Is 8:9 and 5:6 equivalent

Step-by-step explanation:

5. .....................................................

The angle of 'x' is 87°  

The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another is always equal.

Here we have

Two lines are intersected at the point and forms four angles      

As we can see that given angles are vertically opposite angles  

=> x = 82°    

Therefore,

The angle of 'x' is 87°  

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The length (in cm) of the hypotenuse of the triangle is 26 cm.

Let one leg be a and the other leg be b.

According to the question a^2bπ/3 = 800π

ab^2/3π=1920π

Thus, a^2b =2400 ----1

ab^2=5760  -----2

Multiplying 1 and 2 we get

(a^2b)( ab^2)= 2400 x 5760

(a^2b)( ab^2)= (2^3 . 5 . 3^2) (2^7 . 3^2 . 5)

⇒ab =∛(2^13 . 3^3 . 5^3) = 240  ----3

Now addition gives,

(a^2b)( ab^2)=  ab(a+b)= 2400 + 5760

(a^2b)( ab^2) = 240(a+b)=240(10+24)

a+b=34

Let h be hypotenuse,

Now, h =√(a^2 + b^2)

h=√(a+b)^2- 2ab

h=√34^2-2.240

h=√676

h=26

Therefore, The length (in cm) of the hypotenuse of the triangle is 26 cm.

A right triangle is a polygon that has one angle between the base and perpendicular equal to 90°.  The hypotenuse is the longest side of the triangle. The other two angle sum up to be 90°.

Complete question- When a right triangle is rotated about one leg, the volume of the cone produced is 800pi cm^3. When the triangle is rotated about the other leg, the volume of the cone produced is 1920 pi cm^3. What is the length (in cm) of the hypotenuse of the triangle?

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Answer:

3/35 or 0.0857

Answer:

3/35

Step-by-step explanation:

Multiplying fractions

1/7 x 3/5

Multiply the numerators.

1*3 = 3

Multiply the denominators.

7*5 = 35

Put the numerator over the denominator.

3/35

Answer:

$31,031

Step-by-step explanation:

Since 7 people each pay $4,433 which means that you would have to do 7 x 4433 which equals 31031. So the answer is $31,031.

The difference of the rational expressions 5/2-3/5 is 19/10.

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.

A fraction with polynomials as the numerator, denominator, or both is all that a rational expression is. Any equation with at least one rational expression is said to be rational. If the numerator and denominator of a rational expression do not have any common factors, then the expression is said to be simplified.

Given the expressions is 5/2-3/5

⇒ 25 - 6 / 10

⇒ 19/10

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A fraction is a smaller part of a whole number.

A whole number is defined as the number that is natural and it includes numbers such as 0, 1,2,3,4,5,6,7,8,9, 10. This means that is doesn't contain numbers that has decimal points or fractions such as. 1.5 or 1½ respectively.

A fraction is defined as the part of a whole value such as 1/4 which is 25% of 1. This means that it is the smaller part of a whole number.

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The area of the shaded region in the figure in terms of pi is

The shaded portion is a portion of a squared which has two semi circles of diameter equal to the side of the square.

The area of the two semi circle will be subtracted from the area of the square to give the area of the shaded region

Area of a square is solved by the formula

= length *  width

=  9 * 9 = 81 m²

Area of the two semi circle

= 0.5πr² * 2

= πr²

and r  = 9/2 = 4.5

= 20.25π m²

area of shaded portion

= 81 - 20.25π m²

The area of the shaded region in terms of pi is (81 - 20.25π) m²

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Answer:

equal to 1

Step-by-step explanation:

I believe this is the answer. Also I see that ur new. Well welcome to Brainly.

The probability that a given class period runs between 50.5 and 51 minutes is 0.05

Understanding that a uniform probability distribution is essentially a rectangle with a surface area of one will help you to find the simplest solution to this problem.

Find a section of this rectangle's area now.

Her classes are uniformly distributed between 48.0 and 58.0 minutes so,

We have to find the probability that a given class period runs between 50.5 and 51 minutes

51−50.5-/58-48

=0.5/10

=0.05

1 X0.05=0.05

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The full question:

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.0 minutes. Find the probability that a given class period runs between 50.5 and 51 minutes.

Answer:

Step-by-step explanation:

so  do 72÷24= 3 then do x 46= 138

The lines of equations y = 3x - 8 and y = 3x - 12 have same slope but they are parallel to each other and have no solution.

What is system of equations?

A System of Linear Equations is when we have two or more linear equations are working together.

The first equation is y = 3x - 8.

The second equation is y = 3x -12.

Substituting the value of y from equation 1 in equation 2 -

y = 3x -12

3x - 8 = 3x - 12

3x - 3x = -12 + 8

0 = 4

There is no x-intercept.

Substituting the value of x in equation 1 -

y = 3x - 8

y = 3(0) - 8

y = 0 - 8

y = -8

So, the lines do not intersect each other.

Therefore, the equations have same slope but do not have any solution.

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The measure of the angle is 65 degrees.

Two angles are said to be complementary if the sum of the angles is 90°. The complementary pairs 1 and 2 are in the following diagram. It is not necessary for two angles to be contiguous to be complimentary. Since 35° + 55° = 90°, the angles in the following diagram are likewise complimentary. View further angles as well.

Let x be the measure of the angle.

The complement of an angle is the angle that, when added to the original angle, equals 90 degrees. Therefore, the complement of the angle is 90 - x.

Given that the angle is 15 degrees less than two times its complement, we can set up the following equation:

x = 2(90 - x) - 15

Solving for x:

x = 2(90 - x) - 15

x + 15 = 180 - 2x

3x = 195

x = 65

Therefore, the measure of the angle is 65 degrees.

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Answer:

81

Step-by-step explanation:

n = 92 - 11

Therefore,

n = 81

Answer:

A bond is a debt security, meaning that it represents a loan made by an investor to a borrower (typically a corporation or government). The bond issuer promises to pay interest to the bondholder, usually at regular intervals, and to repay the principal when the bond matures.

So, a statement that could describe the returns from a bond is:

"Bonds typically provide a steady stream of income in the form of interest payments, but the return on investment is generally lower than that of stocks."

Another statement that could describe the returns from a bond is:

"Bonds are considered to be a relatively safe investment option, but they are not as profitable as stocks in terms of returns."

In general, bonds are considered to be less risky than stocks, but they also typically offer lower returns.

Answer: B

Step-by-step explanation:

It will take the bus one hour to travel 36 km at a rate of 72 km per hour.

Calculate the rate of speed: 72 km/hr

Calculate the time it will take to travel 36 km: 36 km/72 km/hr = 0.5 hr

Convert 0.5 hr to minutes: 0.5 hr x 60 min/1 hr = 30 min

Add the time in minutes to the hour: 60 min + 30 min = 90 min

Convert 90 min to hours: 90 min/60 min/hr = 1.5 hr

Round the time to the nearest hour: 1.5 hr = 1 hr

The amount of time it will take a bus to travel 36 km at a rate of 72 km/hr can be calculated by dividing the distance (36 km) by the rate of speed (72 km/hr). This yields 0.5 hr. Since time is measured in minutes, 0.5 hr can be converted to 30 min. Adding the time in minutes (30 min) to the hour (60 min) yields 90 min. This can then be converted to 1.5 hr. To get an answer in hours, the time must be rounded to the nearest hour, which gives 1 hr. Therefore, it should take the bus one hour to travel 36 km at a rate of 72 km/hr.

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Answer:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is always the same. In this case, the common difference between the terms 29, 37, 45, is 8.

To find the 59th term of an arithmetic sequence, you can use the formula:

a_n = a_1 + (n-1)d

Where:

a_n is the nth term of the sequence

a_1 is the first term of the sequence

n is the position of the term you are trying to find

d is the common difference between the terms of the sequence

In this case:

a_1 = 29

n = 59

d = 8

So, to find the 59th term of this arithmetic sequence, you would do:

a_n = 29 + (59-1)8 = 29 + (58)8 = 29 + 464 = 493

So, the 59th term of this arithmetic sequence is 493.

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The correct question is

What is the 59th term of the arithmetic sequence 29, 37, 45?

Answer: The answer is 23 hours

Step-by-step explanation: The question tells you that Trevon earns 11.35 dollars per hour and that his total paycheck is 261.05 dollars. To find the answer you must divide what he earns per hour (11.35) from his total paycheck (261.05).

After doing the division you will find that he worked for 23 hours

There are three main measures of central tendency: mean, median, and mode. Each of these measures has its own strengths and weaknesses, and can be affected differently by outliers.

Mean is the most commonly used measure of central tendency, and is calculated by adding all the values in a dataset and dividing by the total number of values. However, when there are outliers in a dataset, the mean can be significantly distorted. This is because outliers, which are extreme values that are far from the other values in a dataset, can skew the mean, making it a less accurate representation of the data than the median or mode.

On the other hand, the median is the middle value of a dataset, and is not affected by outliers as much as the mean. This is because the median is determined by the middle value of a dataset, and does not take into account every individual value.

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Option D. A student who studies for 0 hours can anticipate receiving a test score of roughly 60.

A linear equation is one that satisfies the algebraic formula y=mx+b. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

The value of the y-coordinate when the value of the x-coordinate is equal to zero is known as the y-intercept.

Regarding this issue

The x-coordinate indicates the number of hours spent studying.

The test result is shown by the y-coordinate.

so

For x=0, y=60

It follows

A student with no study time can anticipate to receive a test score of roughly 60.

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Answer:

The answer would be 6

Step-by-step explanation:

first multiply 10*15=150 then 10+15=25 150 divided by 150 is 6

a) The values of x for which trinomial x² −11x + 31 equal to 1 are (11 ± 3i)/2.

b) The values of x for which the polynomials x² − 5x− 3 and 2x − 5 are equal are (7 ± √41)/2.

c) The values of x for which the binomial 7x+1 equal to the trinomial 3x² - 2x + 1 are

x = 0, 1/3.

d) The values of x for which the trinomial −2x² + 5x + 6 equal to the binomial 4x² + 5x are ± √3.

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves arithmetic options and non-negative integer exponentiation of variables.

Now, see the problem, we have to determine the value of x in each case.

a) The trinomial x² - 11x + 31 equal to 1

=> x² - 11x + 31 = 1

Using the quadratic formula,

=> x = ( -(-11)± √121 - 124)/2

=> x = ( 11 ± √-3 )/2 = (11 ± 3i)/2

So, required value of x is (11 ± 3i)/2.

b) The values of the polynomials x² − 5x− 3 and 2x − 5 equal.

=> x² − 5x− 3 = 2x − 5

=>x²− 5x− 3 - 2x + 5 = 0

=> x² - 7x + 2 = 0

=> x = (-(-7) ± √49 - 8)/2

=> x = (7 ± √41)/2

c) The binomial 7x+1 equal to the trinomial 3x² - 2x + 1

=> 7x + 1 = 3x² - 2x + 1

=> 3x² - 2x + 1 - 7x - 1 = 0

=> 3x² - 9x = 0

=> x( 3x - 9 ) = 0

=> x = 0, 1/3

d) The trinomial −2x² + 5x + 6 equal to the binomial 4x² + 5x.

=> 2x² + 5x + 6 = 4x² + 5x

=> 2x² + 5x + 6 - 4x² - 5x = 0

=> - 2x² + 6 = 0

=> 2x² -6 = 0

=> x² = 6/2 = 3

=> x = ± √3

Hence, the required values of x are ±√3.

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Answer:

25

Step-by-step explanation:

5x - 5 + 2x + 10 = 180

7x + 5 = 180

7x = 175

x =25

Answer: the answer to this question is X = 25

The degree for 5x - 5 = 5(25) - 5 = 120 degrees (we are putting 25 in for x to get the sum of the degree)

The degree for 2x+10 = 2(25)+10 = 60 degrees (we are putting 25 in for x to get the sum of the degree)

Let's walk through the steps:

Step 1: Simplify both sides of the equation.

5x−5+2x+10=180

5x+−5+2x+10=180

(5x+2x)+(−5+10)=180 (Combine Like Terms)

7x+5=180

Step 2: Subtract 5 from both sides.

7x+5−5=180−5

7x=175

Step 3: Divide both sides by 7.

7x/7 = 175/7

x = 25

The equation with infinite solution among the options is 7x + 5 = 4x + 5 + 3x. Therefore, the correct option is C. 7x + 5 = 4x + 5 + 3x.

An infinite solution has both sides equal.  In other words, If both sides of the equation are the same (or equivalent), then there are always infinite solutions.

Hence,  let's find the equation with infinite solution in the options

7x + 5 = 4x + 5 + 3x

Let's rearrange the equation to see if it's equivalent on both sides

7x + 5 = 4x + 5 + 3x

combine like terms

7x + 5 = 4x + 3x + 5

7x + 5 = 7x + 5

Therefore, the equation are equivalent on both sides. This makes them equation with infinite solution.

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the percent of cash the Fire branch raised is 5.833 and the pre-sale rate of the TV is $300.

A price or ratio that can be said as a fragment of one hundred is called a percent in mathematics. If we want to compute a percent of a number, we need to divide it with the aid of using its complete after which multiply it with the aid of using one hundred. The percentage consequently refers to an issue in keeping with a hundred. Per one hundred is what the time period percentage signifies. The letter "%" stands for it.

Given,  The fire department hopes to raise $30,000 to repair a firehouse. So far the department has raised $1,750.00

From the general formula of Percentage, we have to divide the value by the total value and then multiply the resultant by 100.

Percentage = (1750/30,000) * 100 = 5.833%

Also given, A TV is advertised for sale. It is 35% off and has a new price of $195.

Price of TV before Sale = (195 / 65) * 100

Price of TV before Sale = 300$

Therefore, the percentage of money the Fire department raised is 5.833 and the pre-sale price of the TV is $300.

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Answer: Yoo

To find out how much more it will rain, we can use the information given to calculate the rate of rain in inches per hour. We know that it rained an inch and a half in 8 hours, so the rate of rain is:

(1.5 inches) / (8 hours) = 0.1875 inches/hour

Now that we know the rate of rain, we can use it to find out how much more it will rain in the rest of the day. We can assume that the rest of the day has 16 hours, so we can use the rate of rain to find out how much more it will rain:

(0.1875 inches/hour) x (16 hours) = 3 inches

So, it will rain 3 inches more the rest of the day.

We can also check this by multiplying the inches per hour (1.5/8) by the number of hours in a day (24) and subtracting the inches of rain fallen (1.5 inches)

(1.5/8)*24-1.5 = 3

This means that it will rain 3 inches more the rest of the day.

Step-by-step explanation:

The inequality that can be used to determine the greatest number of games he can bowl is D. 4.25 + 2.5x ≤ 25.

An inequality is a mathematical statement that compares the value of two expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to). Inequalities are used to express relationships between numbers and can be used to describe constraints or limitations in real-world problems.

Let x be the number of games Manny can bowl

We can write the inequality as:

$2.50(x) + $4.25 ≤ $25.00

2.5x + 4.25 ≤ 25

To solve for x, we subtract 4.25 from each side. Then, divide both sides by 2.5.

2.5x + 4.25 - 4.25 ≤ 25 - 4.25

2.5x ≤ 20.75

x ≤ 8.3

Hence, Manny can bowl as much as 8 games.

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The probability that the mean of the next 100 claims is larger than $1000 is 0.1791 or 17.91%.

Since the sample size of 100 claims is large enough, assume that the sampling distribution of the mean is approximately normal.

The mean of the sampling distribution of the mean is equal to the population mean, which is $920 in this case. The standard deviation of the sampling distribution of the mean, also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard error is $870/√(100) = $87.

Use the normal distribution to calculate the probability that the mean of the next 100 claims is larger than $1000. Use a z-score to find this probability.

The z-score is given by (x - μ)/σ , where x is the value of interest, in this case is $1000, μ is the population mean, which is $920 and σ is the standard error, which is $87.

z = ($1000 - $920)/$87 = 0.9195

Use a standard normal table or a calculator to find the probability corresponding to z-score = 0.9195.

p = 0.8208529999999999

Subtract it from 1.

p = 1 - 0.8208529999999999 = 0.179147

Therefore, the probability that the mean of the next 100 claims is larger than $1000 is 0.1791 or 17.91%.

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Therefore , the solution is  l=3 w + 8 is the formula to solve for the dimensions of a rectangle.

In Euclidean plane geometry, a rectangle is a square with four right angles. You may also refer to it as a quadrilateral that seems to be equiangular, meaning that each of its angles is equal. Another possibility for the parallelogram is a straight angle. Four of the sides of a square are of identical length. Four 90 ° vertices and equal equal sides make up a rectangle-shaped quadrilateral.

Here,

Given that the rectangle's perimeter is 104 cm

W = the rectangle's width

rectangle's length is equal to 3 w + 8.

Rectangle perimeter equals 2 (length + width).

= >104 =2(3 w + 8 + w)

= >104 =2(4 w + 8)

= >104 =8 w + 16

= >8 w = 104- 16

= >8w = 88

= >w = 11

hence the rectangle's length is equal to 3 w plus 8.

= >3 * 11 + 8

=> 33 + 8

=> 41

Consequently, l=3 w + 8 is the formula to solve for the dimensions of a rectangle.

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