Math 5th grade

Roshaun walks around the city park. The square park measures 61 1/4 yards on each side. How far does Roshaun walk?

Answer: To find the distance between Earth and the star in miles, we need to multiply the number of light-years by the number of miles in a light-year.

33.7 light-years * 6,000,000,000,000 miles/light-year = 2.022 x 10^17 miles

So, the distance between Earth and the star is approximately 2.022 x 10^17 miles, written in scientific notation.

Step-by-step explanation:

Answer:

Infinity divided by infinity is undefined because infinity is not a number and cannot be treated as one in mathematical operations. In mathematics, division is a process that involves finding the ratio between two numbers. However, infinity is not a number and has no finite value, so it cannot be used as the denominator or numerator in a division operation.

When dividing infinity by infinity, you are asking for the ratio of two quantities that are both infinite, and the result is not well-defined. The concept of infinity can be useful in certain mathematical contexts, such as limits and calculus, but it cannot be used as a number in the usual sense.

In mathematical terms, the expression infinity divided by infinity is considered indeterminate and has no defined value. This is why it is undefined in mathematical analysis.

Step-by-step explanation:

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 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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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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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:

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! (:

Answer:

12 1/30

Step-by-step explanation:

Sum is the term used for the total amount of something when two or more numbers are added.

In order to add the two fractions, they must have the same denominator.

To do this, we need to find a common denominator.

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 10:  10, 20, 30

Both 3 and 10 have 30 in common, so this is the common denominator.

In order to get to 30, 3 must be multiplied by 10.  Whatever you do to the bottom must be done to the top and vice versa.

7 1/3 becomes 7 10/30.

4 7/10 becomes 4 21/30

Now, we add the whole numbers.

7 + 4 = 11

Now, add the fractions.

10/30 + 21/30 = 31/30

Put it all together.

11 31/30

This is an improper fraction, so we must make it a proper fraction.  To do this, we divide 30 into 31.  It can only go in evenly one time and has a remainder of one.  The remainder is added to the whole numbers and the numerator of the fraction takes the evenly divided one.

11 + 1 1/30  This is adding the remainder to the whole number.

12 1/30  This is the result of adding the remainder and fixing the fraction.

12 1/30 is the answer.

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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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%

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°.

Answer: I'm sorry, but the statement "the answer to the meaning of life that is squared by two" is not a coherent or meaningful concept. The meaning of life is a philosophical question that has been debated by scholars, theologians, and thinkers throughout history and has no single, universally agreed-upon answer. Additionally, squaring by two does not have any inherent relationship to the meaning of life.

Step-by-step explanation:

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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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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The simplification of the  algebraic expression gives:

(5m² + 3mn - 3n²) - (m² - n²) = 4m² + 3mn - 2n²

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

(5m² + 3mn - 3n²) - (m² - n²) = 5m² + 3mn - 3n² - m² + n²

                                              = 5m²- m² + 3mn - 3n²+ n²

                                              = 4m² + 3mn - 2n²

Therefore, (5m² + 3mn - 3n²) - (m² - n²) simplifies to 4m² + 3mn - 2n²

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Answer:

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

y -7 = 1/4 x

y = 1/4 x + 7

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:

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

Therefore , the solution of the given problem of triangle comes out to be it shares an angle with triangle DEF that is equal in measure to angle F.

If a triangle has four quadrants or more, it is referred to as a polygon. It has a straightforward rectangular shape. The letters ABC when combined form a right-angled triangular. A new parallelogram with rectangular shape corners is created by Euclidean geometry when the limits are incompatible. Due to their three edges but also three points, triangles are categorised as polygons. The location of a triangle's corners is determined by where its three edges meet. The sum of the angles on the inside of a trapezoid is 180.

Here,

Part A: To determine if triangle DEF is similar to triangle DBC, we need to check if their corresponding angles are equal in measure and if their corresponding sides are proportional. If both conditions are satisfied, the triangles are similar. Since BC is parallel to EF, we know that angle DBC and angle DEF are corresponding angles and are therefore equal in measure.

Part B: The line segment on triangle DBC that corresponds to line segment EF is the side opposite to angle DBC, which is segment DC. This is because segment DC is parallel to segment EF and shares an angle with triangle DEF that is equal in measure to angle DBC.

Part C: The corresponding angle to angle F in triangle DBC is angle BCD. This is because angle BCD is opposite to side BC, which is parallel to EF and shares an angle with triangle DEF that is equal in measure to angle F.

Therefore , the solution of the given problem of triangle comes out to be it shares an angle with triangle DEF that is equal in measure to angle F.

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Answer: The best estimate for 2/5 hour is 1/2 hour and the best estimate for 5/8 hour is 1/2 hour. So, the total time spent would be 1/2 hour + 1/2 hour = 1 hour.

Therefore, the best estimate for the total time Maria spent with her little sister is 1 hour.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula to calculate the future value of an investment with compound interest is:

FV = PV * (1 + (r/n))^(n*t)

Where:

PV is the present value (the initial investment)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For Investment A:

PV = $4,000

r = 6% = 0.06

n = 2 (semiannual compounding)

t = 5 years

FV = $4,000 * (1 + (0.06/2))^(2*5) = $4,000 * (1.03)^10

FV = $4,000 * 1.664131669 = $6,656.53

So, the total amount of Investment A is $6,656.53 (rounded to the nearest cent).

The equation of line M is given by y = 3x + 6 , where the slope is m = 3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

x + 3y = 18   be equation (1)

when x = 0 , y = 6

So , one point is P ( 0 , 6 )

Now , the line L has the points A , E and B

where ABCD is a rectangle , so AD is perpendicular to the line L

So , the product of slopes of the perpendicular line will be = -1

On simplifying the equation (1) , we get

Subtracting x on both sides of the equation , we get

3y = -x + 18

Divide by 3 on both sides of the equation , we get

y = -( 1/3 )x + 6

Substituting the values in the equation , we get

Slope of line L x Slope if line M = -1

The slope of line L = -1/3

So , the slope of line M = 3

Now , the equation of line L is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 6 = 3 ( x - 0 )

y - 6 = 3x

Adding 6 on both sides of the equation , we get

y = 3x + 6

Hence , the equation of line is y = 3x + 6

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The least squares regression line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's grades.

The least squares regression line for the corrected data would be shifted upwards compared to the least squares regression line for the original data, since the corrected data point has a higher value than the original data point. This shift in the regression line would indicate that, in general, increasing the amount of time spent studying would have a greater impact on the student's grades than the original data indicated.

The least squares regression line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's grades.

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The volume of the composite figure is equal to 3425.333 cubic feet.

In this problem we need to determine the volume of a composite figure, that is, the sum of the volumes of a right prism and a pyramid, whose formulae are described below:

Right prism

V = 0.5 · w · l · h

Pyramid

V = (1 / 3) · (0.5 · w · l) · h

Where:

Now we proceed to determine the volume of the composite figure:

V = 0.5 · (8 ft) · (7 ft) · (12 ft) + (1 / 3) · 0.5 · (8 ft) · (7 ft) · (7 ft)

V = 3425.333 ft³

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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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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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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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As people get older, the proportion of employees with low blood pressure falls and the proportion with high blood pressure rises.

Interactions are regarded to as appropriate when they usually have the same ratio. For instance, the number of plants in an orchard and the number of apples in a production of apples depend upon this average number of apples produced by each tree. A linear relationship among two numbers or objects is considered to as being proportional in mathematics. When the first quantity doubles, the other amount also does so. As soon as one variables is reduced to 1/100th of its previous value, other decreases as well. If two variables are proportional, it means that if one rises, the other climbs as well, and their relationship stays constant at all values. The diameter and circumference of a circle are used as an example.

given

a) 20%, 49.4%, 30.6% (equal 100)

b) 29.7%, 45.5%, 24.8%

20%, 52.6%, 27.4%

14.9%, 48.5%, 36.6%

c) As people get older, the proportion of employees with low blood pressure falls and the proportion with high blood pressure rises.

d) No, because the association between age and blood pressure can only be determined through a carefully designed trial.

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