Patel made a deposit into an account that earns 5%simple interest. After 10 years Patel had earned $1500 in interest. How much was Patel’s initial deposit?

Using Basic Property of Logarithms:

(a) ln ( a⁻² / b c⁴ ) = -27

(b) ln \(\sqrt{b^4 c^4 a^4}\) = 20

(c) ln ( a³ b⁻²) / ln (bc)³ = 0

(d) ( ln c⁻⁴ ) x ( ln (a/b⁻³) ) = -220

1. Product Property

log(mn) = log(m) + log(n)

2. Quotient Property

log(m/n) = log(m) – log(n)

3. Power rule

logmⁿ = n (log(m))

some property for Natural Log (ln).

here, ln a = 2, ln b = 3 and ln c = 5

(a) ln ( a⁻² / b c⁴ )

using Quotient property:

ln a⁻² - ln ( b c⁴)

now using product and power rule property:

-2( ln a) - ln(b) - 4 ( ln c)

putting the values

-2x(2) - 3 - 4 (5)

-4 - 3 - 20

→ -27

(b) ln \(\sqrt{b^4 c^4 a^4}\)

using power rule property:

1/2 ( ln ( b⁴c⁴a⁴ ))

using Product property and Power rule property:

4/2 ( ln b + ln c + ln a)

2 ( 3 + 5 + 2 )

2 ( 10 )

→ 20

(c) ln ( a³ b⁻²) / ln (bc)³

using Product and Power rule property:

3( ln a) -2(ln b) / 3 ( ln b + ln c )

3 (2) -2(3) / 3 ( 3 + 5)

→ 0

(d) ( ln c⁻⁴ ) x ( ln (a/b⁻³) )

using Power rule and Quotient property:

-4 ( ln c) x ( ln a + 3 ( ln b ))

-4 ( 5 ) x ( 2 + 3 ( 3 ) )

(-20) x ( 11 )

→ -220

Hence, Using Basic Property of Logarithms:

(a) ln ( a⁻² / b c⁴ ) = -27

(b) ln \(\sqrt{b^4 c^4 a^4}\) = 20

(c) ln ( a³ b⁻²) / ln (bc)³ = 0

(d) ( ln c⁻⁴ ) x ( ln (a/b⁻³) ) = -220

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An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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Answer:

x=11.34

Step-by-step explanation:

Answer:

The answer is

\( \huge y - 3 = 2(x + 5)\)

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

From the question we have the final answer as

\(y - 3 = 2(x + 5)\)

Hope this helps you

The probability that it will rain on exactly one of the three days they are there is 0.375.

Given that Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%.

The binomial distribution is used when there are exactly two outcomes of a trial that are mutually exclusive.

Use binomial probability:

P = ⁿCʳ pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

probability of rain on any given day =p =0.50

total number of ways,n=3

let X is number of days with rain out of 3 days

So, \(X\sim Bin(3,0.50)\)

P(x=X)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ

P(x=1)=³C₁(0.50)¹(1-0.50)³⁻¹

P(x=1)=3×0.50×(0.5)²

P(x=1)=1.5×0.25

P(x=1)=0.375

Hence, the probability that it will rain on exactly one of the three days they are there where the probability of rain on any given day is 50% is 0.375.

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Answer:

12

Step-by-step explanation:

14/10=(y+9)/15

cross product

10(y+9)=14*15

10y+90=210

10y=210-90

10y=120

y=120/10

y=12

Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

Step-by-step explanation:

To find the total length of both pieces of fabric in centimeters, we need to add the length of the first piece of fabric (142 cm) and the length of the second piece of fabric (2 meters).

However, we need to make sure that the units are consistent before we add the lengths. We can convert the length of the second piece of fabric from meters to centimeters by multiplying by 100. Therefore, the total length in centimeters is:

142 cm + 2 meters * 100 cm/meter = 142 cm + 200 cm = 342 cm

The option that correctly gives the answer is "Multiply 2 by 100, then add 142" (Option C).

Answer:

X=115/22

Step-by-step explanation:

22x-15=100

22x=100+15

22x=115

X= 115/22

Answer:

alternate interior angles

Step-by-step explanation:

The expression to represent the given situation is M =30t.

Let's use the variable M to represent Susan's overall piano practice time over the course of t days.

Given that Susan practices the piano for 30 minutes every day, the sum of her practice time over the course of t days is:

M = 30t

As a result, M = 30t is the equation that describes the total amount of time Susan spends practicing the piano over the course of t days.

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Answer:

hope this help you......

The number of farmers who grew at least one of the three crops is 921

Let's analyze the given information step by step to determine the number of farmers who grew at least one of the three crops, the number of farmers who did not grow any of the three crops, and the number of farmers who grew exactly two of the three crops.

According to the survey results:

125 farmers grow only beans.

107 farmers grow only corn.

87 farmers grow only old.

200 farmers grow wheat and corn.

50 farmers grow wheat and old.

176 farmers grow corn.

To find the number of farmers who grew at least one of the three crops, we need to sum up the number of farmers who grew each crop individually and subtract the number of farmers who grew both combinations of crops:

Number of farmers who grew beans = 125

Number of farmers who grew corn = 107 + 200 + 176 = 483

Number of farmers who grew old = 87 + 50 + 176 = 313

Adding these numbers, we get:

125 + 483 + 313 = 921

Therefore, 921 farmers grew at least one of the three crops.

To find the number of farmers who did not grow any of the three crops, we subtract the total number of farmers in the survey from the number of farmers who grew at least one of the three crops:

500 - 921 = -421

Since we can't have a negative number of farmers, we can conclude that there is an error in the given information.

As for the number of farmers who grew exactly two of the three crops (beans, corn, or old), we don't have enough information to determine this value based on the given data.

In conclusion, the number of farmers who grew at least one of the three crops is 921 (assuming there was an error in the given information). The number of farmers who did not grow any of the three crops cannot be determined with the information provided, and the number of farmers who grew exactly two of the three crops cannot be determined.

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Answer:

pam has x = 7 pennies

sam has 2x + 1 = 14 + 1 = 15 pennies

Step-by-step explanation:

let's take the number of pennies that pam owns be x

sam's pennies = 2× ( pam's pennies ) + 1

=》2x + 1

if the total pennies owned by both = 22

then,

x + 2x +1 = 22

3x = 22 - 1

x = 21 ÷ 3

x = 7

so, pam has x = 7 pennies

sam has 2x + 1 = 14 + 1 = 15 pennies

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

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Answer:

c=2/15 have a great day! :D

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 5/8c from both sides.

Step 3: Add 1/2 to both sides.

Step 4: Multiply both sides by 8/(-15).

Answer:

50(5π + 6) cm²

Step-by-step explanation:

TSA of figure = 1/2 of TSA(Cylinder) + Area of rectangle

= 1/2 of 2πr(h+r) + 20*15

= πr(h+r) + 300

= 10π(15+10) + 300

= 250π + 300 cm²

or 50(5π + 6) cm²

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.

Given that-

Volume of cylinder = πr²h

Volume of cylinder = 3.14 *5²*18

Volume of cylinder = 3.14*25*18

Volume of cylinder = 1413 ft³

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

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Answer:

r = 1

Step-by-step explanation:

(6, -3) ; (14, r)

Slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

\(\frac{r-[-3]}{14-6}=\frac{1}{2}\\\\\frac{r + 3 }{8} = \frac{1}{2}\\\)

Cross multiply,

(r + 3)*2 = 1*8

2r + 6  = 8             {Subtract 6 from both sides }

       2r = 8 - 6

       2r = 2          {divide both sides by 2}

        r = 2/2

r = 1

Answer:

-6x+14 or 14-6x

Step-by-step explanation:

We are given the expression:

9-6x+5

We want to combine like terms.

Let's examine each term.

⇒ 9 : constant, no variable

⇒ -6x : has a variable, x

⇒ 5: constant, no variable.

There are 2 constants and 1 term with a variable. The 2 constants can be combined. Add 9 and 5.

-6x + (9+5)

-6x +14

or

14-6x

The expression 9-6x+5 can be simplified to -6x+14 or 14-6x

A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.

To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.

Let's calculate the sum of the digits in 1234:

1 + 2 + 3 + 4 = 10

The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.

To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.

The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.

1234 + 2 = 1236

we obtain the number 1236, which is divisible by 3.

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Answer:

$16.30

Step-by-step explanation:

So if you can buy 3 lollipops for $4.89, then you can by 1 for $1.63. Then 10 lollipops would be $16.30.  

It would cost $16.30 to buy 10 giant lollipops from the candy store.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

If you can get 3 giant lollipops for $4.89, the cost of each giant lollipop is:

4.89 ÷ 3

= $1.63

To buy 10 giant lollipops, you would need to pay:

10 x 1.63

= $16.30

Therefore,

It would cost $16.30 to buy 10 giant lollipops from the candy store.

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Answer:

its a trick answer for me

Answer:

=8to the 3rd power and =512

Step-by-step explanation:

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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Answer:

A) MP(q) = -3q² + 440q - 13

B) 146.64 units.

Step-by-step explanation:

The profit function is given by the revenue minus the cost function:

\(P(q) = R(q) - C(q)\\P(q) = -q^3+220q^2-500-13q\)

A) The Marginal profit function is the derivate of the profit function as a function of the quantity sold:

\(P(q) = -q^3+220q^2-500-13q\\MP(q) = \frac{dP(q)}{dq} \\MP(q)=-3q^2+440q-13\)

B) The value of "q" for which the marginal profit function is zero is the number of items (in hundreds) that maximizes profit:

\(MP(q)=0=-3q^2+440q-13\\q=\frac{-440\pm \sqrt{440^2-(4*(-3)*(-13))} }{-6}\\q'=146.64\\q'' = - 0.03\)

Therefore, the only reasonable answer is that 146.64 hundred units must be sold in order to maximize profit.

Answer:

36

Step-by-step explanation: you time the number 9*4 equal 36