a. The tension in rope AB is T_AB = (FR/2) + (sqrt((FR/2)^2 + T_AC^2)).
b. The tension in rope AC is T_AC = (FR/2) + (sqrt((FR/2)^2 + T_AB^2)).
To answer this question, we can use the fact that the net force acting on the boater must be zero (assuming they are not accelerating).
Let T_AB be the tension in rope AB and T_AC be the tension in rope AC.
a. In the x-direction: T_AB - T_AC = 0 (since the boater is not moving horizontally).
In the y-direction: T_AB + T_AC - FR = 0 (since the net force acting on the boater must be zero).
Using these two equations, we can solve for T_AB:
T_AB = (FR/2) + (sqrt((FR/2)^2 + T_AC^2))
b. Similarly, we can solve for T_AC:
T_AC = (FR/2) + (sqrt((FR/2)^2 + T_AB^2))
Note that we are given FR = 70 lb, the force exerted by the flowing water on the boater. We can substitute this value into the above equations to find the tensions in the ropes.
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Let f(x) = 32. The line L is the tangent to the curve of f at (0,1). Find the equation of L in the form y = mx + c.
To find the equation of the tangent line to the curve of f at (0,1), we need to find the derivative of f at x=0. Since f(x) = 32 is a constant function, its derivative is 0. Therefore, the slope of the tangent line is 0.
Since the tangent line passes through the point (0,1), we can write its equation in the form y = mx + c, where m is the slope (which we just found to be 0) and c is the y-intercept.
So the equation of the tangent line is simply y = 1.
Since f(x) = 32 is a constant function, its derivative f'(x) will be 0 for all x values. Therefore, the slope (m) of the tangent line L at any point on the curve of f is also 0.
However, the given point (0,1) is not on the curve f(x) = 32, as f(0) = 32, not 1. So, there cannot be a tangent line L to the curve of f at (0,1).
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how do i find the measure of the arc?
The measure of the arc is 57 degrees.
We have to find the measure of the arc yz
The measure of an arc is also called the arc angle and is equal to the measure of the central angle with rays intercepting the arc’s endpoints.
The measure of the central angle is 57 degrees
We know that measure of the central angle = measure of an arc
57 degrees =measure of an arc
Hence, the measure of the arc is 57 degrees.
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The range of a set of numbers is 6.
The maximum value is 4.
What is the minimum value?
-2 is the minimum value of the given set.
Assume that x is the minimum value.
The difference between the largest value and the least value is therefore what we use to determine the range:
Range = Maximum value - Minimum value
6 = 4 - x
Solving for x, we can subtract 4 from both sides:
6 - 4 = 4 - x - 4
2 = -x
Finally, we can multiply both sides by -1 to get x by itself:
x = -2
Therefore, the minimum value is -2.
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please answer correctlyDetermine the interval and radius of convergence for the power series *+2 k21k+2 k1 The interval is [ 1). The radius is r=
The interval and radius of convergence for the power series is (-1/2, 3/2) and the radius of convergence is not inclusive of its boundary.
The interval of convergence for a power series is the range of values of x for which the series converges. It can be found using various tests, such as the ratio test, root test, or alternating series test.
Based on the ratio test, the radius of convergence for the power series is:
r = lim(k→∞) |a_{k+1}/a_k|
= lim(k→∞) |(k+2)/(2(k+1))|
= 1/2
Since the ratio test guarantees convergence for |x - c| < r, where c is the center of the power series, we know that the interval of convergence is:
(-1/2, 3/2)
Note that 1 is included in the interval because the power series converges at x = 1 (as the terms all become 0), and the radius of convergence is not inclusive of its boundary.
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You rent an apartment that costs $800 per month during the first year, but the rent is set to go up $70 per year. What would be the monthly rent during the 11th year of living in the apartment?
The amount for the monthly rent during the 11th year of living in the apartment will be:
[tex]\rightarrow \$1,770[/tex]
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that:
You rent an apartment that costs $800 per month during the first year, but the rent is set to go up $70 per year.
Now,
Since, You rent an apartment that costs $800 per month during the first year, but the rent is set to go up $70 per year.
Hence, The The amount for the monthly rent during the 11th year of living in the apartment will be:
[tex]\rightarrow \$1,000 + 11 \times \$70[/tex]
[tex]\rightarrow \$1,000 + \$770[/tex]
[tex]\rightarrow \$1,770[/tex]
Thus, The amount for the monthly rent during the 11th year of living in the apartment will be:
[tex]\rightarrow \$1,770[/tex]
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suppose that we want to approximate the velocity, , at some point of some particle whose position is given byfor some constant . note: refers to the natural log.recall that the velocity function is the derivative (with respect to time, ) of the position function. assuming has already been calculated, which finite difference method(s) minimize(s) the number of additional function evaluations needed to approximate ?(a)central finite difference(b)backward finite difference(c)forward finite differenceselect all possible options that apply.given that , approximate the velocity of the particle at . you may use any of the selected finite difference methods with a step size of .
The central finite difference of velocity is 2.3127
The central finite difference, backward finite difference, and forward finite difference are all numerical methods used to approximate the derivative of a function.
Central finite difference is the most accurate of the three, and requires two function evaluations, one for the derivative at a given point and one for the derivative at the point before or after it.
Backward finite difference requires one function evaluation for the derivative at a given point minus the derivative at the point before it, while forward finite difference requires one function evaluation for the derivative at a given point plus the derivative at the point after it.
a) Central Finite Difference: = ( - )/2
Velocity = (ln(2.5) - ln(2.4))/0.1
= 2.3127
b) Backward Finite Difference: = -
Velocity = (ln(2.5) - ln(2.3))/0.1
= 3.2186
c) Forward Finite Difference: = -
Velocity = (ln(2.4) - ln(2.3))/0.1
= 2.3026
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[tex]x + 6x + 3y + 4y[/tex]
but it will be
[tex]7x + 7y[/tex]
then what do I do next??
calculate the average rate of change of f (x )equals cube root of x plus 5 end root on the interval [-4, 3].
Answer:
average rate of change = [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ - 4, 3 ] , then
f(b) = f(3) = [tex]\sqrt[3]{3+5}[/tex] = [tex]\sqrt[3]{8}[/tex] = 2
f(a) = f(- 4) = [tex]\sqrt[3]{-4+5}[/tex] = [tex]\sqrt[3]{1}[/tex] = 1
average rate of change = [tex]\frac{2-1}{3-(-4)}[/tex] = [tex]\frac{1}{3+4}[/tex] = [tex]\frac{1}{7}[/tex]
a greenhouse is growing a large number of poinsettia plants. an employee is monitoring their growth and selects 100 of them at random to measure. the plants have an average height of 5.5 inches, with an sd of 2 inches. calculate a 90%-confidence interval for the average height of all the poinsettia plants growing in the greenhouse.
A greenhouse is an enclosed structure made of glass or plastic, designed to provide an environment that is conducive to plant growth. The controlled conditions in a greenhouse allow plants to thrive and reach their full potential. In this scenario, a large number of poinsettia plants are being grown in the greenhouse, and an employee is monitoring their growth.
To estimate the average height of all the poinsettia plants growing in the greenhouse, the employee selects 100 of them at random to measure. The plants have an average height of 5.5 inches, with a standard deviation of 2 inches.
To calculate a 90%-confidence interval for the average height of all the poinsettia plants growing in the greenhouse, we can use the formula:
CI = x ± z(α/2) * (σ/√n)
Where:
- x is the sample mean (5.5 inches)
- z(α/2) is the z-score associated with the level of confidence (90% confidence interval = 1.645)
- σ is the population standard deviation (2 inches)
- n is the sample size (100)
Plugging in the values, we get:
CI = 5.5 ± 1.645 * (2/√100)
CI = 5.5 ± 0.329
CI = (5.17, 5.83)
Therefore, we can say with 90% confidence that the average height of all the poinsettia plants growing in the greenhouse falls between 5.17 and 5.83 inches. This means that if we were to repeat the sampling process multiple times, 90% of the resulting confidence intervals would contain the true population mean.
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Find nth term of the quadratic sequence: 11, 15, 21, 29, 39
Answer:
11+4=15,15+6=21,21+8=29,29+10=39,39+12=51,anwser is 51
Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or com the important aspects of the function. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) f(x, y) = xy - 4x - 4y x² - y² local maximum value(s) local minimum value(s) saddle point(s) (x,y) =
The local maximum and minimum values and saddle point(s) of the function are:
Local Maximum Value(s): (2,-2)
Local Minimum Value(s): (-2,2)
Saddle Point(s): (2,2), (-2,-2)
To find these values, we first need to find the critical points of the function by taking the partial derivatives of f(x,y) with respect to x and y and setting them equal to 0. This gives us two equations:
fx = y - 4 - 2x = 0
fy = x - 4 - 2y = 0
Solving these equations simultaneously, we get the critical points: (2,-2), (-2,2).
Next, we need to determine whether these critical points are local maximums, local minimums, or saddle points. We can use the second derivative test to do this. The second derivative test involves calculating the determinant of the Hessian matrix, which is a matrix of the second partial derivatives of f(x,y).
For the critical point (2,-2), the Hessian matrix is:
| -2 1 |
| 1 0 |
The determinant of this matrix is (-2)(0) - (1)(1) = -1, which is negative. This tells us that (2,-2) is a local maximum.
Similarly, for the critical point (-2,2), the Hessian matrix is:
| -2 1 |
| 1 0 |
The determinant of this matrix is (-2)(0) - (1)(1) = -1, which is negative. This tells us that (-2,2) is also a local maximum.
Finally, we need to check the critical points (2,2) and (-2,-2) to see if they are saddle points. For (2,2), the Hessian matrix is:
| -2 1 |
| 1 -2 |
The determinant of this matrix is (-2)(-2) - (1)(1) = 3, which is positive, and the trace is -4, which is negative. This tells us that (2,2) is a saddle point.
For (-2,-2), the Hessian matrix is:
| -2 1 |
| 1 -2 |
The determinant of this matrix is (-2)(-2) - (1)(1) = 3, which is positive, and the trace is -4, which is negative. This tells us that (-2,-2) is also a saddle point.
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Consider a particle in a one-dimensional box. (a) for a box of length 1 nm, what is the probability of finding the particle within 0.01 nm of the center of the box for the lowest-energy level?
For a particle in a one-dimensional box, the probability of finding the particle within a certain region can be calculated using the wave function and the probability density function.
The wave function for the lowest-energy level (ground state) in a one-dimensional box is given by:
ψ(x) = √(2/L) * sin(πx/L)
where L is the length of the box.
To find the probability of finding the particle within a region, we need to integrate the squared modulus of the wave function over that region.
Let's calculate the probability of finding the particle within 0.01 nm of the center of the box for a box of length 1 nm:
Length of the box (L) = 1 nm
Region of interest (x within 0.01 nm of the center) = [-0.005 nm, 0.005 nm]
Probability = ∫[-0.005, 0.005] |ψ(x)|^2 dx
Substituting the wave function, we have:
Probability = ∫[-0.005, 0.005] |√(2/L) * sin(πx/L)|^2 dx
= ∫[-0.005, 0.005] (2/L) * sin^2(πx/L) dx
Evaluating this integral will give us the probability of finding the particle within the specified region.
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The vertical height, in feet, of a section of a roller coaster track is modeled by the equation given below, where x represents the horizontal distance, in feet.
f(1) = -0.1412 + 2.81 +6
What is the maximum height, in feet, of the section of the roller coaster track?
A.) 20 Feet
B.) 10 Feet
C.) 6 Feet
D.) 22Feet
The maximum height of the the section of the roller coaster track is given as follows:
A. 20 feet.
How to obtain the maximum height?The height of the track after t seconds is modeled as follows:
f(x) = -0.141x² + 2.8x + 6.
The coefficients of the quadratic function are given as follows:
a = -0.141, b = 2.8, c = 6.
The coefficient a is negative, hence the vertex of the quadratic function represents the point of maximum height of the track.
The x-coordinate of the vertex is obtained as follows:
x = -b/2a
b = -2.8/[2 x -0.141]
x = 9.93 s.
Hence the y-coordinate of the vertex, representing the maximum height of the track, is obtained as follows:
f(9.95) = -0.141(9.93)² + 2.8(9.93) + 6
f(9.95) = 20 feet.
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facturise the following concept 2xy_3y?
Answer:
whats the _?
Nvm you factorise the y(2x_3)
7,499,846 rounded to the nearest 1,000,000
Answer:
7,000,000 :)
Hope this helps!
Answer:
7,000,000
Step-by-step explanation:
environmentalists are counting fish along a section of the chattahoochee river thatmeasures approximately 900 cubic yards. over a period of 8 hours, they count 150 fishwhich is about 60% of the fish population that inhabit this section.assuming the rate is constant, what is the approximate population density of fish after1 day?
Based on the given information, we can estimate that the total fish population in the section of the Chattahoochee River is around 250 fish (150 divided by 0.60).
To find the approximate population density of fish after one day, we need to know how many fish are added to or removed from the section in a day. Without this information, we cannot accurately calculate the population density.
However, we can assume that the fish population remains relatively stable over the course of one day. In this case, the population density would be approximately 0.28 fish per cubic yard (250 fish divided by 900 cubic yards).
It is important to note that environmentalists count fish populations for a variety of reasons, including to monitor the health of aquatic ecosystems, inform management decisions, and identify potential threats to biodiversity. Understanding population densities and changes over time can help environmentalists make informed decisions about how to protect and conserve fish populations and their habitats.
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Below, a two-way table is given
for a class of students.
Male
Female
Total
Freshman Sophomore Junior
4
6
2
3
4
6
Senior
2
3
Total
Find the probability the student is a freshman,
given that they are a male.
P(freshman | male) = P(freshman and male) = [?]%
P(male)
Round to the nearest whole percent.
Enter
The probability that a student is a freshman given that they are male is 2/7 or approximately 29%.
We have,
We can see from the table that there are a total of:
= 4 + 6 + 2 + 2
= 14 male students
= 4 + 3 + 6 + 4
= 17 female students.
So,
Total = 31 students.
From the table,
Male freshmen = 4
P(freshman and male) = 4/31
And:
P(male) = 14/31
So:
P(freshman | male)
= (4/31) / (14/31)
= 4/14
= 2/7
Therefore,
The probability that a student is a freshman given that they are male is 2/7 or approximately 29%.
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Which choices are equations for the line shown below
The equation of the line are y = 3x, y - 3 = 3(x - 1) and y + 6 = 3(x + 2)
Writing the equation of the lineFrom the question, we have the following parameters that can be used in our computation:
The linear graph
Where we have the points
(1, 3) and (-2, -6)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
m + c = 3
-2m + c = -6
Next, we have
3m = 9
Evaluate
m = 3
Solving for c, we have
c = 0
So, we have
y = 3x
Hence, the equation of the line in fully simplified slope-intercept form is y = 3x
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A random variable Y has the Density Function
f(y) = { ey, y , 0 0, elsewhere
a. Find E(e3Y/2).
b. Find the Moment Generating Function for Y.
c. Find the V(Y).
(a)the expected value of [tex]e^(3Y/2)[/tex] does not exist.
The mean of Y does not exist. Therefore, we cannot compute the variance of Y.
a. To find[tex]E(e^(3Y/2)),[/tex] we need to use the definition of the expected value for a continuous random variable:
E(e^(3Y/2)) = ∫ e^(3y/2) f(y) dy
where f(y) is the given density function. Since f(y) is only non-zero for y > 0, we can restrict our integration to that region:
E(e^(3Y/2)) = ∫ e^(3y/2) ey dy , from 0 to infinity
= ∫_0^∞ e^(5y/2) dy
= (2/5) * e^(5y/2) | from 0 to ∞
= (2/5) * ∞ = ∞
So the expected value of [tex]e^(3Y/2)[/tex] does not exist.
b. To find the moment generating function for Y, we use the definition:
M(t) = E(e^(tY)) = ∫ e^(ty) f(y) dy
where f(y) is the given density function. For y < 0, f(y) is zero, so we can restrict our integration to the range y ≥ 0:
M(t) = ∫[tex]_0^∞ e^(ty) ey dy[/tex]
= ∫[tex]_0^∞ e^((t+1)y) dy[/tex]
= (1/(t+1)) * e^((t+1)y) | from 0 to ∞
= 1/(t+1) * ∞ = ∞ for t < -1
and
M(t) = ∫[tex]_0^∞ e^(ty) y dy[/tex]
= e^(ty) * y / t | from 0 to ∞
= ∞ for t ≥ 1
Therefore, the moment generating function exists only for -1 < t < 1, and is given by:
M(t) = 1/(t+1) for -1 < t < 1.
c. To find the variance of Y, we first need to find the mean or expected value of Y:
E(Y) = ∫ y f(y) dy
= ∫[tex]_0^∞ y^2 dy[/tex]
= ∞
So the mean of Y does not exist. Therefore, we cannot compute the variance of Y.
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d
ate
90 ft
First
Base
A baseball field is in the shape of a square. The
distance between each pair of bases along the edge of
the square is 90 feet. What is the distance between
home plate and second base?
√2 feet
The distance between home plate and second base is 90√2 feet
What is the distance between home plate and second base?From the question, we have the following parameters that can be used in our computation:
Shape of the field = square
Base edge = 90 ft
The distance between home plate and second base is the diagonal of the square field
This distance is calculated as
Distance = Base edge * √2 feet
Substitute the known values in the above equation, so, we have the following representation
Distance = 90 * √2 feet
Evaluate
Distance = 90√2 feet
Hence, the distance is 90√2 feet
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You can clean the gutters of your house in 5 hours. Working together, you and your friend
can clean the gutters in 3 hours. Let t be the time (in hours) your friend would take to clean
the gutters when working alone. Write and solve an equation to find how long your friend
would take to clean the gutters when working alone.
Your friend would take 11.6 hours to clean the gutters when working alone.
We have,
A rate is a ratio that is used for comparing two different kinds of quantities which have different units. A rate of change is a rate that describes how one quantity changes in relation to another quantity.
Here, we have
Given: You can clean the gutters of your house in 6 hours working together you and your friend can clean the gutters in 3.5 hours let x be the time in hours.
We have to determine an equation to find how long your friend would take to clean the gutters when working alone.
Your Work rate = 1/5
Your and your friend's work rate = 1/3.5
Your friend's rate = 1/3.5 - 1/5 = 3/35
t = 1/(3/35) = 35/3 = 11.6hours
Hence, your friend would take 11.6 hours to clean the gutters when working alone.
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Problem 2 (a) Evaluate the following limit. Show the steps and the limit laws used. sin x cos x lim *+ x(3 - x) x2 x" (b) Suppose the inequality - b 51-cosxs is valid for x values close to zero. Show how this inequality can be used to evaluate the following limit. State any theorem that you use. 1-cOS X lim 24 * +0 x2
(a) The limit found by limit laws is -2.
(b) The limit found by limit laws is 0.
(a) We can simplify the expression using the product-to-sum identities for sine and cosine:
sin x cos x = (1/2) sin 2x
Then, the limit becomes:
lim x→0 (3 - x) / (x^2 sin x cos x)
= lim x→0 (3 - x) / (x^2 (1/2) sin 2x)
= 2 lim x→0 (3 - x) / (x^2 sin 2x)
Using L'Hopital's rule:
= 2 lim x→0 (-1) / (2x cos 2x + sin 2x)
= -2/1 = -2
Therefore, the limit is -2.
(b) Since -b ≤ 1 - cos x ≤ b, we can rewrite the inequality as:
- b/x^2 ≤ (1 - cos x)/x^2 ≤ b/x^2
Taking the limit as x approaches zero, and using the squeeze theorem, we get:
lim x→0 (1 - cos x)/x^2 = 0
Then, using the limit law that states if f(x) → 0 and g(x) is bounded near a, then lim x→a f(x)g(x) = 0, we have:
lim x→0 (1 - cos x)/x^2 * 4/x^2 = 0
Simplifying, we get:
lim x→0 (1 - cos x)/x^2 = 0
Then, using the limit law that states if f(x) → 0 and g(x) → 1 as x → a, then lim x→a f(x)^g(x) = 0, we have:
lim x→0 [(1 - cos x)/x^2]^4 = 0
Therefore, the limit is 0.
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Evaluate the following expression. Leave the answer in exact form.
arctan (tan(-33pi/10))
arctan (tan(-33pi/10)) is equivalent to -33pi/10 + nπ, where n is any integer. Therefore, the answer in exact form is -33pi/10 + nπ.
To evaluate the expression arctan(tan(-33π/10)), we'll follow these steps:
1. Simplify the inner function: tan(-33π/10)
2. Apply the arctan function to the simplified result.
Step 1: Simplify tan(-33π/10)
The tangent function has a period of π, which means that tan(x) = tan(x + nπ) for any integer n. Therefore, we can add or subtract multiples of π to -33π/10 to find an equivalent angle in the range of arctan, which is (-π/2, π/2).
-33π/10 + nπ = -33π/10 + (10n/10)π = (-33 + 10n)π/10
We want to find an integer n such that -π/2 < (-33 + 10n)π/10 < π/2. This simplifies to:
-5 < -33 + 10n < 5
Adding 33 to all sides, we get:
28 < 10n < 38
Dividing by 10:
2.8 < n < 3.8
The only integer in this range is n = 3. So, the equivalent angle in the arctan range is:
(-33 + 10 * 3)π/10 = 7π/10
Step 2: Apply arctan function
arctan(tan(-33π/10)) = arctan(tan(7π/10))
Since tan(7π/10) is already in the range of arctan, we can simply write:
arctan(tan(7π/10)) = 7π/10
So, the exact form of the given expression is:
Your answer: 7π/10
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5. A July 4th promotion included a $5. 00 mail-in rebate for the
purchase of a picnic cooler and a store coupon for $0. 50 off the
price of a case of 24 cans of soda. For the company picnic,
Carl Rhiel purchased a 48-quart cooler for $32. 99 and a case of
soda for $6. 99. What did the cooler cost after the rebate if an
envelope costs $0. 20 and a Forever stamp costs $0. 41?
The cooler costs $27.99 after the rebate, including the cost of the soda, envelope, and stamp.
The cost of the cooler before the rebate = $32.99
The rebate amount = $5.00
Cost of soda =$6. 99
No' cans of soda = 24
The cost of the cooler after the rebate is = $32.99 - $5.00
The cost of the cooler = $27.99
To calculate the total cost of the company, we need to add all the costs of products like soda, the cost of the envelope, and the cost of the stamp:
Total cost = Cost of the cooler after rebate + Cost of soda + Cost of envelope + Cost of stamp
Total cost = $27.99 + $6.99 + $0.20 + $0.41
Total cost = $35.59
Therefore, we can conclude that the cooler cost $27.99 after the rebate, including the cost of the soda, envelope, and stamp.
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according to a recent survey, voter turnout for young people is at an all-time low. from a random sample, it was found that 35% of young people voted in the last primary election. if three people are interviewed, what is the probability that none of them voted in the primary election? what is the probability that only one of them voted in the primary election? what is the probability that 2 of them voted in the primary election? what is the probability that all three of them voted in the primary election?
Probability that none of them voted in the primary election: 0.45, Probability that only one of them voted in the primary election: 0.44, Probability that 2 of them voted in the primary election: 0.18, Probability that all three of them voted in the primary election: 0.04
To calculate these probabilities, we can use the binomial distribution formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
- n is the sample size (in this case, 3)
- k is the number of "successes" (in this case, voting in the primary election)
- p is the probability of success (in this case, 0.35)
Probability that none of them voted in the primary election:
P(X=0) = (3 choose 0) * 0.35^0 * (1-0.35)^(3-0) = 0.45
Probability that only one of them voted in the primary election:
P(X=1) = (3 choose 1) * 0.35^1 * (1-0.35)^(3-1) = 0.44
Probability that 2 of them voted in the primary election:
P(X=2) = (3 choose 2) * 0.35^2 * (1-0.35)^(3-2) = 0.18
Probability that all three of them voted in the primary election:
P(X=3) = (3 choose 3) * 0.35^3 * (1-0.35)^(3-3) = 0.04
So the probabilities are:
- Probability that none of them voted in the primary election: 0.45
- Probability that only one of them voted in the primary election: 0.44
- Probability that 2 of them voted in the primary election: 0.18
- Probability that all three of them voted in the primary election: 0.04
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a social security number contains nine digits, such as 010-50-0257. how many different social security numbers can be formed?
The total number of social security numbers that are possible are 900,000,000.
In the social security number first digit can only fall between 1 and 9, leaving us only nine options because the first three digits cannot all be zeros. There are still 10 possibilities for each of the second and third digits because they may both still be any integer between 0 and 9.
Therefore, the total number of different social security numbers that can be formed is using the combinations,
= 9 × 10⁸
= 900,000,000
So, there are 900,000,000 different possible social security numbers.
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1/4y-3=-18 what is the y
Answer:-60
Step-by-step explanation:
Lets start by adding 3 to both sides.
[tex]\frac{1}{4}y-3=-18[/tex] -->[tex]\frac{1}{4}y-3+3=-18+3[/tex]-->[tex]\frac{1}{4}y=-15[/tex]
[tex]\frac{1}{4}y=-15[/tex]
Now that we have this, we can multiply both sides by 4, the reciprocal of 1/4.
[tex]\frac{1}{4}y\cdot4=-15\cdot4[/tex]
[tex]y=-60[/tex]
Answer:
y = -60
Step-by-step explanation:
1/4y-3=-18 what is the y?
1/4y - 3 = - 18
1/4y = -18 + 3
1/4y = 15
y = 15 : 1/4
y = 15 × (-4)
y = -60
---------------------------
check
1/4 × (-60) - 3 = -18
-15 - 3 = -18
-18 = -18
the answer is good
Use the picture below to answer the question. Price of Cookies A $0.20 11. $0.40 C. $1.00 D. $1.20 Cookies dozen 20g each or $2.00 per Trisha wants to buy I dozen cookies (12 cookies). What is the difference in price between buying 12 cookies individually and buying them by the dozen?
The price difference between buying 12 cookies individually and buying them by the dozen is $0.40
What is the Cookies price about?Note that from the question, the price of Cookies A is $0.20 for each cookie, so to buy 12 cookies solely, Thus Trisha would need to pay:
12 * $0.20
= $2.40
Since price of Cookies A is $2.00 per dozen, to buy 12 cookies by the dozen, Trisha will pay:
1 * $2.00
= $2.00
Hence the difference in price of buying 12 cookies solely and buying by the dozen is:
$2.40 - $2.00
= $0.40
Therefore, the price is $0.40 cheaper for Trisha to buy 12 cookies by the dozen than to buy them individually.
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HELP PLS I HAVE 0 BRAINCELLS!! :(
Answer:
84[tex]m^{2}[/tex]
Step-by-step explanation:
Bottom:
3 x 4 = 12
Top:
3 x 4 = 12
Right side:
3 x 5 = 15
Left side:
3 x 5 = 15
Front:
4 x 5 = 20
Back:
4 x 5 = 20
Add it all up:
12 + 12 + 15 + 15 + 20 + 20 = 84 [tex]m^{2}[/tex]
Helping in the name of Jesus.
we want to determine if the sequence 6−8n is monotonic. using the difference test we get that sn 1−sn= > 0 hence the sequence is monotone decreasing
The difference was negative, indicating that the sequence is monotonic and decreasing.
To determine if a sequence is monotonic, we need to look at whether it is increasing or decreasing. In this case, we are considering the sequence 6−8n. The difference test involves subtracting one term from the next to see if the result is positive, negative or zero. If the result is positive, then the sequence is decreasing. If it is negative, then the sequence is increasing. If it is zero, then the sequence is constant.
In this case, we apply the difference test by subtracting sn from sn+1 to get (6-8(n+1)) - (6-8n) = -8. Since this result is negative, we can conclude that the sequence is decreasing. Therefore, we can say that the sequence 6−8n is monotonic decreasing.
In summary, a difference test is a useful tool for determining if a sequence is monotonic. By calculating the difference between consecutive terms, we can tell whether the sequence is increasing, decreasing, or constant. In this case, the difference was negative, indicating that the sequence is monotonic decreasing.
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