Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent

The value of x in the equation 9(x − 6) = 8(x + 6) is 102.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It should be noted that from the information given, the equation is illustrated as:

9(x − 6) = 8(x + 6)

9x - 54 = 8x + 48

Collect the like terms

9x - 8x = 48 + 54

x = 102

The value of x is 102.

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does it want the answer in a specific form?

slope intercept form; y = mx + b

slope = 2

b = -1

plug the values in

y = 2x -1 or y = 2/1x -1

Answer: the equations has no solution

Step-by-step explanation:

[tex]9^{3x+1}=27^{2x}\\\\(3^2)^{3x+1}=(3^3)^{2x}\\\\3^{2(3x+1)}=3^{3(2x)}\\\\3^{6x+2}=3^{6x}\\\\Hence,\\\\6x+2=6x\\\\6x+2-6x=6x-6x\\\\2\neq 0\\\\Thus,\ the\ equations\ has\ no\ solution[/tex]

A 60-inch piece is the shorter one. 180 inches long is the longer piece.

Step-by-step explanation:

L + S = 240

L = 3 S

L + S = 240 ( 3 S ) + S = 240 \s 4 S = 240 \s S = 60

L = 3 S L = 3 ( 60 )

L =180

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Using listing method the elements in the set are +2 and -2.

What is listing method ?

The listing approach involves writing the members of the set as a list, with commas separating the items and curly brackets enclosing the list. The rule or condition that may be used to determine if an object can belong to the set is specified when using the rule method for sets.

The members of a set are listed using this technique, with commas used to separate them and curly braces used to enclose the list. The four distinct seasons, for instance, can all be written as "Summer, Autumn, Spring, and Winter." The list's elements can be in any order, so don't worry.

We are given the set [tex]\left\{x \mid x^2=4\right\}[/tex]

all such x such that the perfect square is 4. Now, we have

[tex]$x^2=4 \Rightarrow x=\pm 2$[/tex]

Therefore, the elements in the set are +2 and -2.

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Answer:

1km\h

Step-by-step explanation:

like in physics, the calculation of speed is total distance divided by total time, you should do the same in math, and so you do 1 hour (60 minutes)  + 15 minutes which gives you 75 minutes, and then you divide 75 km by the time so it should look something like this:

[tex]\frac{75 km}{75 minutes}[/tex] which gives you 1

so raphael is going 1 km\h

Answer:

[tex]\huge\boxed{\sf v = 60\ km/hr}[/tex]

Step-by-step explanation:

Distance = S = 75 km

Time = t = 1.25 hours

Speed = v = ?

v = S/t

v = 75/1.25

v = 60 km/hr

[tex]\rule[225]{225}{2}[/tex]

Answer:

2. Definition of Midpoint

3. Vertical Angles Theorem

Step-by-step explanation:

Definition of Midpoint is the middle point of a line segment

Vertical Angles Theorem is proving angles that are opposite each other and formed by two intersecting straight lines, are congruent.

1) The mean and the standard deviation of the total amount of money that she earns in a month are of:

2) The probability that she earns more than $2750 in a given month is of: 0.3192 = 31.92%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

When two variables are added, the mean is given by the sum of the means, hence:

[tex]\mu = 2100 + 550 = 2650[/tex]

The standard deviation is given by the square root of the sum of the variances, hence:

[tex]\sigma = \sqrt{200^2 + 70^2} = 211.9[/tex]

The probability that she earns more than $2750 in a given month is  one subtracted by the p-value of Z = 2750, hence:

Z = (2750 - 2650)/211.9

Z = 0.47

Z = 0.47 has a p-value of 0.6808.

1 - 0.6808 = 0.3192 = 31.92%.

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To determine whether Juakali can successfully save the document on the flash disk, you can calculate the total number of words in the document and compare it to the amount of free space on the flash disk.

First, calculate the total number of lines in the document by multiplying the number of pages by the number of lines per page:

Total number of lines = 123 pages * 70 lines/page

= 8610 lines

Next, calculate the number of lines with 14 words by multiplying the total number of lines by the proportion of lines with 14 words:

Number of lines with 14 words = 8610 lines * 36/70

= 4380 lines

Calculate the total number of words in the lines with 14 words by multiplying the number of lines by the number of words per line:

Total number of words in lines with 14 words = 4380 lines * 14 words/line

= 61320 words

Calculate the number of lines with 18 words by subtracting the number of lines with 14 words from the total number of lines:

Number of lines with 18 words = 8610 lines - 4380 lines

= 4230 lines

Calculate the total number of words in the lines with 18 words by multiplying the number of lines by the number of words per line:

Total number of words in lines with 18 words = 4230 lines * 18 words/line

= 76140 words

Finally, add the total number of words in the lines with 14 words and the total number of words in the lines with 18 words to find the total number of words in the document:

Total number of words = 61320 words + 76140 words

= 137,460 words

To determine whether Juakali can successfully save the document on the flash disk, you can compare the total number of words in the document to the amount of free space on the flash disk. Since the flash disk has 256 KB of free space and there are 137,460 words in the document, Juakali will not be able to save the document on the flash disk. This is because the document is larger than the amount of free space available on the flash disk.

It is important to note that the capacity of a storage device is usually measured in bytes, and 1 KB is equal to 1024 bytes.

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Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .

In mathematics, a function from a set X to a set Y assigns each item in X exactly one element in the other set. The sets X and Y represent the function's domain and codomain, respectively.

Here,

Given :

function :8-9x/5-4x

To find the inverse ,

Inverse of 8-9x. 8-5x 5 4x -4x+9

Steps Function Inverse definition A function g is the inverse of function F if for y=√(x), x=g(v)

y= 8-9x 5-4x

Replace x with y

x = 8-9y/ 5-4y

Solve for y,

x = 8-97/ 5-4y

=>8-5x /-4x+9

Therefore , the inverse  function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .

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Answer:  The percent that the house's value is going up each year is given by the factor 1.04 - 1, which is 0.04. This represents a 4% increase in the value of the house each year.

ii) To find the value of the home in 15 years, you can substitute x = 15 into the equation to get:

A = 400,000 (1.04)^15

= 400,000 (1.7589)

= 700,356

Therefore, the value of the home in 15 years is $700,356.

iii) To find when the value of the home will double, you can set the value of A equal to 2*400,000 and solve for x:

2*400,000 = 400,000 (1.04)^x

2 = (1.04)^x

x = log(2)/log(1.04)

= 10.67

Therefore, it will take approximately 10.67 years for the value of the home to double, assuming the trend continues.

There are 3 tens in 7x30 or 30x7.

What is an equation?

A mathematical statement is referred to as an equation when two expressions are connected by the equal sign. A mathematical equation serves as the connection between two expressions on each side of the sign. Usually, there is only one variable and an equal sign.

Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.

An equation is created by joining two expressions with an equal sign. The solution to an equation is a number that may be used as the variable to generate a true number statement.

Here, we have

7x30 = 7 x 10 x 10 x 10

The value of 7x30 = 210

Hence, there are 3 tens in 7x30 or 30x7.

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The percentage of her students that ride the school bus every morning would be = 84%

A percentage expression is an representation of a data set to a fraction of 100.

The total number of students = 25 students

The number of students that ride the school bus = 21

To calculate the percentage of the students that ride the bus the following is done;

= 21/25 × 100

= 2100/25

= 84%

Therefore, the percentage of her students that ride the school bus every morning is 84%

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The simplified form of [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex] is [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex].

= [tex]\sqrt{4 - 4\sqrt{5} + 5}+ \sqrt{4 + 4\sqrt{5} + 5}[/tex].

= [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].

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Answer:

the answer will be the options A

If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.

The rational zero theorem is used to determine the rational roots of a polynomial function.

Rational Zero Theorem statement:-

The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients

f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,

p is a factor of the constant a₀,

q  is a factor of the leading coefficient an,

and p and q are relatively prime.

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Answer: C

Step-by-step explanation:

pythagorean theorem : a^2 + b^2 = c^2

8^2 + 8^2 = x^2

64 + 64 = x^2

128 = x^2

x = sqrt(128) square root both sides

x = 8sqrt(2) simplified

Answer: c, [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

     Since this is a right triangle, we will use the Pythagorean theorem to help us solve for x.

    Theorem:

a² + b² = c²

    Substitue values:

8² + 8² = c²

    To the power of 2:

64 + 64 = c²

    Addition:

128 = c²

   Square root both sides of the equation:

[tex]\sqrt{128}[/tex] = c

    Reflexive property and breaking up 128 into two factors:

c = [tex]\sqrt{64*2}[/tex]

    Square root of 64:

c = 8[tex]\sqrt{2}[/tex]

   So, x = 8[tex]\sqrt{2}[/tex]

Answer:

  2184

Step-by-step explanation:

You want to know the possible number of ways 3 flavors can be chosen from 14 when order matters.

The number of permutations of 14 flavors taken 3 at a time is ...

  14 × 13 × 12 = 2184

There are 14 ways to choose the bottom flavor, then 13 ways to choose a different middle flavor, and finally 12 ways to choose a different top flavor. Each flavor can go with any combination of the others, so the total number is the product of 14·13·12, or 2184.

The formula for the number of n things taken k at a time is ...

  P(n, k) + n!/(n-k)!

For n=14, k=3, this is the product shown above.

The substance will weigh 9 pounds after  4.5123 hours.

Here it is given that every 3 hours the weight of the substance doubles.

At 12 noon it weighed 2 pounds. Hence we will consider the initial weight to be 2.

Let the weight after x hours be w(x)

Here it doubles in 3 hours, hence the growth rate is 100%

Since the growth rate is given, the equation for the growth rate will be

w(x) = w₀.eˣ

where x = no. of 3-hour spans.

Here

w₀ = 2

and w(x) is given 9

Hence,

2eˣ = 9

or, e²ˣ = 9/2

Taking log on both sides we get

loge²ˣ = ln(9/2)

or, 2xloge = ln(9/2)

Since loge = 1 we get

2x = log(9/2)

or, x = 1.5041

Hence they will become 9 pounds after

3 X 1.5041 hours

= 4.5123 hours

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The new perimeter will be 2 times larger then the old perimeter, if both dimensions of rectangle are doubled.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width.

The figure's length is essentially revealed by the perimeter. Assume that the perimeter of a square with equal sides will be four times that square's sides. The perimeter of a circle, which is determined by its radius, is known as its circumference.

The new dimensions  of rectangle = 4mm and 9mm

The original dimension = 2mm and 4.5 mm

Perimeter of rectangle = P=2(l+w) = 2 (4.5 +2 ) = 13 mm

Perimeter of rectangle after doubled dimension = 2 (9 + 4) = 26

So, the new perimeter will be 2 times larger then the old perimeter

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Answer:

2/5 ≠ 25

Step-by-step explanation:

Given question,

→ Is 2/5 equivalent to 25?

Let's check the problem,

→ 2/5 = 25

→ 0.4 ≠ 25

The equivalent fractions of 2/5 are,

→ 2/5 = 4/10

→ 2/5 = 6/15

→ 2/5 = 8/20

→ 2/5 = 10/25

Hence, 2/5 is not equivalent to 25.

The numbers are -19 and -13 by the given conditions.

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach. Aloud to yourself, read the issue.

Let the two numbers be x and y

One number is six less than a second number: x = y - 6 ⇒ i

Four times the first is 2 more than 6 times the second: 4x = 6y + 2 ⇒ ii

Substitute the value of x in (ii)

4(y-6) = 6y + 2

4y - 24 = 6y + 2

2y = -26

y = -13

Now substitute the value of y in (i);

x = -13 - 6

x = -19

Hence, the numbers are -19 and -13 by the given conditions.

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The relative frequency probability that the forecast for tomorrow will be accurate = 16/33.

What is probability?

P(A) = Number of accurate days/ Total number of days

Here, the number of accurate days is 25 and total number of days is 37.

Substitute the above values as follows:

P(A) = 25/37

Hence, the relative frequency probability that the forecast for tomorrow will be accurate = 16/33.

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The number of the digits after the decimal point is 7. The correct option is C.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.

Given that the numbers are 0.3568 and 0.042. The multiplication of the two numbers will be done as,

P = 0.3568 x 0.042

P = 0.0149856

The number of the digits after the decimal is 7.

Therefore, the number of the digits after the decimal point is 7. The correct option is C.

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{25} is the solution set of the equation  {10, 24, 25, 36}.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given set of equation is {10, 24, 25, 36}

Since, The equation is represented by the sentence that is 5/6 of a number is 30.

So the required solution,

5/6 of the number 30 = 25

The solution set of the equation is {25}.

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95% confidence that machine calibrated properly is (48.536, 51.424).

We have given that,

n = 25

mean of x = 49.98 mm

S = 0.14 mm

μ = 50.00 mm

and CI = 95%

from t-table we know that,

t at 95% and n - 1 = 25 - 1 = 24 is 2.064

Therefore 95% of CI means that

(x - 2.064 × S√n, x + 2.064 × S√n)

(49.98 - 2.064 × 0.14√25, 49.98 + 2.064 × 0.14√25)

(49.98 - 2.064 × 0.7, 49.98 + 2.064 × 0.7)

(49.98 - 1.444 , 49.98 + 1.444)

(48.536, 51.424)

Therefore 95% confidence that machine calibrated properly is

(48.536, 51.424).

The 95% confidence interval is a range of values that you can be 95% confident contains the true mean of the population.

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Answer: B C and D

Step-by-step explanation: