A store owner offers a discount of 20% off the regular price of all jackets. Jessica has a coupon that gives her an additional 5% off the discounted price. The original price of the jacket Jessica buys is $84. What is the price of the jacket after the discount and Jessica's coupon? ​

The time it takes for the principle to triple in value is t = 18.792 years.

To determine how long it would take for a principal of $10,000 to triple in value at an interest rate of 3.75% compounded semi-annually, we can use the compound interest formula. By rearranging the formula and solving for time, we can find the answer.

The compound interest formula can be expressed as A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the time in years.

In this case, we have P = $10,000, r = 3.75% (or 0.0375 as a decimal), and n = 2 since compounding occurs semi-annually.

We want to find the time it takes for the principal to triple, so A = 3P. Substituting the known values into the compound interest formula, we have:

3P = P(1 + r/n)^(nt)

Canceling out the common factor of P on both sides, we get:

3 = (1 + r/n)^(nt)

Taking the natural logarithm (ln) of both sides to isolate the exponent, we have:

ln(3) = nt ln(1 + r/n)

Now, we can solve for t by dividing both sides of the equation by n ln(1 + r/n) and simplifying:

t = ln(3) / (n ln(1 + r/n))

Substituting the given values of r = 0.0375 and n = 2, we can calculate the value of t.

Learn more about common factor here:

https://brainly.com/question/28201305

#SPJ11

Answer:

x = -8 and y = -7

Step-by-step explanation:

I will solve your system by substitution.

(You can also solve this system by elimination.)

8x−12y=20;4x−4y=−4

Step: Solve8x−12y=20for x:

8x−12y+12y=20+12y(Add 12y to both sides)

8x=12y+20

8x

8

=

12y+20

8

(Divide both sides by 8)

x=

3

2

y+

5

2

Step: Substitute

3

2

y+

5

2

forxin4x−4y=−4:

4x−4y=−4

4(

3

2

y+

5

2

)−4y=−4

2y+10=−4(Simplify both sides of the equation)

2y+10+−10=−4+−10(Add -10 to both sides)

2y=−14

2y

2

=

−14

2

(Divide both sides by 2)

y=−7

Step: Substitute−7foryinx=

3

2

y+

5

2

:

x=

3

2

y+

5

2

x=

3

2

(−7)+

5

2

x=−8(Simplify both sides of the equation)

Both the given statements are true

1. Two equilateral triangles are always similar: True.

An equilateral triangle is a triangle in which all three sides are equal. Since two equilateral triangles have the same shape and size, they are always similar. Similarity means that the corresponding angles are equal, and the corresponding sides are in proportion.

2. The diagonals of a rhombus are perpendicular to each other: True.

In a rhombus, opposite sides are parallel, and all sides have equal length. The diagonals of a rhombus bisect each other at right angles, which means they are perpendicular to each other. This property holds true for all rhombuses, regardless of their size or orientation.

Learn more about equilateral triangle here

https://brainly.com/question/22660891

#SPJ4

Given question is incomplete, the complete question is below

State true or false

1. Two equilateral triangles are always similar.

2. The diagonals of a rhombus are perpendicular to each other.

Answer:

960

Step-by-step explanation:

Let P, R and T denote principal amount, rate of interest and time period.

Principal amount of loan (P) = 4,000

Time period (T) = 4 years

Rate of interest (R) = 6%

Simple interest is calculated using the following formula:

Simple interest [tex]=\frac{4000(4)(6)}{100} =960[/tex]

So,

Simple interest is equal to 960

(a) `dy/dx = (2y - 2x)/(3y - 2x)`.

(b) The slope of the tangent line at points where x = 6 is 0.

(c) the curve has a vertical tangent line when x = (3/2)y.

(a) To show that `dy/dx = (2y - 2x)/(3y - 2x)`, we need to find the derivative of `y` with respect to `x`. We can do this by implicitly differentiating the given equation.

Differentiating both sides of the equation with respect to `x`, we get:

4x(dx/dx) + 6y(dy/dx) - 4[(dx/dx)y + x(dy/dx)] = 0

Simplifying the equation, we have:

4x + 6y(dy/dx) - 4xy - 4xy - 4x(dy/dx) = 0

Rearranging the terms and combining like terms, we get:

(6y - 4x)(dy/dx) = 8x - 8xy

Dividing both sides by (6y - 4x), we obtain:

dy/dx = (8x - 8xy)/(6y - 4x)

Simplifying further, we have:

dy/dx = (2x(4 - 4y))/(2(3y - 2x))

Canceling out the common factors, we get:

dy/dx = (2y - 2x)/(3y - 2x)

Therefore, `dy/dx = (2y - 2x)/(3y - 2x)`.

(b) To find the slope of the tangent line at the points where x = 6, substitute x = 6 into the expression we found for `dy/dx` in part (a):

dy/dx = (2(6) - 2(6))/(3y - 2(6))

      = 0/(3y - 12)

      = 0

The slope of the tangent line at points where x = 6 is 0.

(c) To find the value of x at which the curve has a vertical tangent line, we need to find the point(s) where the slope `dy/dx` is undefined. In other words, we need to find the values of x where the denominator of `dy/dx` becomes zero.

Setting the denominator equal to zero and solving for x:

3y - 2x = 0

2x = 3y

x = (3/2)y

So, the curve has a vertical tangent line when x = (3/2)y.

Visit here to learn more about slope brainly.com/question/3605446

#SPJ11

Given that the probability of event A is Pr(A) = 1/3 and the probability of the union of event A and event B, namely AUB, is Pr(AUB) = 5/6. The probability of event B is Pr(B) = 2/3.

Suppose that event A and event B are disjoint.

The probability of event B is Pr(B) = 1/2.

To find the probability of event B.

For disjoint events A and B, we know that A ∩ B = Φ (empty set).

Thus, we can express the union of A and B as: AUB = A + B, where A and B are disjoint.

In general, the probability of the union of two events can be expressed as: P(AUB) = P(A) + P(B) - P(A ∩ B).

For disjoint events, the intersection of the events is always an empty set.

Thus, P(A ∩ B) = 0.

Using this information, we can write:

P(AUB) = P(A) + P(B) - P(A ∩ B)

= P(A) + P(B) - 0

= P(A) + P(B)

Given P(A) = 1/3 and P(AUB) = 5/6, we can solve for P(B) as follows:

5/6 = P(A) + P(B)

=> P(B) = 5/6 - P(A)

=> P(B)  = 5/6 - 1/3

=> P(B)  = 2/3

Thus, the probability of event B is Pr(B) = 2/3.

To know more about disjoint events, visit:

https://brainly.com/question/30675682

#SPJ11

Answer:

If you are looking at a graph then yes it will have a y-axis

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

A horizontal line goes on infinitely on both ends will eventually cross the y-axis, making a y-intercept.

Answer:

x = 43

Step-by-step explanation:

x = 98 - 55

x = 43

Answer:

x=43

Step-by-step explanation:

have a nice day and stay safe:)

Answer:

[tex]Range = 3.169m[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the difference between the shortest and the longest

This question implies that we calculate the range.

[tex]Range = Longest - Shortest[/tex]

From the table, we have:

[tex]Longest = 8.7m[/tex]

[tex]Shortest = 5.531m[/tex]

So, we have:

[tex]Range = 8.7m- 5.531m[/tex]

[tex]Range = 3.169m[/tex]

Answer:

36 cubic feet

Step-by-step explanation:

Answer:

To find volume use the solution of l x w x h

Length x Width x Height

Step-by-step explanation:

16. 2 x 3 x 6 = 36 cubic feet

???. 5/8 x 3/4 x 2  = 15/16

???. 2 x 1 1/4 x 1 1/2 = 3 3/4 cubic inches

25.

1 = 4.89 / 3 = 1.63

3 = $4.89

9 = 4.89 + 4.89 + 4.89 = 14.67

10 = 14.67 + 1.63 = $16.30

???. Interquartile Range = Q3 - Q1

65 - 62 = 3

If i remember correctly

Given function is { x) = {0, if 0 < x < 1/2, 1, if 1/2 < x < 1}.

Step-by-step explanation: Given function is { x) = {0, if 0 < x < 1/2, 1, if 1/2 < x < 1}.

The function is an even function because the function is symmetric with respect to the y-axis (i.e.) { -x) = {x). So, the Fourier series has only cosine terms. Therefore, the Fourier cosine series of the given function is given by:

f(x) = a0/2 + Σ an cos(nπx/L),

where L is the period of the function.

Since the function is even, the Fourier series reduces to  f(x) = a0/2 + Σ an cos(nπx/L) ...(1) , where a0 = 1/L ∫f(x)dx, an = 2/L ∫f(x)cos(nπx/L)dx for n = 1, 2, 3, ..., n. Let L = 1,

then a0 = 1/1 ∫0^1 f(x)dx = 1/2 an = 2/1 ∫0^1 f(x)cos(nπx)dx for n = 1, 2, 3, ..., n.
a1 = 2 ∫1/2^1 cos(nπx)dx = 1/nπ sin(nπx) from 1/2 to 1
= [1/nπ sin(nπ/2) - 1/nπ sin(0)]
= 2/nπ sin(nπ/2)

Hence, the Fourier cosine series is given by f(x) = 1/2 + 2/π ∑[sin(nπ/2)/n] cos(nπx) ...(2)for n = 1, 2, 3, ...Similarly, the Fourier sine series of the given function is given by: f(x) = Σ bn sin(nπx/L)where L is the period of the function. Since the function is even, there are no sine terms in the Fourier series. So, the Fourier sine series is zero, i.e., bn = 0 for n = 1, 2, 3, ....Hence, the full Fourier series is the same as the Fourier cosine series, which is given byf(x) = 1/2 + 2/π ∑[sin(nπ/2)/n] cos(nπx) ...(3)for n = 1, 2, 3, ...The Fourier series converges pointwise to f(x) for x in (0, 1/2) U (1/2, 1).The Fourier series does not converge at x = 0 and x = 1/2 because the function is not continuous at these points.

To know more about Fourier series refer to:

https://brainly.com/question/31472899

#SPJ11

There are many possible solutions, but one example in the case of three functions f, g, and h would be: f(0) = 0, f(1) = 1g(0) = 1, g(1) = 0h(0) = 0, h(1) = 1

We have the set J2 = {0,1} and we need to estimate three functions f, g, and h such that f:

J2→ J2, g: J2→ J2, and h:

J2→ J2, and f = g = h.

To do this, we can simply assign values to each element of the set J2 for each of the three functions. For example, we can let f(0) = 0 and f(1) = 1, which means that the function f maps 0 to 0 and 1 to 1. We can also let g(0) = 1 and g(1) = 0, which means that the function g maps 0 to 1 and 1 to 0.

Finally, we can let h(0) = 0 and h(1) = 1, which means that the function h maps 0 to 0 and 1 to 1. Note that all three functions have the same values for each element in J2, so we can say that f = g = h.

You can learn more about functions at: brainly.com/question/31062578

#SPJ11

The volume of the oblique cylinder is calculated as: B. 96π units³.

Volume = πr²h, where h is the height and r is the radius of the given cylinder.

Given the following:

Volume = πr²h = π(4²)(6)

Volume = 96π units³ (option B)

Learn more about the volume of a cylinder on:

https://brainly.com/question/9554871

#SPJ1

The expected value E(X) of a binomial random variable X can be calculated as n * p, and the variance Var(X) can be calculated as n * p * (1 - p). These formulas can be generalized for any values of p and n, and the value of p that minimizes the variance can be found by setting the derivative of Var(X) with respect to p equal to zero.

a. In part (a), we are given specific values for n (3) and p (3/4). The expected value E(X) of a binomial random variable X can be calculated as n * p, which gives us:

3 * 3/4

= 2.25.

The variance Var(X) can be calculated as n * p * (1 - p), which gives us:

3 * 3/4 * (1 - 3/4)

= 0.5625.

b. In part (b), we generalize the calculation of E(X) and Var(X) for any value of p and n. Using the binomial theorem, we can expand (p + (1 - p))ⁿ and differentiate it to find the coefficients for E(X) and Var(X).

c. To find the value of p that minimizes the variance Var(X), we can take the derivative of Var(X) with respect to p binomial, set it equal to zero, and solve for p. This will give us the value of p that minimizes the variance.

d. For any t > 0, we can calculate E(e^(tx)) using the binomial theorem by substituting e^t for p in the expansion of (p + (1 - p))ⁿ. This will give us the expected value of the exponential of tx.

Therefore, the expected value E(X) of a binomial random variable X can be calculated as n * p, and the variance Var(X) can be calculated as n * p * (1 - p). These formulas can be generalized for any values of p and n, and the value of p that minimizes the variance can be found by setting the derivative of Var(X) with respect to p equal to zero.

To know more about binomial check the below link:

https://brainly.com/question/15246027

#SPJ4

Answer:

A. Third period

Step-by-step explanation:

- hope this helped!

Answer:

3rd

Step-by-step explanation:

Answer:

7/20

Step-by-step explanation:

Answer:8 cars

Step-by-step explanation:

to find the least amount of cars dived 30/4 which equilds 7.5

Since there are 2 remaining students, an additional car will be needed bringing the total to 8 cars.

Answer

6.

Steps

30/100×30

=6

Answer:

6

Step-by-step explanation:

There are 30 students

So,

20÷100×30=6

Answer:

44

Step-by-step explanation:

because it a millon and not a bilolon

The volume of the cuboid as a function of x is V(x) = x * 3x * y.

the volume of the cuboid as a function of x is V(x) = 675/4 - (9/4)x^2.

The surface area of the cuboid is given as 450 cm, which can be expressed as:

2(x * 3x) + 2(x * y) + 2(3x * y) = 450.

Simplifying this equation, we get:

6x^2 + 2xy + 6xy = 450,

6x^2 + 8xy = 450,

3x^2 + 4xy = 225.

Now, we need to express y in terms of x. From the given dimensions, we know that the surface area is formed by six rectangular faces of the cuboid. Therefore, the length of one face is x, the width is 3x, and the remaining face (height) is y.

To find y, we can use the equation for the surface area. Rearranging the equation above, we have:

3x^2 + 4xy = 225,

y(4x) = 225 - 3x^2,

y = (225 - 3x^2) / (4x).

Now we can substitute the value of y into the expression for the volume:

V(x) = x * 3x * [(225 - 3x^2) / (4x)].

Simplifying further:

V(x) = (3/4) * (225 - 3x^2),

V(x) = 675/4 - (9/4)x^2.

Therefore, the volume of the cuboid as a function of x is V(x) = 675/4 - (9/4)x^2.

To know more about volume of the cuboid , refer here:

https://brainly.com/question/29568631#

#SPJ11

The values of N and p that define the random graph ensemble G(N, p) with an average degree (k) of 40 and a variance of the degree distribution (σ²) of 50 are N = 201 and p = 0.2.

The values of N and p that define a random graph ensemble G(N, p) with an average degree (k) of 40 and a variance of the degree distribution (σ²) of 50, we can use the following formulas:

k = (N-1) × p

σ² = (N-1) × p × (1-p)

Plugging in the given values:

k = 40

σ² = 50

We can solve these equations to find the values of N and p:

From the first equation:

40 = (N-1) × p

From the second equation:

50 = (N-1) × p × (1-p)

By substituting the value of (N-1) × p from the first equation into the second equation, we can solve for p.

40 = 50 × (1-p)

1-p = 40/50

1-p = 0.8

p = 1 - 0.8

p = 0.2

Now, we can substitute the value of p back into the first equation to solve for N:

40 = (N-1) × 0.2

200 = N-1

N = 200 + 1

N = 201

Therefore, the correct values of N and p that define the random graph ensemble G(N, p) with an average degree (k) of 40 and a variance of the degree distribution (σ²) of 50 are N = 201 and p = 0.2.

To know more about variance click here :

https://brainly.com/question/29139178

#SPJ4

Given the expression |x - 4|, condition on |x - 4| that will assure that:(a)|x - 2| < 2/1(b)|x - 2| < 0.01

Given expression |x - 4|, the two possible values are: x - 4 if x > 4 -(x - 4) if x < 4Let us solve each part of the question separately:

(a)Part (a) can be expressed as follows:|x - 2| < 2/1Subtracting 2 from both sides of the in equality |x - 2| - 2 < 0Adding 4 to both sides of the inequality. |x - 2| - 2 + 4 < 0|x - 2| - 2 + 4 = |x - 4| < 0Since it is impossible to have an absolute value less than 0, therefore there is no solution.

(b)Part (b) can be expressed as follows:|x - 2| < 0.01 Subtracting 2 from both sides of the inequality |x - 2| - 2 < -0.01Adding 4 to both sides of the inequality. |x - 2| - 2 + 4 < -0.01|x - 2| - 2 + 4 = |x - 4| < -0.01Since it is impossible to have an absolute value less than 0, therefore there is no solution.

Thus, there are no solutions for the given conditions.

Know more about expressions:

https://brainly.com/question/28170201

#SPJ11

Answer: 5/4

Step-by-step explanation: That should be right because I have big brain. Mark brainlist please :)

Answer:

14

Step-by-step explanation:

42:?

3:1

42/3=14

42:14

3:1

The positive constant b is 0. This is obtained by setting the coefficient of the xy^2 term to zero in the equation derived from equating the integral of the joint probability density function to 1.

To compute the positive constant b, we need to calculate the integral of the joint probability density function (pdf) over the entire probability space and set it equal to 1 since it represents a valid probability density.

∫∫ f(x, y) dx dy = 1

Since the joint pdf is defined as:

f(x, y) = 5 - bcx * cb - bzycb

And it is zero otherwise, we can set up the integral as follows:

∫∫ (5 - bcx * cb - bzycb) dx dy = 1

To solve this integral, we need to determine the limits of integration. Since the joint pdf is not specified outside of the equation, we assume it is defined for all real values of x and y.

∫∫ (5 - bcx * cb - bzycb) dx dy = ∫∫ 5 - bcx * cb - bzycb dx dy

Integrating with respect to x first:

∫ (5x - bcx^2/2 * cb - bzy * cb) ∣∣ dy = 1

Now integrating with respect to y:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) ∣∣ dy = 1

Since this equation holds for all real values of x and y, we can ignore the limits of integration.

Next, we can solve for b by equating the integral to 1 and simplifying:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) = 1

Simplifying further:

5xy - bcxy^2/2 - bzy^2/2 = 1

Now, we can compare the coefficients of the terms on both sides of the equation:

- bc/2 = 0 (since there is no xy^2 term on the right-hand side)

Solving for b:

bc = 0

Since we are looking for a positive constant b, we can conclude that b = 0.

Therefore, the positive constant b is 0.

To know more about positive constant refer here:

https://brainly.com/question/31692182#

#SPJ11

The probability that the girls would randomly choose their two favorite movies to watch is 0.0034.

The number of favorable outcomes is 2 (since Rhonda has two favorite movies).

Using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

In this case, n = 35 (total number of movies) and r = 2 (number of movies to be chosen).

C(35, 2) = 35! / (2! x (35 - 2)!)

C(35, 2) = 35! / (2! x 33!)

= (35 x 34 x 33!) / (2! x 33!)

= (35 x 34) / 2

= 595

Therefore, there are 595 possible outcomes when choosing any two movies from Laura's collection.

Now, Probability = Favorable Outcomes / Total Outcomes

Probability = 2 / 595

Therefore, the probability that the girls would randomly choose their two favorite movies to watch is 0.0034.

Learn more about Probability here:

https://brainly.com/question/31828911

#SPJ1

Answer:

12

..................................................

Step-by-step explanation:

2 + 2 + 1 + 2 + 1 + 4 = 12

Answer:

12 centimeters

Step-by-step explanation:

The double dashes are both the same number. Since the base is 4cm and they have to be two of the same number, the double dashes are each 2cm long. Meanwhile, the height is 2cm, and the single dashes are two of the same numbers (but not 2cm, because that's what the double dashes are). So, each dash must be 1cm long. When you add them up: [tex]4+2+2+2+1+1=12[/tex]

The test value for this hypothesis is 3.0.

The test value for this hypothesis can be calculated using the formula for a one-sample t-test:

test value = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Calculating the test value:

Learn more about hypothesis

brainly.com/question/29576929

#SPJ11

In multilevel signaling over an Additive White Gaussian Noise (AWGN) channel, the received signal can be represented as:

Y = X + N

where Y is the received signal, X is the transmitted signal, and N is the AWGN with zero mean and variance σ^2.

In this case, M = 4, which means we have 4 symbols: -2v, -v, +2v, +v. The pulse values assigned to these symbols are: -2v, -v, +2v, +v.

To find the optimum threshold values, we need to consider the decision regions between adjacent symbols. Let's denote the threshold values as T1, T2, and T3, corresponding to the decision boundaries between -2v and -v, -v and +2v, and +2v and +v, respectively.

For correct transmission of the symbol -2v, the received signal Y should be greater than T1 and less than or equal to T2. Mathematically, this can be expressed as:

T1 < Y ≤ T2

The probability of correct transmission for the symbol -2v can be obtained by integrating the probability density function (PDF) of the received signal Y over the region T1 < Y ≤ T2.

Now, let's find the expression for the total probability of error. The total probability of error (P_e) can be obtained by summing the probabilities of error for each symbol. In this case, we have four symbols, so the expression for P_e is:

[tex]P_e = P_error(-2v) + P_error(-v) + P_error(+2v) + P_error(+v)[/tex]

where P_error(-2v) is the probability of error for symbol -2v, P_error(-v) is the probability of error for symbol -v, and so on.

Finally, to evaluate the total probability of error when σ^2 = 0.40 and v = 0, we need more information. Specifically, we need the signal-to-noise ratio (SNR) or the value of σ^2 in order to proceed with the calculation.

know more about Gaussian Noise

https://brainly.com/question/31002596

#SPJ11

Answer:

15(6.5% * 7000)+7000=y

Step-by-step explanation:

15(6.5% * 7000)+7000=y

im not sure tho