find the compound interest
on Rs 4000 for 30 months at 10% per annum​

Answer:

The choice B.

\(x > 4 \\ x < - 1\)

I hope I helped you^_^

Answer:

2.3inches

Step-by-step explanation:

The p-value is less than the significance level of 0.10, we reject the null hypothesis. Therefore, there is enough evidence to conclude that the mean discharge differs from 7 fluid ounces.

The null hypothesis (H₀) states that the population mean discharge (µ) is equal to 7 fluid ounces, while the alternative hypothesis (H₁) states that µ differs from 7 fluid ounces.

Since the sample size is small (n < 30) and the population standard deviation is unknown, a t-test should be used for hypothesis testing.

To calculate the test statistic, we use the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / √n). Substituting the values, we get t = (7.08 - 7) / (0.25 / √14) = 2.40.

The p-value is the probability of observing a test statistic as extreme as the calculated t-value, assuming the null hypothesis is true. By referring to the t-distribution table or using statistical software, we find that the p-value is less than 0.10.

Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Therefore, there is enough evidence to conclude that the mean discharge differs from 7 fluid ounces.

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The confidence interval for the average difference between the reading and writing scores is [-1.776 , 0.689]

In statistics, a confidence interval denotes the probability/likelihood that a population parameter will fall between a set of values for a certain proportion of the time. Analysts frequently employ confidence intervals that contain 95% or 99% of the expected observations.

Given,

sample size =200

Mean = -0.545

standard deviation = 8.887

confidence level = 95%

Confidence interval can be determined by formula,

\(C.I=mean \pm z(\frac{S}{\sqrt{n}})\)

where, s=standard deviation

n= sample size

z-value at 95% =1.96

\(C.I=-0.545 \pm 1.96(\frac{8.887}{\sqrt{200}})\\\\C.I=-0.545 \pm 1.96(\frac{8.887}{14.142})\\\\C.I=-0.545 \pm 1.96(0.628)\\\\C.I=-0.545 \pm 1.231\\\\C.I=-0.545 - 1.231 \ ,\ -0.545 +1.231\\\\C.I=-1.776\ ,\ 0.689\)

Thus, the confidence interval is [-1.776 , 0.689]

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Answer:

Step-by-step explanation:

Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. ...

Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.

Answer: y = 1/9x - 3 8/9

Step-by-step explanation:

To find the slope, you must do y2-y1/x2-x1

-3+5/8+10

2/18

1/9 is the slope.

Then, you put the slope into slope-intercept form and take one of the coordinates and add it into the equation. Let's do the second coordinate.

slope-intercept form is y=mx+b

y=mx+b

-3 = 1/9(8) + b

-3 =  8/9 +b

-3 8/9 = b

y = 1/9x - 3 8/9

Hope this helps!

The area between z = -1.30 and z = 1.50 is B. 0.0968.

To get the area between z = -1.30 and z = 1.50, we need to subtract the area to the left of z = -1.30 from the area to the left of z = 1.50.
The area to the left of z = -1.30 is the same as the area to the right of z = 1.30, which is 1 - 0.4032 = 0.5968.
The area to the left of z = 1.50 is 0.4332.
Therefore, the area between z = -1.30 and z = 1.50 is 0.4332 - 0.5968 = 0.0968.
So the answer is B. 0.0968.

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Answer:

y = -1/2x + 3.5

Step-by-step explanation:

In order to pass through the point (1, 3), and is perpendicular to y = 2x - 1, then the line must be y = -1/2x + 3.5. Hope this helps!

Answer:

Step-by-step explanation:

Step one:

given data

day one

x shirts that cost $19.99 each and

y pairs of shorts that cost $14.99 each.

Day two

3 more shirts that cost $19.99 each and

4 more pairs of shorts cost $14.99 each.

Step two:

the total number of shirts is

x+3

and the total number of shorts is

y+4

The total cost is ex[ressed as

19.99(x+3)+ 14.99(y+4)

Answer:

its c!!

Step-by-step explanation:

Answer:

√x+6=x-6

squarring both side

x+6=x²-12x+36

0=x²-12x-x+36-6

x2-13x+30=0

x²-10x-3x+30=0

x(x-10)-3(x-10)=0

(x-10)(x-3)=0

either

x=10

or

x=3

Answer:

D:X=10

Explanation

A rational equation is defined as the quotient of two polynomials, with the denominator not being zero. It is a type of algebraic expression that involves variables and rational functions with rational exponents.

The error in the given rational equation is that it's not allowed to cancel out the x-2 and X+2 terms, as they are in the denominators. It is because of the fact that it may make the denominator zero, which would result in undefined expressions. Therefore, we need to find the least common multiple (LCM) of the denominators and then convert the equation into equivalent forms with the same denominator.B):

Correction of the error1-2/x-2 = x+1/X+2Given rational equation can be re-written as:((1 - 2)/(x - 2)) = ((x + 1)/(X + 2))The LCM of x - 2 and X + 2 is (x - 2) (X + 2).Multiplying the numerator and denominator of the left side by (X + 2) and the numerator and denominator of the right side by (x - 2) we get,(1 - 2)(X + 2) = (x + 1) (x - 2)Now simplify the equation:2X - 3x = -3The given rational equation becomes 2X - 3x = -3 after correction.Note: You should always double-check if the obtained solution satisfies the initial equation.

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The correct analytical solution is \((1 + x) / (1 - x) = e^(2t + C)\)

Assuming that the value of u is 1, we can proceed with solving the differential equation analytically using the variable separable method.

The differential equation is: dx/dt + x² = u

Substituting u = 1, we have: dx/dt + x² = 1To solve this equation analytically, we can use the method of variable separation:

Separate the variables:dx / (1 - x²) = dt

Integrate both sides:

∫ dx / (1 - x²) = ∫ dt

To integrate the left-hand side, we can use partial fraction decomposition or trigonometric substitution. Let's use partial fraction decomposition:

The equation becomes:

∫ (1/2) * (1 / (1 + x)) + (1/2) * (1 / (1 - x)) dx = ∫ dt

Integrating both sides:

(1/2) * ln|1 + x| - (1/2) * ln|1 - x| = t + C

Simplifying:

ln|1 + x| - ln|1 - x| = 2t + C

Using logarithmic properties, we can combine the logarithms:

ln((1 + x) / (1 - x)) = 2t + C

Exponentiating both sides:

\((1 + x) / (1 - x) = e^(2t + C)\)

Simplifying:

\((1 + x) = C' * e^(2t) * (1 - x)where C' = e^C\)

Solving for x:

\(1 + x = C' * e^(2t) - C' * e^(2t) * xx + C' * e^(2t) * x = C' * e^(2t) - 1Factor out x:x * (1 + C' * e^(2t)) = C' * e^(2t) - 1x = (C' * e^(2t) - 1) / (1 + C' * e^(2t))\)

Given the initial condition x(0) = 0.1, we can substitute t = 0 and x = 0.1 into the equation to solve for the constant C':

\(0.1 = (C' * e^0 - 1) / (1 + C' * e^0)0.1 = (C' - 1) / (1 + C')\)

Solving for C', we can multiply both sides by (1 + C'):

0.1 * (1 + C') = C' - 1

0.1 + 0.1 * C' = C' - 1

0.1 = 0.9 * C'

C' = 0.1 / 0.9

C' = 1/9

Substituting C' back into the equation:x = \(((1/9) * e^(2t) - 1) / (1 + (1/9) * e^(2t))\)

Now, we have the analytical solution for the differential equation with u = 1.

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An equation that relates y, the amount of yellow paint in liters, and the amount of blue paint in liters, needed to make the Green Goober's special green paint is 3y + 5b = 8x.

An equation is a mathematical statement that shows that two or more mathematical or algebraic expressions are equal or equivalent.

Mathematical expressions combine variables with constants, numbers, or values with the mathematical operands, addition, subtraction, multiplication, and division.

The yellow paint mixed with the blue paint = 3 liters

The blue paint mixed with the yellow paint = 5 liters

The quantity of the special green paint = 8 liters

Let the yellow paints = 3y

Let the blue paints = 5b

Let the special green paints = 8x

3y + 5b = 8x

Thus, the equation that represents the situation is 3y + 5b = 8x.

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Answer:

16777216

Step-by-step explanation:

64 times 64 equals 4096. 4096 to the power of 2 is 16777216.

(a) The velocity of the rocket 6 seconds after being fired is 280 feet/sec.(b) The correct answer is: Speeding up in (0, 0.5) U (2, [infinity]) and slowing down in (0.5, 2).

(a) To find the velocity of the rocket 6 seconds after being fired, we need to find the derivative of the position function s(t) with respect to time t.

Given: s(t) = -18t² + 496t

Velocity is the derivative of position, so we differentiate s(t) with respect to t:

v(t) = s'(t) = d/dt (-18t² + 496t)

Using the power rule of differentiation, we differentiate each term separately:

v(t) = -36t + 496

Now, substitute t = 6 into the velocity function to find the velocity of the rocket 6 seconds after being fired:

v(6) = -36(6) + 496

v(6) = -216 + 496

v(6) = 280 feet/sec

Therefore, the velocity of the rocket 6 seconds after being fired is 280 feet/sec.

(b) To find the acceleration of the rocket 6 seconds after being fired, we need to find the derivative of the velocity function v(t) with respect to time t.

Given: v(t) = -36t + 496

Acceleration is the derivative of velocity, so we differentiate v(t) with respect to t:

a(t) = v'(t) = d/dt (-36t + 496)

Using the power rule of differentiation, we differentiate each term separately:

a(t) = -36

The acceleration is constant and does not depend on time. Therefore, the acceleration of the rocket 6 seconds after being fired is -36 feet/sec².

For the second part of the question:

Given: s(t) = 4t³ – 6t² – 24t + 3

To determine the time intervals when the object is slowing down or speeding up, we need to analyze the sign of the velocity and acceleration functions.

First, let's find the velocity function by taking the derivative of s(t):

v(t) = s'(t) = d/dt (4t³ – 6t² – 24t + 3)

Using the power rule of differentiation, we differentiate each term separately:

v(t) = 12t² - 12t - 24

Next, let's find the acceleration function by taking the derivative of v(t):

a(t) = v'(t) = d/dt (12t² - 12t - 24)

Using the power rule of differentiation, we differentiate each term separately:

a(t) = 24t - 12

To determine when the object is slowing down or speeding up, we need to examine the signs of both velocity and acceleration.

For speeding up, both velocity and acceleration should have the same sign.

For slowing down, velocity and acceleration should have opposite signs.

Let's analyze the signs of velocity and acceleration in different intervals:

Interval (0, 0.5):

In this interval, both velocity and acceleration are positive.

The object is speeding up.

Interval (0.5, 2):

In this interval, velocity is positive and acceleration is negative.

The object is slowing down.

Interval (2, [infinity]):

In this interval, both velocity and acceleration are positive.

The object is speeding up.

Therefore, the correct answer is: Speeding up in (0, 0.5) U (2, [infinity]) and slowing down in (0.5, 2).

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Sure! Here's a table to represent the information given in the word problem: Item Amount per Omelet Eggs 3    Cheese 4 ounces To find out how many eggs and ounces of cheese Jenny used for her family.

we need to multiply the amounts per omelet by the number of omelets she made. Since there are 5 people in her family, we assume she made one omelet per person. Therefore, she made a total of 5 omelets Using the table, we can calculate: Eggs: 3 eggs per omelet × 5 omelets = 15 eggs  Cheese: 4 ounces of cheese per omelet × 5 omelets = 20 ounces of cheese So, Jenny used 15 eggs and 20 ounces of cheese for her family.

To find out how many eggs and ounces of cheese Jenny used for her family, we need to multiply the amounts per omelet by the total number of omelets she made. Since there are 5 people in her family, she needs to make 5 omelets Using the table, we can calculate Eggs: 3 eggs per omelet × 5 omelets = 15 eggs Cheese: 4 ounces of cheese per omelet × 5 omelets = 20 ounces of cheese.

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We are told that Jason has $325 and that he earns $105 per week. That means that if "w" is the number of weeks then the amount of money he has in total is what he has saved by the product of $105 by the number of weeks. That is, if A is the amount he has, then:

Now, we are asked how many weeks it takes to get to $900. This means that we set A = 900 and solve for "w".

To solve for "w" we first subtract 325 on both sides:

Now we divide both sides by 105

Solving the operations:

Therefore, it takes Jason 5.5 weeks to get to $900

Answer:

Jimena tiene 8 años de edad.

Step-by-step explanation:

Sean \(x\), \(y\), \(z\) las edades de Jimena, su padre y su madre. A continuación, traducimos cada oración relevante del enunciado a expresiones matemáticas:

(i) Si su papá tiene 27 años más que Jimena:

\(y = x+27\) (1)

(ii) Su mamá tiene 34 años:

\(z = 34\) (2)

(iii) La suma de las tres edades es igual a la diferencia de 10 veces la edad de Jimena, menos 3 años:

\(x+y+z = 10\cdot x-3\) (3)

Al aplicar (1) y (2) en (3), tenemos la siguiente ecuación resultante:

\(x +(x+27)+34 = 10\cdot x-3\)

\(2\cdot x +61=10\cdot x-3\)

\(8\cdot x = 64\)

\(x = 8\)

Jimena tiene 8 años de edad.

Step-by-step explanation:

if you mean x multiply 2 :

j(x) = 2x + 1

j(a+1) = 2(a+1) + 1

= 2a+ 2 +1

=2a + 3

if you mean x to the power of 2

j(x) = x^2 +1

j(a+1) = (a+1)^2 + 1

= a^2 + 2a + 1 +1

= a^2 + 2a + 2

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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6, 3 surfboard per wet suit

Answer:

6

Step-by-step explanation

3x2=6

Answer:

The product to this problem is simplified to:  \(1+14f+49f^{2}\)

Step-by-step explanation:

1) First place out what was given:

\((-1 -7f)^{2}\)

Squared is the same thing as multiply to itself, so you would create a pair of

\((-1 -7f)^{2}\)  

(For example, if you said: \(x^{2}\) it is the same as saying or putting: x · x)

2) Then create your pair which would look like:

\((-1 -7f)(-1 -7f)\)

3) Next step is to do the FOIL method

(Like how it is shown in the picture, we will do this method and create one whole expression!)

4) Creating and combining your expression into one whole problem, by using the foil method.

\((-1 -7f)(-1 -7f)\)

First - F: \(1\)

Outside - O: \(7f\)

Inside - I: \(7f\)

Last: \(49f^{2}\)

This will be:

\(1+14f+49f^{2}\)

And this will be your answer!

Answer:

are this the answers?  

Step-by-step explanation:

The value of x is 16 degrees and the measure of the arc DFG for circles of homework 2 are 1 6.056 times radius of circle.

The property of straight angle says that, the angle of a straight line is equal to the 180 degrees.

It can also be define as the sum of all the angle made on the straight line is equal to the 180 degrees.

For the first problem, the line GE, which is the diameter of the circle has two angles over it (x-3) degree and (12x-25) degrees.

For the diameter GE the sum of these two angle will be equal to 180 degrees. Thus,

\((x-3)+(12x-25)=180\\x-3+12x-25=180\\13x-28=180\\13x=180+28\\x=\dfrac{208}{13}\\x=16^o\)

The value of mDE will be equal to (12x-25) as it is verticle angle of mGF. Thus,

\(arcDE=(12x-25)\\arcDE=(12(16)-25)\\arcDE=167^o\)

Similarly the value of mEF

\(arcEF=(x-3)\\arcEF=(16-3)\\arcEF=13^o\)

Let the radius of the circle is R. Then the measure of arc DFG is equal to the sum of areDEF and arc GF. Thus,

\(arcDFG=\dfrac{2\pi R}{2}+\dfrac{2 \pi R \angle GHF}{360}\\arcDFG=\dfrac{2\pi R}{2}+\dfrac{2 \pi R (167^o)}{360}\\arcDFG=6.056R\)

For the second problem, the angle MN and QO are equal due to the vertical angle property. Therefore,

\((10x-45)=(6x-1)\\10x-6x=-1+45\\4x=44\\x=11\)

The value of mMN is,

\(MN=(10x-45)\\MN=(10(11)-45)\\MN=65^o\)

The value of NP using the property of straight line for line segment MP can be given as,

\(NP=180-MN\\NP=180-65\\NP=115^o\)

Thus, the value of x is 16 degrees and the measure of the arc DFG for circles of homework 2 are 1 6.056 times radius of circle.

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