Stat 2300 a survey was conducted that asked randomly selected students nationwide if they traveled outside the country for spring break. a 99% confidence interval for the proportion of all students who traveled outside the country is (0.0994, .1406). how many students were surveyed

=============================================================

Explanation:

When you have a 10% discount, the customer pays the remaining 90% of the original cost (note how the percentages add to 100%)

The decimal form of 90% is 0.90

When you apply a 20% discount, then the customer pays the remaining 80% which converts to 0.80

Chaining these discounts together means the final multiplier will be 0.90*0.80 = 0.72 which means that the customer is paying 72% of the original price when both discounts are applied at the same time. The order of the discounts doesn't matter because we can multiply in any order.

If the item was originally $360 before either discount kicks in, then the final price is 0.72*360 = 259.20 dollars

Side note: the final discount rate is 100% - 72% = 28% (it's fairly close to 30% but not quite there; so we can't simply just add the 10% and 20% to get 30%)

Answer:

15

Step-by-step explanation:

(brainiest)

Answer:

\(-2x^2-x\). Your answer was wrong because "x-squared" terms didn't cancel.

Step-by-step explanation:

To solve this problem, set up an equation.  We know something is supposed to be added to the expression \(2x^2+2x\), and the result should be x. So:

\(2x^2+2x+(\text{ ? })=x\)

We want to solve for the question mark... the unknown thing that we're adding to the original expression, in order to get x.

It is uncommon to put question marks in equations to represent quantities. Usually we use a letter. Since x is already being used in the equation, we should pick something else ... we could use "y".

\(2x^2+2x+(\text{ } y \text{ })=x\)

...or just...

\(2x^2+2x+y=x\)

Algebra allows us to solve the equation and find out what "y" is equivalent to.

To solve, we want to get the "y" by itself. To do so, we try to eliminate the other "terms" from the left side of the equation.

Understanding "terms" & "like terms"

Terms

"Terms" in an equation are either a number multiplied to other things, or just a single number that isn't multiplied to anything else.

For example, the various terms in our equation above are

\(2x^2\), \(2x\), \(y\), \(x\)

You might ask why the last things, which don't have a number, are considered terms.

Remember that multiplying by 1 doesn't change anything, so we could imagine each of the last two terms as being 1 times the letter.

So, we can rewrite our equation:

 \(2x^2+2x+1y=1x\)

Like terms

"Like terms" are terms where the "other stuff the numbers are multiplied to" is the same, so for instance, the \(2x\) and the \(1x\) are like terms. They are like terms because, the "other stuff" that the numbers are multiplied to are "x" for both terms. Note that \(2x\) and \(2x^2\) are not "like terms" because the "stuff" is different:

\(x\) is different than \(x^2\)

"Like terms" are important because only like terms can be "combined" into a single simplified term.

Solving equations

To solve an equation, we isolate what we're solving for, y, by disconnecting the other terms from it, and simplify.

Starting with subtracting 2x from both sides of the equation:

\(2x^2+2x+1y=1x\\(2x^2+2x+1y)-2x=(1x)-2x\)

Subtraction is the same as "adding a negative":

\(2x^2+2x+1y+(-2x)=1x+(-2x)\)

Since all terms are now connected by addition, we can add in any order we want (because of the Commutative Property of Addition), and we can combine like terms.

Thinking just about the number parts, since \(1+(-2)=-1\),  then \(1x+(-2x)=-1x\).

Returning to our main equation, the right side simplifies:

\(2x^2+2x+1y+(-2x)=1x+(-2x)\\2x^2+2x+1y+(-2x)=-1x\)

On the left side: \(2x\) and \(-2x\) are like terms.

Fact: \(2+(-2)=0\)

So, \(2x+(-2x)=0x\)

Since anything times zero is just zero, \(0x=0\). Furthermore, adding zero to anything doesn't change it.  So when the \(2x\) and \(-2x\) terms on the left side of our main equation are combined, they "disappear" (While we talked through are a lot of rules/steps to justify why that works, it is common to omit those justifications, and to just combine those like terms and make them disappear.)

So, \(2x^2+2x+1y+(-2x)=-1x\) simplifies to:

\(2x^2+1y=-1x\)

Similarly for the \(2x^2\) term, we subtract from both sides:

\(2x^2+1y=-1x\\(2x^2+1y)-2x^2=(-1x)-2x^2\\2x^2+1y+(-2x^2)=-1x+(-2x^2)\)

Combining like terms on the left, they disappear.

\(1y=-1x+(-2x^2)\)

There are no like terms on the right.

Since the two terms on the right are added together, we can use the commutative property of addition to rearrange:

\(1y=-2x^2+(-1x)\)

Addition of a negative can turn back into subtraction, and simplify multiplication by 1.

\(y=-2x^2-x\)

Remembering we chose "y" as the unknown thing we wanted to know, that's why the "correct answer" is what it is.

Verifying an answer

Verifying can double check an answer, and helps explain why the answer you chose doesn't work.

To verify an answer, the original statement said add something to the expression and get a result of "x". So, let's see if the "correct answer" does:

\(2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-2x^2-x)\\2x^2+2x+(-2x^2-1x)\\2x^2+2x+(-2x^2)+(-1x)\)

Combining the "x-squared" terms, completely cancels...

\(2x+(-1x)\)

Combining the "x" terms, and simplifying...

\(1x\\x\)

So it works.

Why isn't the answer what you chose:

\(2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-x^2-x)\\2x^2+2x+(-1x^2-1x)\\2x^2+2x+(-1x^2)+(-1x)\)

Combining the x-squared terms, things don't completely cancel...

\(1x^2+2x+(-1x)\)

Combining the x terms...

\(1x^2+1x\\x^2+x\)

So adding the answer that you chose to the expression would not give a result of "x", which is why it is "wrong"

Answer: yes, aas

Step-by-step explanation:

They have the two angles, and then the side after the angles

Answer:

The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Step-by-step explanation:

hope this helps

correct me if this is wrong

Answer:

I don't understand the question but I think the answer is either 10 or 30

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{0}{h}~~,~~\underset{0}{k})}\qquad \stackrel{radius}{\underset{7}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 0 ~~ )^2 ~~ + ~~ ( ~~ y-0 ~~ )^2~~ = ~~7^2\implies x^2+y^2=49\)

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


To learn more about Tension click here: brainly.com/question/31500075

#SPJ11

Answer:

GE = 14

Step-by-step explanation:

3x + 5 = 6x - 4

x = 3

Plug it in.

3 (3) + 5 = 14 = GD

6 (3) - 4 = 14 = GF

With that information, you know all the blue lines are the same.

GE = 14

The length of v is given as follows:

v = 267.1 cm.

The law of sines is used in the context of this problem as we have two sides and two opposite angles, hence it is the most straightforward way to relate the side lengths.

Each side length is related with the sine of the opposite angle as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(26º)/v = sin(80º)/600

Hence we apply cross multiplication to obtain the length v is obtained as follows:

sin(26º)/v = sin(80º)/600

v = 600 x sine of 26 degrees/sine of 80 degrees

v = 267.1 cm.

More can be learned about the law of sines at https://brainly.com/question/4372174

#SPJ1

The conditional probability is 0.25.

To calculate the conditional probability, we need to find the probability that a randomly generated bit string of length four contains at least two consecutive 0s, given that the first bit is a 1.

Let's consider the possible bit strings of length four that start with 1:

1xxx (where x can be 0 or 1)

There are two possibilities for the first bit (1 or 0), and for each of these possibilities, there are two possibilities for each of the remaining three bits (0 or 1).

Now, let's find the bit strings that contain at least two consecutive 0s:

1xxx (where x is 0)

1000

1010

1100

1110

Out of the possible 1xxx bit strings, there are four that contain at least two consecutive 0s.

Now, the conditional probability is calculated as the probability of the event (bit string contains at least two consecutive 0s) given the condition (first bit is 1).

Conditional Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Conditional Probability = 4 / (2 * 2 * 2 * 2) = 4 / 16 = 1/4 = 0.25

So, the conditional probability that a randomly generated bit string of length four contains at least two consecutive 0s, given that the first bit is a 1, is 0.25 or 25%.

To learn more about probability here:

https://brainly.com/question/31828911

#SPJ4

The density of the liquid substance Y can be determined by using the conversion factor 1 atm = 41.5 ft⁻Y and the density of the liquid substance Y is approximately 19.68 ft⁻Y.

Conversion factor: 1 atm = 41.5 ft⁻Y

The "feet of liquid substance - Y" unit is defined as the pressure equivalent to the pressure that exists one foot below the surface of substance Y. In other words, if we go one foot below the surface of substance Y, the pressure will be equivalent to 1 ft⁻Y.

Since pressure is directly related to the density of a liquid, we can equate the pressure in units of atm to the pressure in units of ft⁻Y.

Therefore, we can say:

1 atm = 41.5 ft⁻Y

From this equation, we can conclude that the conversion factor for pressure between atm and ft⁻Y is 41.5.

we can calculate the conversion factor from "feet of liquid substance - Y" (ft⁻Y) to atm.

To convert from ft⁻Y to atm, we can use the inverse of the given conversion factor:

Conversion factor: 1 atm = 41.5 ft⁻Y

Taking the reciprocal of both sides:

1 / 1 atm = 1 / 41.5 ft⁻Y

Simplifying the equation:

1 atm⁻¹ = 0.024096 ft⁻Y⁻¹

Now, to find the density of the liquid substance Y in units of ft⁻Y, we can multiply the given density in g/cm³ by the conversion factor:

Density in ft⁻Y = 816.55 g/cm³ * 0.024096 ft⁻Y⁻¹

Calculating the density in ft⁻Y:

Density in ft⁻Y ≈ 19.68 ft⁻Y

learn more about conversion factor here:

https://brainly.com/question/30166433

#SPJ11

The third charge q should be placed 4.47 m from the origin along the x-axis.

The net force on the third charge q will be zero if it is placed such that the electric force due to the charge -5q at the origin is balanced by the electric force due to the charge q at x = 4.0 m.

The electric force F on a point charge q due to a point charge Q separated by a distance r is given by Coulomb's law:

F = kQq/r^2

where k is the Coulomb constant (k = 9 × 10^9 N m^2/C^2).

Let's call the position of the third charge q x meters from the origin along the x-axis. Then the distance between the charge -5q at the origin and the charge q at x = 4.0 m is d = x - 4.0 m.

The electric force on q due to the charge -5q is

F1 = k×(-5q)×q/d^2

The electric force on q due to the charge q at x = 4.0 m is

F2 = kqq/(4.0 m)^2

For the net force to be zero, F1 and F2 must have equal magnitudes and opposite directions:

|F1| = |F2|

k×(-5q)q/d^2 = kq×q/(4.0 m)^2

Solving for d, we get:

d = sqrt(20.0) m = 4.47 m

Learn more about electric force here

brainly.com/question/30186912

#SPJ4

To solve this problem, we can use the binomial probability distribution. Let's define a "success" as scoring a goal and a "failure" as missing a goal.

Then, each attempt by Sky can be considered a Bernoulli trial with probability of success p = 1/2.

Let X be the number of goals that Sky scores in five attempts. Then, X follows a binomial distribution with parameters n = 5 and p = 1/2.

To find the probability that Sky scores at least two goals, we need to calculate the probability of the following events:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

We can use the binomial probability formula to calculate these probabilities:

P(X = k) = (n choose k) * \(p^k\) *\((1-p)^(n-k)\)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we get:

P(X = 2) = (5 choose 2) * \((1/2)^2\) * \((1/2)^3\) = 10/32

P(X = 3) = (5 choose 3) * \((1/2)^3\) * \((1/2)^2\) = 10/32

P(X = 4) = (5 choose 4) * \((1/2)^4\) *\((1/2)^1\) = 5/32

P(X = 5) = (5 choose 5) * \((1/2)^5\) * \((1/2)^0\) = 1/32

Therefore, the probability that Sky scores at least two goals is:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = (10 + 10 + 5 + 1)/32 = 26/32 = 13/16

So the probability that Sky scored at least two goals is 13/16.

Learn more about “  binomial distribution “ visit here;

https://brainly.com/question/31197941

#SPJ4

The total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. So the probability that Sky scored at least two goals is 13/16.

To find the probability that Sky scored at least two goals, we can use complementary probability, which means finding the probability that she scored fewer than two goals (either 0 or 1 goal) and subtracting that from 1.1.

Probability of scoring 0 goals: Since there are 5 attempts and she is equally likely to make a goal or miss (1/2 chance for each), the probability of missing all 5 is (1/2)^5 = 1/32.2.

Probability of scoring 1 goal: Sky could score in any of the 5 attempts, so we need to consider all possible ways of scoring one goal.

There are 5 ways (score in the 1st, 2nd, 3rd, 4th, or 5th attempt). The probability for each of these scenarios is (1/2)^5 = 1/32.

Therefore, the total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

To express this as a common fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:26/32 = (26/2) / (32/2) = 13/16So the probability that Sky scored at least two goals is 13/16.

to learn more about probability click here:

brainly.com/question/13604758

#SPJ11

Answer:

\((x+6)^2+(y-5)^2=65\)

Step-by-step explanation:

Plug center into the equation of a circle

\((x-h)^2+(y-k)^2=r^2\)

\((x-(-6))^2+(y-5)^2=r^2\)

\((x+6)^2+(y-5)^2=r^2\)

Determine r²

\((2+6)^2+(6-5)^2=r^2\)

\(8^2+1^2=r^2\)

\(64+1=r^2\)

\(65=r^2\)

Final equation

\((x+6)^2+(y-5)^2=65\)

Answer:

<1 and <5

are adjacent and complementary angles

Step-by-step explanation:

hope I'm I'm right tell me if I'm wrong

26 square feet is the exact surface area of the composed figure with two cones.

The composed figure has two cones.

The formula to find the surface area of cone is A=πr(r+√h²+r²))

Where r is radius and h is height of the cone.

Both the cones have radius of 1 ft and height of 2ft and 4 ft.

Area of cone 1=3.14×1(1+√4+1)

=3.14(1+√5)

=10.16 square fee

Area of cone 2=3.14×1(1+√16+1)

=3.14(1+√17)

=16.01square feet.

Total surface area = 10.16+16.01

=26.17 square feet.

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

Learn more about differential equations click;

https://brainly.com/question/32645495

#SPJ4

Answer:

v=6

Step-by-step explanation:

v²=u²+2as

v²=12²+2(-3)(18)

v²=144-108

v²=30

v=6

So 3 have no pets, so 25 - 3 = 22 students have a pet.

There are 15 cats and 16 dogs so 15 + 16 = 31.

And then 31 - 22 = 9. The 9 means that 9 students have both pets.

So the probability is 9/25.

Answer:

number of students who have cat and dog

= y

= 9

P( student chosen has a dog and cat )

= 9/25

The value of the integral is \((137/2) \sqrt(\pi).\)

To determine the convergence of the integral, we can use the limit comparison test. We compare the given integral with the integral of a known function that has the same behavior for large values of x.

Let's choose the function \(f(x) = e^(^-^x^2).\)

Then we have:

∫ from -∞ to ∞ 137x \(e^(^-^x^2)\)dx ≤ ∫ from -∞ to ∞ \(e^-^x^2 dx\)

To evaluate the integral on the right-hand side, we can use the fact that:

∫ from -∞ to ∞ \(e^-^x^2 dx\) = \(\sqrt(\pi)\)

Therefore, we have:

∫ from -∞ to ∞ 137x \(e^-^x^2 dx\) ≤ \(\sqrt(\pi)\)

Since \(\sqrt(\pi)\) is a finite constant, the given integral is convergent.

To evaluate the integral, we can use integration by parts.

Let u = x and dv = 137 \(e^-^x^2 dx\), so that du/dx = 1 and v = (-137/2) \(e^-^x^2 dx\).

Then we have:

∫ from -∞ to ∞ 137x \(e^-^x^2 dx\) = [-137x \(e^-^x^2^/^2 dx\)] from -∞ to ∞ + ∫ from -∞ to ∞ (137/2) \(e^-^x^2 dx\)

The first term evaluates to zero because \(e^-^x^2\) goes to zero faster than x as x approaches infinity. Therefore, we have:

∫ from -∞ to ∞ 137x \(e^-^x^2dx\) = (137/2)∫ from -∞ to ∞ \(e^-^x^2 dx\)= \((137/2) \sqrt(\pi)\)

Therefore, the value of the integral is \((137/2) \sqrt(\pi).\)

Learn more about integral

brainly.com/question/30900582

#SPJ11

Answer:

Answer is D. 2 & -2

Answer:D

I THINK

Step-by-step explanation:

Hopefully this is the right one

Answer:

a

Step-by-step explanation:

Answer:

A

I know this is a year later lol

The difference between the two expressions:

2x^5 and (2x)^5

Is the coefficient that multiplies the variable.

We want to see how the expressions:

2x^5 and (2x)^5

Are different.

Remember that the exponents can be distributed, then we can write the rule:

(a*b)^n = (a^n)*(b^n)

Then we can rewrite the second expression as:

(2x)^5 = (2^5)*x^5 = (2*2*2*2*2)*x^5 = 32x^5

So the difference between the two expressions is the coefficient that is multiplying the variable x.

Learn more about exponents by reading:

https://brainly.com/question/847241

#SPJ1

False. The total shrink for a three- and four-bend saddle is equal to that of an offset.

The statement "total shrink for a three- and four-bend saddle is twice that of an offset" is true.

1. Shrink: Shrink refers to the amount of extra conduit length needed to account for bends in the conduit, so it maintains the required distance between two points after bending.

2. Offset: An offset is a two-bend conduit configuration used to navigate around obstacles while maintaining a straight path. The total shrink for an offset can be calculated using the formula: Shrink = offset height x (multiplier for the specific angle).

3. Saddle: A saddle is a conduit configuration with either three or four bends. It is used to navigate over or under obstructions while maintaining a straight path.

4. Comparison: For both three- and four-bend saddles, the total shrink is twice that of an offset. This is because a saddle consists of two sets of bends (either two offsets or an offset and a U-bend) and requires additional conduit length to accommodate these extra bends.

In conclusion, the statement is true, as the total shrink for a three- and four-bend saddle is indeed twice that of an offset.

Learn more about four:

brainly.com/question/27704437

#SPJ11

Answer:

The answers final

Simplify the expression

-2+6x+1/2x^2

Factor the expression

1/2x(-4+12x+x^2)

Step-by-step explanation:

I hope it will help you :)

Answer:

y=10+5x

Step-by-step explanation:

Have a great day

Step-by-step explanation:

n=an-a

n=1--15

n=16

this might be helpful for you of it isnt I am super sorry

Rich should build a travel crate with a volume of 30,240 cubic inches to ensure that Thomas can travel safely. We can calculate it in the following manner.

Since the travel crate needs to be a rectangular prism, we can calculate its volume using the formula:

Volume = length x width x height

We know that the length of the crate should be 12 inches greater than Thomas's length (30 inches), so the length of the crate should be 30 + 12 = 42 inches.

We also know that the width of the crate should be 12 inches greater than Thomas's width (12 inches), so the width of the crate should be 12 + 12 = 24 inches.

Finally, we know that the height of the crate should be 6 inches greater than Thomas's height (24 inches), so the height of the crate should be 24 + 6 = 30 inches.

Therefore, the volume of the travel crate that Rich should build is:

Volume = length x width x height

= 42 inches x 24 inches x 30 inches

= 30,240 cubic inches

So Rich should build a travel crate with a volume of 30,240 cubic inches to ensure that Thomas can travel safely.

Learn more about volume here brainly.com/question/1578538

#SPJ4