Jessica then goes to Macy’s to buy a pair of panths. Find the rate of discount for her purchase if the pants cost $54 and are on sale for $41.99

The exact value of sin(θ/2) is -1/√5. To find the exact value of sin(θ/2), we can use the half-angle identity for sine. The half-angle identity states that sin(θ/2) = ±√[(1 - cosθ) / 2].

Since cosθ = 3/5, we can substitute this value into the half-angle identity:
sin(θ/2) = ±√[(1 - 3/5) / 2]
          = ±√[(2/5) / 2]
          = ±√[(2/5) * (1/2)]
          = ±√[1/5]
          = ±1/√5
Now, we need to determine the sign of the exact value. Since θ is in the range 270° < θ < 360°, which is in the fourth quadrant, sin(θ/2) will be negative.
Therefore, the exact value of sin(θ/2) is -1/√5.

To know more about sine visit :

https://brainly.com/question/30162646

#SPJ11

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

For more information on actual weight visit: brainly.com/question/31170036

#SPJ11

(a) The maturity value of the loan is $15,246.33.

(b) The amount of interest paid on the loan is $7,246.33.

To calculate the maturity value of the loan, we can use the formula for compound interest: A = \(P(1 + r/n)^(nt)\), where A is the maturity value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount (P) is $8000, the interest rate (r) is 9%, the loan duration is 9 years, and interest is compounded quarterly, so n = 4. Plugging these values into the formula, we get A = \(8000(1 + 0.09/4)^(4*9)\) = $15,246.33.

To calculate the amount of interest paid on the loan, we subtract the principal amount from the maturity value: Interest = Maturity value - Principal amount = $15,246.33 - $8000 = $7,246.33.

Learn more about maturity value here:

https://brainly.com/question/2132909

#SPJ11

Answer:She sold 21 magazines on Thursday

Step-by-step explanation:

Step 1

The Total price  of magazine sold on Thursday, Friday and Saturday, she sold $66 .

if she sold $3 more on Thursday than she did on Friday and $6 more on Saturday than she did on Thursday. The expression of the sales can be given as    

Let T represent  Thursday

F represent Friday

S represent Saturday such that

 T + F+ S= 66

T+ T-3 + T+6= 66

Step 2----- Solving

T+ T-3 + T+6= 66

3T - 3+ 6=66

3T+3= 66

3T= 66-3

3T=63

T= 63/3

T= 21

F= T-3= 21-3 =18

S = T+6 = 21+6= 27

She sold 21 magazines on Thursday, 18 on Friday and 27 on Saturday

The limit of the given expression as x approaches 1 from the right is 1.8.

To evaluate the limit of the given expression:

\(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

We can start by directly substituting x = 1 into the expression:

[ln(1⁹ - 1) - ln(1⁵ - 1)]

= [ln(0) - ln(0)]

However, ln(0) is undefined, so this approach doesn't provide a meaningful answer.

To apply L'Hôpital's Rule, we need to rewrite the expression as a fraction and differentiate the numerator and denominator separately. Let's proceed with this approach:

\(lim_{x - > 1}\)+ [ln(x⁹ - 1) - ln(x⁵ - 1)]

= \(lim_{x - > 1}\)+ [ln((x⁹ - 1)/(x⁵ - 1))]

Now, we can differentiate the numerator and denominator with respect to x:

Numerator:

d/dx[(x⁹ - 1)] = 9x⁸

Denominator:

d/dx[(x⁵ - 1)] = 5x⁴

Taking the limit again:

\(lim_{x - > 1}\)+ [9x⁸ / 5x⁴]

= \(lim_{x - > 1}\)+ (9/5) * (x⁸ / x⁴)

= (9/5) * \(lim_{x - > 1}\)+ (x⁸ / x⁴)

Now, we can substitute x = 1 into the expression:

(9/5) * \(lim_{x - > 1}\)+ (1⁸ / 1⁴)

= (9/5) * \(lim_{x - > 1}\)+ 1

= (9/5) * 1

= 9/5

= 1.8

The complete question is:

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. \(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

To know more about limit:

https://brainly.com/question/12211820

#SPJ4

The minimum height of the cone is 17.87 in (approx)

In geometry, the cylinder is a fundamental 3 dimension shape that has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center.  

Total surface area, A = 2πr²+ 2πrh square units

The volume of the Cylinder, V = πr²h cubic units

Here we have

A cylindrical can with an open top is to be constructed so that

The volume of the cone is 167 in³  

As we know volume of cone = (1/3) πr²h

=> (1/3) πr²h = 167

=> h = 501/πr²  

As we know Surface Area of the cone = 2πrh + 2πr²  

Substitute h = 501/πr² in Surface Area of cone  

=> SA = 2πr(501)/πr² + 2πr²  

=> SA = 1002r⁻¹+ 2πr²        

Differentiate SA with respect to r

=> SA' = (-1) 1002r⁻²+ 4πr  

=> SA' = - 1002r⁻² + 4πr  

Here  - 1002r⁻² + 4πr = 0

=>  - 501r⁻² + 2πr = 0  

=>  - 501/r² + 2πr = 0  

=>  [-501 + 2πr³ ]/r² = 0

=>  [-501 + 2πr³ ] = 0  

=>  2πr³ = 501

=>  πr³ = 250.5

=>  r³ = 79.70

=>  r = 8.92  (approx)

Hence the height of the cone, h = 501/πr²    

= 501/π(8.92)

= 17.87 (approx)

Therefore,

The minimum height of the cone is 17.87 in (approx)  

Learn more about height

https://brainly.com/question/1161452

#SPJ4

Answer:

−9.3¯6

Step-by-step explanation:

Convert it to a mixed number

-281/30

Divide the two numbers

−9.3¯6

Hope this helps plz mark as brainliest! :)

The angle subtended at the center of the arc is 102⁰

Recall that to find the length of an arc on a circle, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.  If the central angle is measured in degrees, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.

Lenght of arc = A/360 *2пr

A = angle at center = ?

п = 22/7 r = radius = 840 feet

⇒1500 = A/360  2 *22/7 * 840

1500 = 36960A/2520

3780000= 36960A

making A the subject we have

3780000/36960 = A

A = 102.27

A= 102⁰

The angle is 102⁰

Learn more about length of arc on https://brainly.com/question/31762064

#SPJ1

Answer:

what was your old answer?

Step-by-step explanation:

so I could solve this

Answer:

40.3°

Step-by-step explanation:

sin x/ (5.3) = sin 90/ (8.2)

sin x = (5.3 sin 90) / 8.2

= 5.3/8.2

x = arcsin (5.3/8.2)

= 40.3° to 1 dp

The measure of angle x using Trigonometry is 40.263215° or 40.3.

Trigonometry is a branch of mathematics that deals with the study of relationships involving the angles and sides of triangles. It is especially useful in understanding the properties and behavior of right-angled triangles.

Sine ratio is defined as the ratio of the length of the side opposite an angle to the length of the triangle's hypotenuse.

From the figure,

Perpendicular = 5.3 m

Hypotenuse = 8.2 m

Using Trigonometry

sin x = P / H

sin x = 5.3/ 8.2

sin x = 0.6463

Using Inverse Trigonometry

x = \(sin^{-1}\)(0.6463)

x= 40.263215°

Thus, the measure of angle x is 40.3.

Learn more about Trigonometry here:

https://brainly.com/question/12068045

#SPJ4

Answer:

C

Step-by-step explanation:

Answer:

percentage loss = 20%

Step-by-step explanation:

percentage loss is calculated as

\(\frac{loss}{CP}\) × 100% ( CP is the cost price )

loss = SP - CP ( SP is selling price )

loss = CP - SP = 350 - 280 = 70 , then

percentage loss = \(\frac{70}{350}\) × 100% = 0.2 × 100% = 20%

Answer:

488305

Step-by-step explanation:

100 plus 4.8 percent then add 4.8 percent gets you 109.83

then apply 9.83 percent to random numbers in a calculator

When you use a timer, you need to define a class that implements the ActionListener interface.

Here's a step-by-step explanation:

STEP 1: Create a class.
STEP 2: Implement the ActionListener interface in your class.
STEP 3: Define the actionPerformed() method, which will be called when the timer triggers an event.
STEP 4: Create an instance of the Timer class and pass in the required parameters, such as delay and your ActionListener.
STEP 5: Start the timer using the start() method.

To know more about timer:

https://brainly.com/question/31113155

#SPJ11

On solving the provided question, by substitution method we can say that -  x=-2y+9,  and answer is y = -17

Using the equations for the other variables as a guide, determine the value of one variable as the first step in the substitution procedure. For instance, you may determine x=7-y from the first equation if you have two equations, x+y=7 and x-y=8. Applying alternative techniques begins with this.

The substitution policy. A method for calculating integrals is the substitution rule. The following equivalence between differentials—where u is a function of x—is the foundation for it: du = u dx .

here we will use the substitution method

as x=-2y+9,

so,

\(6y+(-2y+9)=-59\\6y-2y+9=-59\\4y+9=-59\\4y=-68\\y=-17\)

To know more about substitution method visit:
https://brainly.com/question/14619835

#SPJ4

Answer:

230 + m less-than or equal to 500

Step-by-step explanation:

230 + m ≤ 500- this inequality determines how many minutes can be used

correct answer option

The inequality that can be used to determine how many more minutes more that Tom has is m + 230 ≤ 500

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is ≤ . This is the less than or equal to sign. It is used because Tom does not want to exceed 500 minutes.

To learn more about inequality, please check: https://brainly.com/question/5031619

About 20% of the time Aaron tunes in to his favored station, there will be a commercial playing.

Given info;

The assumption is that over a significant number of days, 20% of the time he tunes in to his favorite station, an ad will be playing. This is based on the idea of relative frequency.

The relative frequency of event A, which is calculated by dividing the number of desired outcomes by the total outcomes, will be off over a large number of experiments, according to the likelihood of an outcome A of a%.

When he dials into his preferred station, there is a 0.2 probability that a commercial will start playing.

The conclusion is that over a long number of days, an advertisement will be playing about 20% of the time he tunes in to his preferred station.

To learn more about probability click here:

brainly.com/question/11234923

#SPJ4

The probability of getting three or more heads out of five tosses for a bent coin is compared to the probability for a fair coin. For a fair coin, the binomial probability of getting three or more heads out of five tosses is 0.3438.

In the case of a bent coin, the probability of getting three or more heads out of five tosses would likely be different compared to a fair coin. A bent coin is one that has a biased distribution, meaning it is more likely to land on one side (heads or tails) than the other. The exact probability would depend on the degree of bias in the coin. However, without specific information about the bias of the bent coin, it is challenging to provide a precise probability.

On the other hand, for a fair coin, the probability of getting three or more heads out of five tosses can be calculated using the binomial probability formula. In this case, the formula is:

\(\[P(X \geq 3) = \binom{5}{3} \times 0.5^3 \times 0.5^2 + \binom{5}{4} \times 0.5^4 \times 0.5^1 + \binom{5}{5} \times 0.5^5 \times 0.5^0\]\)

Simplifying this expression gives us:

\(\[P(X \geq 3) = 0.3125 + 0.15625 + 0.03125 = 0.5 - 0.03125 = 0.3438\]\)

Therefore, for a fair coin, the probability of getting three or more heads out of five tosses is 0.3438.

To learn more about probability refer:

https://brainly.com/question/25839839

#SPJ11

The general solution of the associated homogeneous differential equation \(y'' + 2y' + 2y = 0\) is given by

             \(y_h = c₁ e^(-x) cos(x) + c₂ e^(-x) sin(x)\)

We can use the method of undetermined coefficients or variation of parameters to find y_p, depending on the form of g(x).

For each of problems 4 through 9, we need to find the general solution of the given differential equation.

Problem:

             \(4y'' + 4y' + 13y = 0\)

By solving the auxiliary equation \(r² + 4r + 13 = 0,\)

we get

         \(r = -2 + 3i, -2 - 3i.\)

Hence, the general solution is

          \(y = c₁ e^(-2x) cos(3x) + c₂ e^(-2x) sin(3x)\)

Problem: \(5y'' + 4y' + 3y = 0\)

By solving the auxiliary equation \(r² + 4r + 3 = 0,\)

we get

          \(r = -2 + √1, -2 - √1.\)

Hence, the general solution is

     \(y = c₁ e^(-x) + c₂ e^(-3x)\)

Problem \(6y'' + y = 0\)

By solving the auxiliary equation \(r² + 1 = 0\),

we get

             r = -i, i.

Hence, the general solution is

           \(y = c₁ cos(x) + c₂ sin(x)\)

Problem\(7y'' - 3y' - 4y = 0\)

By solving the auxiliary equation \(r² - 3r - 4 = 0\),

we get

  r = 4, -1.

Hence, the general solution is

            \(y = c₁ e^(4x) + c₂ e^(-x)\)

Problem \(8y'' + 3y' + 2y = 0\)

By solving the auxiliary equation \(r² + 3r + 2 = 0,\)

we get

              r = -1, -2.

Hence, the general solution is

                  \(y = c₁ e^(-x) + c₂ e^(-2x)\)

Problem:

               \(9y'' + 2y' + 2y = g(x)\)

This is a non-homogeneous differential equation.

The general solution of the associated homogeneous differential equation \(y'' + 2y' + 2y = 0\) is given by

       \(y_h = c₁ e^(-x) cos(x) + c₂ e^(-x) sin(x)\)

For the non-homogeneous equation, the general solution is given by

      \(y = y_h + y_p\)

Where y_p is any particular solution of the non-homogeneous differential equation.

To know more about,non-homogeneous visit

https://brainly.com/question/18271118

#SPJ11

Answer:

7

Step-by-step explanation:

Answer:

How does she make 14 pound servings with 5 pounds ?

Answer:

4/5

Step-by-step explanation:

cus i said so

The null hypothesis (H0) states that the average bowling score (μ) is greater than or equal to 168 points, while the alternative hypothesis (Ha) states that the average bowling score is less than 168 points.

To test this hypothesis, Jamie uses a significance level of 1%. The sample data consists of 17 games, with a mean score of 155 points and a standard deviation of 19 points.

To perform the hypothesis test, Jamie can use a one-sample t-test because the population standard deviation is unknown. The test statistic can be calculated as (sample mean - hypothesized mean) / (sample standard deviation / √sample size).

Substituting the given values, the test statistic is (-13) / (19 / √17) ≈ -3.02.

With 16 degrees of freedom (sample size - 1), Jamie can compare this test statistic to the critical t-value at a 1% significance level. If the test statistic falls within the critical region, Jamie can reject the null hypothesis and conclude that her bowling score is significantly less than 168 points on average.

For more similar questions on hypothesis test

brainly.com/question/4232174

#SPJ8

Answer:

Step-by-step explanation:

To find out how many people in the United States did not live in Texas in 1900, we can subtract the population of Texas from the population of the United States:

Number of people in the United States who did not live in Texas = Population of the United States - Population of Texas

Number of people in the United States who did not live in Texas = 76.1 million - 3.05 million

Number of people in the United States who did not live in Texas = 73.05 million

Therefore, about 73.05 million people in the United States did not live in Texas in 1900.

Answer: 73.05 million people in the United States did not live in Texas in 1900.

Step-by-step explanation:

Answer:

x+2

Step-by-step explanation:

write the problem out and then understand

Substituting the given values into the formula, we get logistic growth as

\(P(t) = 2392 / (1 + 18.748 * e^{(-0.013 * t)})\)

A pattern of population expansion known as logistic growth sees population growth begin slowly, pick up speed, then slow to a stop as resources run out. It can be shown as an S-shaped curve or a logistic function.

The formula for logistic growth can be expressed as:

\(P(t) = K / (1 + A * e^{(-r * t)})\)

where:

P(t) is the population at time t,

K is the carrying capacity,

A = (K - P₀) / P₀,

P₀ is the initial population,

r is the growth rate per unit of time, and

e is the base of the natural logarithm (approximately 2.71828).

Given the information you provided:

r = 0.013 (per year)

K = 2392

P₀ = 127

First, let's calculate the value of A:

A = (K - P₀) / P₀ = (2392 - 127) / 127 = 18.748

Now, substituting the given values into the formula, we get:

\(P(t) = 2392 / (1 + 18.748 * e^{(-0.013 * t)})\)

Remember to round the parameters to three decimal places when performing calculations.

Learn more about logistic growth on:

https://brainly.com/question/15631218

#SPJ4

Answer:

D 40°

Step-by-step explanation:

52= X + 64 /2

*2.      *2

104 = X + 64

-64        -64

40 =X

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129. We can assume a linear growth model on the based of given information.

The given data states that in the year 1985, there were 13 US billionaires. Whereas in 1990, there were 99 US billionaires. We have to find out the formula that predicts the number of US billionaires in any given year (t).

The yearly increase remains constant, so we can consider the formula for the linear function.f(t) = mt + b

where

t is the year and f(t) is the number of US billionaires in that year (t).

m is the slope of the line and b is the y-intercept.

The slope of the line is given by the formula:m = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given values to find the slope of the line.m = (99 - 13) / (1990 - 1985)m = 86 / 5m = 17.2 .The y-intercept of the line can be found by substituting the values of t and f(t) from any of the given points into the equation of the line.

Let's use the point (1985, 13).f(t) = mt + b => f(1985) =17.2(1985) + b => f(1985) = 34,142 + b =>b = 13 - 34,142 & b = -34,129.

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129

To know more about linear growth model refer here:

https://brainly.com/question/28033207

#SPJ11

Answer:

The volume of the cylinder section is about 82.8, and the volume of the cone is about 28.2.

Step-by-step explanation:

To find the cone's volume, it is v=pir^2*h/3

To find the cylinder, it is v=pir^2*h

I'm sure you can do the rest.

Answer:

You will get paid $220.88

Step-by-step explanation:

Answer: 220.875

Step-by-step explanation:

Just multiply those two numbers