Jana paid an initial fee of $75 to join a fitness gym. She pays $15 per month for her membership. How many months did she have the membership if she spent a total of $255.

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The student must pay $123.75 as the interest amount and the future value of the loan is $2123.75.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

(a) Given,

Principal amount of the loan, P = $2000

Time, t = 9 months = 0.75 year

Rate of interest, r = 8.25% = 0.0825

Amount of interest = P × r × t

                               = 2000 × 0.0825 × 0.75

                               = $123.75

(b) Future value of the loan = $2000 + $123.75 = $2123.75

Hence the interest amount is $123.75 and the future amount of the loan is $2123.75.

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ANSWER:

50 miles per hour

450 miles

865 miles

STEP-BY-STEP EXPLANATION:

We can calculate the rate with the help of the points we have, just like this:

Therefore, the rate is 50 miles per hour

We know the rate, therefore, after 9 hours, the distance would be:

Therefore, every 9 hours, a total distance of 450 miles is traveled.

We know that they are 415 miles from Seattle after 8 hours, so the total distance can be calculated as follows:

Which means that after 17 hours, it is 865 miles away.

Problem 1

y = tan(3x+4)

f(x) = tan(3x+4)

f ' (x) = 3sec^2(3x+4) .... apply derivative chain rule

dy/dx = f ' (x)

dy = f ' (x) * dx

dy = ( 3sec^2(3x+4) ) * dx

Now plug in x = 5 and dx = 0.3

dy = ( 3sec^2(3*5+4) ) * 0.3

dy = 0.920681 which is approximate

Make sure your calculator is in radian mode.  Calculus textbooks will be in radian mode for the special sine limit definition \(\lim_{x\to0}\frac{\sin x}{x} = 1\) to be true.

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Problem 2

We'll have the same derivative function and same x value. The only difference is that dx = 0.6 this time.

dy = f ' (x) * dx

dy = ( 3sec^2(3*5+4) ) * 0.6

dy = 1.84136 approximately

Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

Answer:

f(1) = -7

Step-by-step explanation:

Step 1: Define

f(x) = -x² + x - 7

f(1) = x = 1

Step 2: Substitute and Evaluate

f(1) = -(1)² + 1 - 7

f(1) = -1 + 1 - 7

f(1) = -7

Answer:

88 is a solution to 1/8 x =11, since a solution means that x is equal to that number, so in this scenario, x=88. When substituted(88*0.125), the same answer, 11, is obtained.

Step-by-step explanation:

Answer:

20months

Step-by-step explanation:

$580/ $29 = 20months

Answer: 2.41666666667

Step-by-step explanation: .

The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.

To determine the time interval of the water in the pool the following is carried out.

At 0 hour, the water is at the level of = 40 gallons

At 1 hour, the water decreased to = 25 gallons.

At 2 hours, the water decreased to = 10 gallons.

The water remained at a constant level till 4 hours.

Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.

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Answer:

Step-by-step explanation:

A

The percentage of drivers who are at least 45 is 62%

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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Answer:

2/3

this question doesn't make sense

Answer:

a) [-9,8)

b) [-5,5]

c) (-4,0), (1,6)

d) [-9,-4), (6,8)

e) [0,1]

f) just the y-value: 5;  as a point: (-8,5)

g) just the y-value: -5;  as a point: (-4,-5)

Step-by-step explanation:

a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).

b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.

For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.

c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?

d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?

e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?

f) Look for the highest non-infinity point on the graph

g) Look for the lowest non-infinity point on the graph

We are given the following inequality:

First, we will apply the distributive property on the term on the right side of the inequality:

Now we will subtract 5x to both sides:

Now we will subtract 2 to both sides:

Dividing both sides by -2, since we are dividing by a negative number we need to invert the direction of the inequality sign:

Therefore, the solution is x >= 11

Answer:

The distance between -6 and 7 is 13 units.

Step-by-step explanation:

I hope I helped! :)

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer:

No Solution

Step-by-step explanation:

if one side is 4, another side -8z and +8z cancels, left -7

4 ≠ -7

Answer:

statement is false

Step-by-step explanation:

See image below:)

Answer:

See Below

Step-by-step explanation:

The probability of the combined event that the next six days are all sunny is 1/4096

From the question, we have the following parameters that can be used in our computation:

Probability that it is sunny = 1/4

Probability that it is cloudy = 3/4

Number of days = 6

The probability for all six days, it is sunny is represented as

Probability = Probability that it is sunny^Number of days

Substitute the known values in the above equation, so, we have the following representation

Probability = (1/4)⁶

Express as decimal

Probability = (0.25)⁶

Evaluate the exponent

Probability = 1/4096

Hence, the probability is 1/4096

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Answer:

Step-by-step explanation:

Total amount of money = cost of 13 manicures + tips for 13 manicures

        = 13x ( ∵ Given cost of 1 manicure = x) + 52 ( given she get 52 in tips)

= 13x + 52

Answer: 2^3 x 3 x 5^2

Step-by-step explanation:

All we have to do is divide 600

alright

Chopping off the two zeros:

6x100

Factoring 6:

2x3x100

Factoring 100:

2x3x10x10:

Factoring both 10s:

2x3x2x5x2x5

2^3 x 3 x 5^2

Therefore, we have factored 600 into 2^3 x 3 x 5^2

Answer:

x = -1

Step-by-step explanation:

6+4 = 10

14-10 = 4

2x + 6 = 4

2x (-2) = -2

-2 + 6 = 4

Answer: 22/3 I think

sorry if it’s wrong

Answer:

7 1/3

i hope this helps you can do it

Answer:

Rectangle with l = 13 and h = 9

Step-by-step explanation:

To find the area of the rhombus, you multiply base and length.

The base here is 13 and the length is 9.

Multiplying 13 x 9 = 117.

The area of a square is side x side.

So, 11 x 11 = 121.

The area of the rectangle is length x base.

So 13 x 9 = 117.

We see the rhombus and rectangle have the same area.

Answer: C

Step-by-step explanation:

I just took the quiz and I got it right

Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit

Modulus of the complex number is the distance of the point on the argand plane representing the complex number z from the origin

Given,

Complex number z divides by a second complex number w

To divide a complex number a complex number then multiply the conjugate with the numerator and the denominator of the complex fraction

From the given statements Scale of z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w

Hence, Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

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Complete Question

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is  7.5

Answer:

The minimum sample size is  \(n =97\)

Step-by-step explanation:

From the question  we are told that

 The margin of error is  \(E = 1.25\)

   The  standard deviation is  \(s = 7.5\)

Given that the confidence level is  90% then the level of significance is mathematically represented as

             \(\alpha = 100 - 90\)  

             \(\alpha =10\%\)  

             \(\alpha =0.10\)

Next we obtain the critical value of \(\frac{\alpha }{2}\) from the normal distribution table  

    The value is  \(Z_{\frac{ \alpha }{2} } = 1.645\)

   The  minimum sample size is mathematically evaluated as

         \(n = \frac{Z_{\frac{\alpha }{2} * s^2 }}{E^2 }\)

=>        \(n = \frac{1.645^2 * 7.5^2 }{1.25^2 }\)

=>        \(n =97\)

Answer:

The equation that represents the situation is: 30w = 150.

Step-by-step explanation:

We can set up an equation to find the value of w:

30w = 150

To solve for w, we can divide both sides of the equation by 30:

w = 150 / 30

w = 5

So April walks dogs for 5 weeks to earn $150.