Warren bought a shirt on sale for $25. the original price of the shirt was 3 times that amount. warren also bought a pair of shoes on sale for $29. the original price of the shoes was 4 times that amount. together, how much money did the shirt and shoes cost before they went on sale?

π/16 is the area enclosed by the curve r= sin(4θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(4θ) =0

=> sin(4θ) =0

=> 4θ = 0,π

=> θ = 0, π/4

so a=0 , b= π/4

now  

  A =  \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)   ------(i)

so   \(r^2\) = (sin(4θ))^2

=>   \(sin^2\)( 4θ )

ans we know that

cos(2α) = 1 -  \(2sin^2\)2 α

so     \(sin^2\)= (1- cos(8θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta\)

=> 1/4*  \(\int\limits^b_a {(1-cos8\theta) } \, d\theta\)

here a=0 and b=π/4

after putting the value and solving the integral

A = π/16

so A is the area enclosed by r=sin(4θ) is π/16

To know more about polar curve click on below link:

brainly.com/question/1094340#

#SPJ4

Step-by-step explanation:

the answer is 53 :))))))

The answer is 45


------------------------------------------------------------

Given:

The total = 846.

The number of hot dogs sold at Tuesday night = 150.

Required:

We need to find the approximate probability of a person buying a hot dog and going to a Tuesday night game.

Explanation:

The total possible outcomes = 846.

Let A be the given event.

The favourable outcomes = The number of hot dogs sold at Tuesday night = 150.

The approximate probability of a person buying a hot dog and going to a Tuesday night game.

Final answer:

Step-by-step explanation:

if the 2 matrices are inverse, then their product must be the identity matrix

1 0

0 1

so,

m×3 + 2×-7 = 1

7×3 + 3×-7 = 0

m×-2 + 2×m = 0

7×-2 + 3×m = 1

that means we have to solve only

3m - 14 = 1

3m = 15

m = 5

The three possible sources of error when performing a kinetics experiment using a spectrophotometer

to determine the transmittance of crystal violet concentration with sodium hydroxide include;

errors due to the instrument itself, errors due to the sample solution, and errors due to the experiment.

The instrument itself, which can be an error source, includes improper calibration of the instrument, inaccuracies in instrument readings, or the presence of stray light.

The second possible source of error is the sample solution.

The sample solution may contain impurities, foreign substances, or air bubbles, all of which can affect the measurement.

The final possible source of error is the experimenter. If the experimenter does not take readings at the appropriate time, use incorrect amounts of chemicals, or not wash the instrument correctly, measurement errors may occur.

Therefore, the experimenter should be cautious in handling the instrument and recording data, and should follow the instructions exactly to minimize errors. The above three possible sources of error are only a few examples that can contribute to inaccuracy in kinetic experiments when using a spectrophotometer.

By identifying these possible errors, the experimenter can take steps to minimize their effects and increase the accuracy of the experiment.

Learn more about spectrophotometer, visit here

https://brainly.com/question/24864511

#SPJ11

There are two possible values for t: one positive and one negative. However, since time cannot be negative, we only consider the positive value: t ≈ 2.02 seconds; So, it will take approximately 2.02 seconds for the stone to hit the water.

To find out how long it will take for the stone to hit the water, we need to determine when h(t) equals 0 (since the water's surface is considered to be at height 0). We can use the given function: h(t) = -4.9t^2 + t + 10.

Set h(t) to 0 and solve for t:

0 = -4.9t^2 + t + 10

Now, we need to solve this quadratic equation for t. We can do this by applying the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = -4.9, b = 1, and c = 10. Plugging these values into the formula:

t = (-(1) ± √((1)^2 - 4(-4.9)(10))) / 2(-4.9)

t = (-1 ± √(1 + 196)) / -9.8

t = (-1 ± √197) / -9.8

There are two possible values for t: one positive and one negative. However, since time cannot be negative, we only consider the positive value:

t ≈ 2.02 seconds

So, it will take approximately 2.02 seconds for the stone to hit the water.

Visit here to learn more about quadratic equation  : https://brainly.com/question/30098550
#SPJ11

Answer:

1 vase arrangement when 10 roses are left

Step-by-step explanation:

1. so 50 divided by 5 is 10.

That means every arrangement is 10 roses.

2. it asks us to find how many vase arrangement will be needed to have only 10 roses left. We already know that we only need 1 arrangement, because we already found that out in step 1.

A trinomial is a polynomial with three terms that has a leading coefficient of 3 and a constant term of -5 is

3m²+m-5

Here the degree of the trinomial is 2, so the leading coefficient is the coefficient of the term with m², which is 3.

The constant term is the term without a variable, which is -5

To find the coefficient of middle term of the trinomial, formula is:

coefficient of middle term =

(sum of the coefficients of the first and last terms)

                                    2

The sum of the coefficients of the first and last terms is 3 - 5 = -2.

Dividing by 2, we get -1 as the coefficient of the middle term.

Putting all of this together, we can write the trinomial as:                     3m² +m - 5

Learn  more about polynomials here:

https://brainly.com/question/11536910

#SPJ11

(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

To know more about  Schwarzschild radius

https://brainly.com/question/29534114

#SPJ11

Answer:

44.5 minutes on her phone to stay within budget

Step-by-step explanation:

65.50-21.00 = 44.50

44.50x0.12 = 5.34

5.34 divided by 0.12 = 44.5

Answer:

The values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Step-by-step explanation:

Since we are given the points (-2.5,0), (-0.75, 0), (0, -3) and (1,0) where the coordinates are in ordered pairs of (x, y) where y = f(x).

To find the values in the domain where f(x) = 0, we look at the ordered pairs given.

We look for the pair in which f(x) = 0.

So f(x) = 0 in (-2.5, 0)

f(x) = 0 in (-0.75, 0)

and f(x) = 0 in (1, 0)

The corresponding values of x  in which f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

So, the values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Answer:

C. \(x=1\)

Step-by-step explanation:

When x is 1, y is 0.

18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.

19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.

If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.

The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.

The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.

This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.

Learn more about Daily Fluid Requirements (DFR) here:

https://brainly.com/question/28334028

#SPJ4

The value of the variable is 9

It is important to note that  inequalities are described as non- equal comparison of numbers or expressions.

The signs of inequalities represents;

From the information given, we have that;

7x - 1  is less than or equal to 62

This is represented as;

7x - 1≤ 62

collect the like terms, we have;

7x ≤ 62 + 1

Add the values

7x ≤ 63

Divide both sides by the coefficient, we get;

x ≤ 63/7

x ≤ 9

Learn more about inequalities at: https://brainly.com/question/25275758

#SPJ1

Answer:

180 most likely

Answer:

The second job because, it pays more and it has less hours.

Step-by-step explanation:

The requreid Miriam's test does not provide significant evidence that the true population mean is less than 18.

Since the sample size is small (n = 7) and the population standard deviation is unknown, we should use a t-test for this hypothesis test.

The test statistic is calculated as follows:

t = (x - μ) / (s / √n)

Given that Miriam's test statistic is t = -1.9, we can estimate the p-value associated with this test statistic. This denotes the probability of observing a test statistic as extreme as -1.9 or more extreme, assuming the null hypothesis is true.

Using a t-distribution table with 6 degrees of freedom (n-1), we find that the p-value for a one-tailed test at the 5% significance level is approximately 0.051.

Since the p-value (0.051) is greater than the significance level (0.05), we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that the population mean is less than 18 at a 5% level of significance.

Thus, Miriam's test does not provide significant evidence that the true population mean is less than 18.

Learn more about the hypothesis here:

https://brainly.com/question/29519577

#SPJ1

The breadth of the rectangular plot is equal to the area divided by the length. Therefore, the breadth of the plot is 180 divided by 15, which is equal to 12 meters.

The area of a rectangular plot is equal to the length multiplied by the breadth. This means that if the area of the plot is 180 square meters and the length is 15 meters, then the breadth can be calculated by dividing the area by the length. Therefore, the breadth of the plot is 180 divided by 15, which is equal to 12 meters. This means that the area of the plot is equal to 15 multiplied by 12 which is equal to 180 square meters. As the area and the length are given, the breadth can be easily calculated by dividing the area by the length. This is a simple way to calculate the breadth of a rectangular plot when the area and the length are known.

Learn more about rectangle here

https://brainly.com/question/29068457

#SPJ4

Use this:

The basic formula to find the scale factor of a figure is: Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape. This can also be used to calculate the dimensions of the new figure or the original figure by simply substituting the values in the same formula.

Answer:

1 2/3 is the scale factor

Step-by-step explanation:

So the scale factor either makes soemthing bigger or smaller

In this case it’s getting bigger

So we have one side already so we jsut find the value that was multiplied

so 9 * ? Is 15

You

d get 1 2/3

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

Learn more about Confidence intervals

brainly.com/question/32546207

#SPJ11

The distance (d) between the two planes is approximately 5.55 units.

To find the distance (d) between two parallel planes, we can use the formula for the distance between a point and a plane. We need to find a point that lies on one of the planes and calculate the perpendicular distance from that point to the other plane. The normal vector of the planes can be used to determine the perpendicular distance.

In this case, the given planes are -5x - 4y + 4z = 42 and -5x - 4y + 4z = -101. The coefficients of x, y, and z represent the normal vector of the planes.

Taking the normal vector (a, b, c) as (-5, -4, 4) from either of the planes, we can select a point on one of the planes. For simplicity, let's choose the point (0, 0, 0) which lies on both planes.

Now, we can calculate the perpendicular distance (d) between the two planes using the formula:

d = |a*x + b*y + c*z - d| / sqrt(a^2 + b^2 + c^2)

In this case, substituting the values into the formula, we have:

d = |(-5)*(0) + (-4)*(0) + (4)*(0) - 42| / sqrt((-5)^2 + (-4)^2 + 4^2)

  = |-42| / sqrt(25 + 16 + 16)

  = 42 / sqrt(57)

  ≈ 5.55

Therefore, the distance (d) between the two planes is approximately 5.55 units.

To find the distance between two parallel planes, we can utilize the concept of a perpendicular distance. Two planes are considered parallel if their normal vectors are parallel. The normal vector is a vector that is perpendicular to the plane and helps define its orientation.

In this problem, we are given two planes: -5x - 4y + 4z = 42 and -5x - 4y + 4z = -101. Notice that the coefficients of x, y, and z are the same in both planes, indicating that they are parallel.

To calculate the distance between these planes, we need to determine the perpendicular distance from one plane to the other. We can achieve this by selecting a point on one of the planes and finding the distance between that point and the other plane.

Choosing the point (0, 0, 0) as it lies on both planes, we can substitute its coordinates into the equation of the second plane (-5x - 4y + 4z = -101) to calculate the perpendicular distance.

Using the distance formula, which involves the coefficients of x, y, and z in the plane equation, as well as the coordinates of the selected point, we can compute the perpendicular distance. The formula takes into account the absolute difference between the two planes' equations and divides it by the magnitude of the normal vector.

By substituting the values into the formula and simplifying, we find that the distance between the two planes is approximately 5.55 units. This means that any point on one plane is approximately 5.55 units away from the other plane in a direction perpendicular to both planes.

Learn more about perpendicular distance here:

brainly.com/question/31658149

#SPJ11

Answer:

yes you use kilometers

Step-by-step explanation:

The inverse of the transpose of matrix A is equal to the transpose of the inverse of matrix A.

To verify that the inverse of A transpose (A^T) is equal to the transpose of the inverse of A (A^-1), we can use the multiplication rule for transposes, which states that (CD)^T = D^T * C^T.

Let's assume that A is an invertible matrix. We want to show that (A^T)^-1 = (A^-1)^T.

First, let's take the inverse of A^T:

(A^T)^-1 * A^T = I,

where I is the identity matrix.

Now, let's take the transpose of both sides:

(A^T)^T * (A^T)^-1 = I^T.

Simplifying the equation:

A^-1 * (A^T)^T = I.

Since the transpose of a transpose is the original matrix, we have:

A^-1 * A^T = I.

Now, let's take the transpose of both sides:

(A^-1 * A^T)^T = I^T.

Using the multiplication rule for transposes, we have:

(A^T)^T * (A^-1)^T = I.

Again, since the transpose of a transpose is the original matrix, we get:

A * (A^-1)^T = I.

Now, let's take the transpose of both sides:

(A * (A^-1)^T)^T = I^T.

Using the multiplication rule for transposes, we have:

((A^-1)^T)^T * A^T = I.

Simplifying further, we get:

A^-1 * A^T = I.

Comparing this with the earlier equation, we see that they are identical. Therefore, we have verified that the inverse of A transpose (A^T) is equal to the transpose of the inverse of A (A^-1).

In conclusion, (A^T)^-1 = (A^-1)^T.

To know more about inverse,

https://brainly.com/question/13593989

#SPJ11

Answer:

1 solution , x = 0

Step-by-step explanation:

8(x + 9) = 72 - 5x ← distribute parenthesis on left side

8x + 72 = 72 - 5x ( add 5x to both sides )

13x + 72 = 72 ( subtract 72 from both sides )

13x = 0 ⇒ x = 0

x = 0 is the only solution to the equation

Given:

z = -2 + 2 √3 i​

The objective is to write the number in trigonometric form.

The trigonometric form can be represented as,

The general form of complex number is, z = x+iy.

By comparing with the given equation.

x = -2

y = 2 √3

The value of r can be calculated as,

The value of theta can be calculated as,

Now, substitute the obtained values of r and theta in the general equation of trigonometric form.

Since,

Then,

Hence, the required trigonometric form is obtained.

The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1