At a music store, Rita got a $12 discount on an item originally priced at $48. What percent discount did she get?

Answer:

a. Au = 9cos(30) + 11cos(31)

b. AB = 9sin(30) + 11sin(31) and B = -9sin(30) + 11sin(31)

3. a. 9cos(30) + 2cos(80)

b. 3cos(15) + 4cos(12)

4. The ground velocity of the plane would be 349.4 km/h on a bearing of 225°.

By using the midpoint rule, the value of n to approximate the integral is 9.24.

The integral of a function is a measure of the total area under the curve of the function over a given interval. The Midpoint Rule is a method used to approximate the value of an integral by dividing the interval into smaller subintervals, finding the midpoint of each subinterval, and using the height of the function at the midpoint to estimate the area of the subinterval.

In this specific problem, we are asked to approximate the integral of the function f(x) = sin root x from x = 0 to x = 48, using the Midpoint Rule with n = 4 subintervals. To do this, we divide the interval [0,48] into 4 equal subintervals of width

=> (48-0)/4 = 12.

The midpoint of each subinterval is calculated as follows:

1st subinterval: (0 + 12)/2 = 6

2nd subinterval: (12 + 24)/2 = 18

3rd subinterval: (24 + 36)/2 = 30

4th subinterval: (36 + 48)/2 = 42

Next, we find the height of the function f(x) = sin root x at each of these midpoints.

1st subinterval: sin root 6 = 0.77

2nd subinterval: sin root 18 = 0.97

3rd subinterval: sin root 30 = 0.87

4th subinterval: sin root 42 = 0.71

Finally, we multiply each height by the width of the subinterval to find the estimated area of each subinterval, and add up these areas to obtain the final estimate of the integral:

(0.77 * 12) + (0.97 * 12) + (0.87 * 12) + (0.71 * 12) = 9.24

So, our final estimate of the integral of f(x) = sin root x from x = 0 to x = 48 using the Midpoint Rule with n = 4 is 9.24. Rounding to 4 decimal places, our answer is 9.2400.

Complete Question:

Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.

∫0 to 48 sin √x dx, n=4

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The correct answer is option b.The approximate value of pool in that area is $20.000c.

A value that is similar to another value but not exactly equal to it is referred to as an approximation number. When the outcomes of the numerical calculations are unknown, the approximation is applied. They are typically used when greater place value decimal numbers emerge as a result.

Approximate value of a pool in the area = Value of home with a swimming pool in the area - Value of home without a swimming pool in the same area.

Value of home with a swimming pool in the area = $250,000

Value of home without a swimming pool in the same area = $230,000.

The approximate value of pool in the area = 250000 - 230000 = 20000.

Hence, the correct answer is option b. The approximate value of pool in that area is $20.000c.

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Answer:

Step-by-step explanation:

3+d<3-d

3+d<3-dcancel equal terms

3+d<3-dcancel equal termsd<-d

3+d<3-dcancel equal termsd<-dMove the variable to the left

3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0

3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms

3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0

3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0divide both sides

3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0divide both sidesd<0

The value of b form the logarithmic equation [tex]log_b}3=0.7925[/tex] is 3.9998688.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

Given that, [tex]log_b}25=2.3219[/tex] and [tex]log_b}3=0.7925[/tex].

Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.

We know that, logₐN=x is written exponential form as aˣ=N

Here, [tex]b^{2.3219}=25[/tex]

b=4.00006709

[tex]b^{0.7925}=3[/tex]

b=3.9998688

Therefore, the value of b is 3.9998688.

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Answer:

5025π m³

Step-by-step explanation:

the figure consists of two figures;

a cone and phere

volume of a cone=1/3πr²h

volume of hemisphere=2/3πr³

1/3×π×15×15×37=2775π

2/3×π×15×15×15=2250π

sum up the volumes

2775π+2250π

=5025π m³

Answer:

7-12=x

5(x+2)

7-12=-5

5(-5+2)

5(-3)

Step-by-step explanation:

The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is 6/7. Then the equation is given as,

y = (6/7)x + c

The equation passes through (-5, 4). Then we have

4 = (6/7) (-5) + c

4 = -30/7 + c

c = 58 / 7

Then the equation is given as,

y = (6/7)x + 58/7

7y = 6x + 58

The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.

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The fith letter Diego will type is the letter a

From the question, we have the following parameters that can be used in our computation:

Letters: a, s, d and f

When the letters are repeated, we have

a s d f a s d f a s d f a s d f a s d f......

using the above as a guide, we have the following:

Fifth letter = a

Hence. the fifth letter is a

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Nathan biked a total of 135 miles.

Miles  unit of distance  between 2.1 map of the link of a johnny the tomb my list divided for the letting word thousand and the world to 1.609 kilometers my life report unit measurement is a united states uk kannada some other countries.

To solve this problem, we need to use the given information to find the amount of miles that Jeremy biked. Since Jeremy biked 3 times as many miles as Riley, we know that Jeremy biked 15 x 3 = 45 miles.

Since Nathan biked 3 times as many miles as Jeremy, we know that Nathan biked 45 x 3 = 135 miles. Therefore, Nathan biked a total of 135 miles.

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Answer: 17%

Step-by-step explanation:

So, the formula to get the area of a circle is [tex]\pi r^{2}[/tex].

USA: [tex]4.2^{2} \pi[/tex] = 55.42cm

India: [tex]8.7^2\pi[/tex] = 237.79cm

From this, we can divide India by USA:

237.79 / 55.42 = 4.291

Then, with that we can multiply our 4% by 4.291:

4 * 4.291 = 17.16400

Rounded to the nearest percent is 17%

The solution is, prime factorization of 756 = 3*2*3*2*3*7

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

756

we know,

756 = 6*6*21

       =3*2*3*2*3*7

as, we know, 2,3,7 all are prime.

so, prime factorization of 756 = 3*2*3*2*3*7

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Answer: 67.69%

Step-by-step explanation:

To calculate the completion percentage,

Divide the completed passes by the total passing attempts.

>      7142/10551

Then, multiply that answer by 100 to get the percentage.

>      67.69%

The Bernoulli equation for this particular differential equation is [tex]dy/dx = 6x(y-1)[/tex]  the final solution is [tex]y = x^3 + 1[/tex].

The Bernoulli equation for this particular differential equation is [tex]dy/dx = 6x(y-1)[/tex]. To solve the equation, we first use the substitution u = y – 1. This substitution simplifies the equation to [tex]dy/dx = 6xu[/tex], which is a first-order linear equation with constant coefficients. Now we can use the method for solving Bernoulli equations to find the solution.

We first find the integrating factor, which is [tex]I(x) = exp(∫6xdx)= exp(3x^2)[/tex]. Then we multiply both sides of the equation by I(x) to get [tex]I(x)dy/dx = 6xI(x)u[/tex]. We can now integrate both sides with respect to x and get the general solution of [tex]y = u + 1 = (1/I(x))∫6xI(x)dx + 1[/tex]. After calculating the integral, the final solution is [tex]y = x^3 + 1[/tex].

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The requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
Interquartile range (IQR), The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.

In the given question we have 3 IQR data sets that jointly vary from 10 to 17 by this we can conclude that, at least half of the trout in both lakes measure between 12 and 18 inches.

Thus, the requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.

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The population of the town is 2564 people after 4 years.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

Given:

The initial population of the town is 1652 people.

And the town's population is tripling every 10 years.

Let y₀ be the initial population, r be the growth rate and t be the time.

So,

y = y₀(e[tex])^{rt}[/tex]

Substituting the values to the function,

y = 1652(e[tex])^{rt}[/tex]

In 10 years,

3y₀= y₀(e[tex])^{rt}[/tex]

r = log(3)/10

Now, the population of town after 4 years is,

y = 1652(e[tex])^{{ln(3)/10} \cdot {t}}[/tex]

y = 2563.64

y ≈ 2564 people.

Therefore, the population is y ≈ 2564, people.

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Answer:

$2,450

Step-by-step explanation:
2/10, n/30 = discounts of 2%

Credit sale = $2,700
Sale return = $200

Net Receivable =$ 2,700 - $ 200 = $2,500

Discount = 2,500 x %2 = 50
Payment Receipt = $2,500 - $50 = $2,450
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Answer:

y - 7 = 1/4 ( x - 0 )

y -7 = 1/4 x

y = 1/4 x + 7

Answer:

[tex]b[/tex] ≈ [tex]7.7[/tex]

Step-by-step explanation:

We need to use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

In this case we have a and c. So let's plug those into the equation:

[tex](5.7)^2+b^2=(9.6)^2[/tex]

Solve:

[tex]32.49+b^2=92.16[/tex]

Round to the nearest tenth:

[tex]32.5+b^2=92.2[/tex]

Subtract 32.5

[tex]b^2=59.7[/tex]

Find 'b'

[tex]b=\sqrt{59.7}[/tex]

[tex]b[/tex] ≈ [tex]7.7[/tex]

I hope this helped you!

Be safe and have great day! (:

This program implements a user interface that can convert between the units centimeters (cm), meters (m), and inches (in) using the conversion formulas outlined.

#include <iostream>

using namespace std;

int main()

{

// Declare variables

double value;

char fromUnit;

char toUnit;

// Get input

cout << "Enter a value and the units you wish to convert from and to (cm, m, in): ";

cin >> value >> fromUnit >> toUnit;

// Convert the value

if (fromUnit == 'm' && toUnit == 'cm') {

 value *= 100;

} else if (fromUnit == 'cm' && toUnit == 'm') {

 value /= 100;

} else if (fromUnit == 'in' && toUnit == 'm') {

 value /= 100 * 2.54;

} else if (fromUnit == 'm' && toUnit == 'in') {

 value *= 100 * 2.54;

}

// Output the result

cout << "Result: " << value << toUnit << endl;

return 0;

}

The formula used in this program is the conversion between the units centimeters (cm), meters (m), and inches (in). The conversion formula used is as follows:

1 meter (m) = 100 centimeters (cm)

1 inch (in) = 2.54 centimeters (cm)

Therefore, if we are converting from centimeters (cm) to meters (m), the conversion formula is to divide the value by 100. If we are converting from meters (m) to centimeters (cm), the conversion formula is to multiply the value by 100. For the conversion from inches (in) to meters (m), the conversion formula is to divide the value by 100 and multiply it by 2.54. For the conversion from meters (m) to inches (in), the conversion formula is to multiply the value by 100 and divide it by 2.54.

For example, if we want to convert 5 meters (m) to centimeters (cm), we use the formula 5 * 100 = 500 centimeters (cm).

This program implements a user interface that can convert between the units centimeters (cm), meters (m), and inches (in) using the conversion formulas outlined above.

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The union of the set elements is [2, ∞)

From the question, we have the following parameters that can be used in our computation:

[2,3] ∪ (3,∞)

The above is a union set

The definition of the union set is that we write out all the elements in the set

Using the above as a guide, we have the following:

[2,3] ∪ (3,∞) = [2, ∞)

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The name special quadrilateral that have four right angles. are Square  , Rhombus , Rectangle have 4 right angle.

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

Square - The properties of square is it have 4 side and all side are equal and make 90 degree angle on all 4 side. that's why it has 4 right angle.

Rhombus - The properties of rhombus  is it have 4 side and all side are equal and there diagonal cut each other at 90 degree that's why it has 4 right angle

Rectangle- The properties of square is it have 4 side and parallel sides are equal and make 90 degree angle on all 4 side.that's why it has 4 right angle.

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Using the cross product property, the value of d is 5.76.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as  p : q = r : s or p/q = r/s

Given proportional relation is,

9 / 10=d / 6.4

Doing the cross multiplication,

9 × 6.4 = 10 × d

57.6 = 10d

d = 57.6 / 10

d = 5.76

Hence the solution of the proportion is d = 5.76.

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Suppose that So, S1, S2,... is a sequence of subsets of N the following sets is guaranteed to be different from all sets in the sequence is S = {n² | n² & Sn}.

Subsets are a part of the mathematical concept of sets. A set is anything that is wrapped in curly braces, such as "a,b,c,d." If set A is a collection of even integers and set B is composed of the numbers 2, 4, and 6, then set A is the superset of set B and set B is said to be a subset of set A. Review Sets Subset and Superset for further details.

Set A is referred to as a subset of Set B if each element of Set A is also present in Set B. In other words, Set B includes Set A.

As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.

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A counterexample that shows that all the integers are not divisible by 3 is given as follows:

2.

The statement for this problem is given as follows:

"All the positive integers are divisible by 3".

The statement is false, as only numbers whose sum of the digits is a multiple of 3 are divisible by 3, hence for example, the number 2 is not divisible by 3.

The counterexample is the statement that proves that a conjecture(another statement) is false, hence the number 2 is the counterexample showing that not all positive statements are divisible by 3.

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The median of 20 is the most accurate to use since the data is skewed.

Option C is the correct answer.

A histogram is a representation of the distribution of data with intervals.

We have,

The data given shows a histogram that is skewed to the right.

Now,

Since the data is skewed.

The median is a better measure of the center of data than the mean.

Now,

Arrange the data in order:

10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55

Median = middle value.

Median = 20

Thus,

The median of 20 is the most accurate to use since the data is skewed.

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Answer:

your question is a bit confusing...

Step-by-step explanation:

the simplest radical form of the exact value of cos A will be 7/8.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given a right-angle triangle that has a base of 14 height of √60 and a hypotenuse of 16.

From the general formula of cosine in a right-angle triangle:

Cos α = base/ hypotaneuse

In our case,

base = 14 and

hypotenuse = 16

Thus,

Cos A = 14/16

A = 0.5053 radians

Therefore, the simplest radical form of the exact value of cos A will be 7/8.

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Complete question: