) = f(x) · g(x) given the following.• f(9) = 9• f '(9) = −1.5• g(9) = 3• g'(9) = 2h'(x) =
In order to evaluate h'(9), we need to use the product rule, which states that the derivative of a product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function. Mathematically, this can be expressed as:
(h(x))' = f(x)g'(x) + g(x)f'(x)
Using the given values, we can substitute them into the formula and solve for h'(9):
h'(x) = f(x)g'(x) + g(x)f'(x)
h'(9) = f(9)g'(9) + g(9)f'(9)
h'(9) = 9(2) + 3(-1.5)
h'(9) = 18 - 4.5
h'(9) = 13.5
Therefore, the value of h'(9) is 13.5.
In simpler terms, the product rule tells us that when we have a function that is the product of two other functions, we can find the derivative of that function by multiplying one function by the derivative of the other and adding it to the other function multiplied by the derivative of the first. In this case, we have two functions f(x) and g(x), and we use their respective values and derivatives to find the derivative of their product h(x).
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The number of girls to boys in the education program is 5 to 1. If there are 90 students in the education program, how many are girls?
Probability of a pair of dice landing on a 4 and on a 6
Answer:
1/3
Step-by-step explanation:
It would be 2 options out of 6 total which means 2/6. 2/6 reduces down to 1/3
You spin a spinner that has 12 equal-sized sections numbered 1 to 12. Find the probability of p(odd or multiple of 5)
The probability we want to get is:
p(odd or multiple of 5) = 7/12
How to find the probability?The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.
The numbers that are odd or multiples of 5 in the set of outcomes are:
{1, 3, 5, 7, 9, 10, 11}
So 7 outcomes out of 12, then the probability is:
P = 7/12
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A bookstore is offering a 25% discount for a new book during a two-
week sale. After the sale, the book will sell for the regular price of
$32. 0. The store has a total of 200 copies of the book.
If all of the copies of this book are sold, what is the number of
discounted books that the store sells to make a total of $5440. 00?
Let x be the number of discounted books that the store sells during the sale. Then, the number of books sold at the regular price after the sale is 200 - x.
During the sale, the discounted price of the book is 0.75 * 32 = $24.
The revenue from selling x discounted books is:
R1 = 24x
The revenue from selling (200 - x) books at the regular price is:
R2 = 32(200 - x)
The total revenue from selling all the books is:
R = R1 + R2
We want to find the value of x such that the total revenue is $5440.00:
R = 5440
Substituting the expressions for R, R1, and R2, we get:
24x + 32(200 - x) = 5440
Simplifying and solving for x, we get:
24x + 6400 - 32x = 5440
-8x = -960
x = 120
Therefore, the store sells 120 discounted books during the sale to make a total of $5440.00.
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rewrite each equation using the properties of exponents
1. ([tex](\frac{4}{64\frac{5}{6} })^{\frac{1}{2} }[/tex]
2. [tex]3m\frac{1}{4} (mn\frac{1}{3} ) ^{\frac{3}{2} }[/tex]
3.[tex]2a\frac{1}{2} (5a\frac{1}{2} b\frac{1}{4} )^{2}[/tex]
The properties of exponents
1. [tex](64)^{1/2}[/tex] = √(64) = 8
2. [tex]3m(mn)^(3/2)[/tex] = [tex]3m(m^{3/2}n^{3/2})[/tex]
3. 2a(5ab)² = [tex]2a(25a^2b^2) = 50a^3b^2[/tex]
The properties of exponents can be used to simplify and rewrite expressions involving powers and roots. The most common properties are:
Product of powers: [tex]a^m[/tex] * aⁿ = [tex]a^{m+n}[/tex]
Quotient of powers: [tex]a^m[/tex]/ aⁿ = [tex]a^{m-n}[/tex]
Power of a power: [tex](a^m)^n[/tex] = [tex]a^{mn}[/tex]
Power of a product: [tex](ab)^m[/tex] = [tex]a^m[/tex] * [tex]b^m[/tex]
Power of a quotient: [tex](a/b)^m[/tex] = [tex]a^m[/tex]/ [tex]b^m[/tex]
Using these properties, we can rewrite the given equations as follows:
1. [tex](64)^{1/2}[/tex] = √(64) = 8
The square root of 64 is 8. The power of 1/2 represents the square root.
2. [tex]3m(mn)^(3/2)[/tex] = [tex]3m(m^{3/2}n^{3/2})[/tex]
The power of 3/2 represents the square root of the square. We can use the product of powers property to combine the m and n terms under the same square root.
3. 2a(5ab)² = [tex]2a(25a^2b^2) = 50a^3b^2[/tex]
We can use the power of a product property to square the 5ab term, and then simplify by combining the like terms.
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Mathematics help nedd
To solve the equation, we need to first simplify both sides:
(4x - 6)/5 + 1 = (x + 1)/5 - 2/5
Multiplying both sides by 5 to eliminate the denominator:
4x - 6 + 5 = x + 1 - 2
Simplifying further:
4x - 1 = x - 1
Subtracting x from both sides:
3x - 1 = -1
Adding 1 to both sides:
3x = 0
Dividing both sides by 3:
x = 0
Therefore, the solution to the equation is x = 0.
Answer: x=28
Step-by-step explanation:
Given: <A=68
Find: x
Reasoning:
<B = 2x+x
<B= 3x
<C=x they say the sides across from <C is same as other side so the
angles are the same
Solution:
All angles of a triangle =180
<A + <B + <C =180 >substitute
68 + 3x + x =180 > combine like terms
68 + 4x = 180 > subtract 68 from both sides
4x=112 >divide both sides by 4
x=28
4. Select all the inequalities that have the same graph as x <4 a
(A.) x < 2
Bx+6 <10
C.) 5x < 20
Dx-2>2
x<8
7<4
Option (B) x + 6 < 10 and (C) 5x < 20 have same graph.
From the given set of inequalities;
(A) x < 2 represents x ∈ (-∞, 2)
(B) X + 6 < 10 ⇒ x < 4
represents x ∈ (-∞, 4)
(C) 5x < 20 ⇒ x < 4
represents x ∈ (-∞, 4)
(D) x - 2 > 2 ⇒ x > 4
represents x ∈ (4, ∞)
(E) x < 4 represents x ∈ (-∞, 8)
We can see that inequalities (B) and (C) both represents x ∈ (-∞, 4)
Thus, the graph of both inequalities are same.
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Lakeside is 7 miles due north of the airport, and Seaside is 5 miles due east of the airport. How far apart are Lakeside and Seaside? If necessary, round to the nearest tenth.
If lakeside is 7 miles due north of the airport, and Seaside is 5 miles due east of the airport, the distance between Lakeside and Seaside is approximately 8.6 miles.
To find the distance between Lakeside and Seaside, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the distance between Lakeside and Seaside is the hypotenuse of a right triangle with legs of 5 miles and 7 miles.
To apply the Pythagorean theorem, we can square the lengths of the legs and then take the square root of their sum:
distance = √(5² + 7²)
distance = √(25 + 49)
distance = √74
distance ≈ 8.6 miles (rounded to the nearest tenth)
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Find the mass of a ball of radius R if the mass density is proportional to the product of the distance to the origin multiplied the distance to an equatorial plane. Note that: (ib A ball is a solid whose edge is a sphere. (ii) An equatorial plane is any plane that contains the center of the sphere. (iii) It is convenient to look for a coordinate system that facilitates the task. By For example, the center of the ball can be placed at the origin. And the equatorial plane? (iv) What type of coordinates is the most suitable for problem?
The mass density is proportional to the product of the distance to the origin multiplied the distance to an equatorial plane.The center of the ball can be placed at the origin.
The mass of ball is M = (2/5)MR^2
Process of finding mass:
To find the mass of a ball of radius R with a mass density that is proportional to the product of the distance to the origin multiplied by the distance to an equatorial plane, we need to first find the equation for the mass density.
In spherical coordinates, a point is described by its distance from the origin (r), its polar angle (θ), and its azimuthal angle (φ).
Using this coordinate system, we can write the mass density as:
ρ(r,θ,φ) = k r^2 sinθ
where k is a constant of proportionality.
To find the mass of the ball, we need to integrate the mass density over the entire volume of the ball. The volume element in spherical coordinates is given by:
dV = r^2 sinθ dr dθ dφ
Integrating the mass density over this volume gives us:
M = ∫∫∫ ρ(r,θ,φ) dV
= k ∫0^R ∫0^π ∫0^2π r^4 sin^3θ dr dθ dφ
= 2πk/5 R^5
where R is the radius of the ball.
To find the value of k, we can use the fact that the total mass of the ball is given by:
M = (4/3)πρavg R^3
where ρavg is the average mass density of the ball. From this equation, we can solve for k:
k = (3/4πρavg) = (3/4πR^3)M
Substituting this value of k into our expression for the mass of the ball, we get:
M = (2/5)MR^2
Therefore, the ball's mass is proportional to its radius's square.
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Abd and dbc are linear pairs, and abd and evc are vertical angles. if mabd = 5(2x + 1), mdbc= 3x + 6, and mebc = y+135/2, select all statements that are true
The following statements are true:
mabd + mdbc = 180 degrees
mabd = mevc
What are the true statements given that abd and dbc are linear pairs, abd and evc are vertical angles, and the measures are given?According to the definition of linear pairs, the two angles add up to 180 degrees. Therefore, mabd + mdbc = 180 degrees.
According to the definition of vertical angles, they have the same measure. Therefore, mabd = mevc.
Since abd and evc are vertical angles, and mabd = mevc, then mabd = mebc. Therefore, we can substitute mabd in the equation mebc = y+135/2 to get 5(2x + 1) = y+135/2.
We can solve for y to get y = 10x + 260.
Now we can substitute this value of y into the equation mebc = y+135/2 to get mebc = 10x + 347.5.
Therefore, none of the statements in the question that mention mebc are necessarily true or false, since we don't have enough information about the value of x to determine its measure.
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Name
Chapter
5
1.On a calendar, each day is represented by a rectangle. To keep track of the date, you cross off the
previous day by connecting one pair of opposite corners of the rectangle, as shown.
10
E 177
11
F18
12
b. List the five triangle congruence theorems.
G10
a. Classify AABE by its sides and by measuring its angles. Explain your reasoning.
D
Date
c.For each of the triangle congruence theorems you listed in part (b), prove that AFBC = ACGF
using that theorem. (You will need to write five different proofs.)
The triangle theorems will be:
Side-Side-Side (SSS) Congruence Theorem:Side-Angle-Side (SAS) Congruence Theorem:Angle-Side-Angle (ASA) Congruence Theorem:Hypotenuse-Leg (HL) Congruence Theorem:Angle-Angle-Side (AAS) Congruence TheoremHow to explain the theoremSide-Side-Side (SSS) Congruence Theorem: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence Theorem: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent.
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