O EXPONENTAL AND LOGARITHMIC FUNCTIONS
Finding the initial or final amount in a word problem on...
An initial amount of money is placed in an account at an interest rate of 2% per year, compounded continuously. After two years, there is $1269.79 in the
account. Find the initial amount placed in the account. Round your answer to the nearest cent.

Answer:

gradient = 2

line: y = 2x - 4

Step-by-step explanation:

Find the slope from the slope intercept formula

y = mx + b

b is the y intercept

b = -4 and the point is (0,-4)

So far the equation looks like this.

y = mx - 4

Use the other intercept (x intercept) to find m

x = 2

y = 0

0 = m*2 - 4                Add 4 to both sides

4 = 2m                      Divide by 2

4/2 = m

m = 2

So the gradient or slope is 2

Answer:

7.07 (3 significant figures)

Step-by-step explanation:

the distance between the two points on the x axis is 5 and the distance between the two point son the y axis is 5. thus by using pythagerous theorem you are able to get the hypotenuse which is the distance between the two points which in this case is 7.07 when rounded to 3 significant figures. not sure if im correct but i hope it helps

Answer:

Y = 2/3X + 4/3

Step-by-step explanation:

(1,2) (4,4)

M = 2/3

Y = 2/3X + b

4 = 8/3 + b

12 = 8 + 3b

4 = 3b

B = 4/3

Y = 2/3X + 4/3

Answer:

5

Step-by-step explanation:

Given :

To Find :

Solution:

Put on the respective values ,

⇒ 4b - y = 4 × 3 - 7

⇒ 4b - y = 12 - 7

⇒ 4b - y = 5

Hence the required answer is 5 .

Answer: 5

Step-by-step explanation:

We can plug in the numbers for variables. So, our new equation would becomes 4x3-7. We first evaluate 4x3=12. Then, 12-7=5. Hence, your answer is 5.

Answer:

f(6) = 3

f'(6) = 1/6

Step-by-step explanation:

Remember that for a function f(x), we define f'(x) as the slope of the tangent line to the point (x, f(x))

We know that:

y = f(x) passes through the point (6, 3)

Then we already know that:

f(6) = 3.

Now we also know that the tangent at this point, also passes through (0, 2)

Remember that a line can be written as:

y = a*x + b

Where in this case, a = f'(6)

so we just want to find the slope of this line.

Remember that for a line that passes through (x₁, y₁) and (x₂, y₂) the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

And we know that the tangent line passes through the points (0, 2) and (6, 3)

Then the slope is:

a = (3 - 2)/(6 - 0)  = 1/6

Then we have:

a =  f'(6)  =1/6

Answer:

A

Step-by-step explanation:

small dog eats 3/4 cup each day

large dog eats 1 cup each day

~after 1 week (x7)~

small dog = 5.25 cups

large dog = 7 cups

(7-5.25=1.75)

= therefore 1 and 3/4 cups

Answer:

You would expect 807 babies  to weigh between 3 and 6 pounds.

Step-by-step explanation:

We are given that

Mean,[tex]\mu=5.4[/tex]pounds

Standard deviation,[tex]\sigma=1.8[/tex]pounds

n=1500

We have to find how  many would you expect to weigh between 3 and 6 pounds.

The weights for newborn babies is approximately normally distributed.

Now,

[tex]P(3<x<6)=P(\frac{3-5.4}{1.8}<\frac{x-\mu}{\sigma}<\frac{6-5.4}{1.8})[/tex]

[tex]=P(-1.33<Z<0.33)[/tex]

[tex]P(3<x<6)=P(Z<0.33)-P(Z<-1.33)[/tex]

[tex]P(3<x<6)=0.62930-0.09176[/tex]

[tex]P(3<x<6)=0.538[/tex]

Number of newborn  babies expect to weigh between 3 and 6 pounds

=[tex]1500\times 0.538=807[/tex]

10x-5

Answer:

5(2x-1)

5*2x 5*-1

10x-5

Hey there!

5(2x - 1)

= 5(2x) + 5(-1)

= 10x - 5

Therefore, your answer should be: 5x - 5

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).

Step-by-step explanation:

We have the standard deviation for the differences, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 8 - 1 = 7

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8946

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.8946\frac{15.9274}{\sqrt{8}} = 10.67[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 9.582 - 10.67 = -1.088

The upper end of the interval is the sample mean added to M. So it is 9.582 + 10.67 = 20.252

The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).

Answer:

CI  95 %  =  (  28.92  ;  41.08 )

Step-by-step explanation:

Sample Information:

sample size    n  =  30

sample mean  =  35 %

sample standard deviation   s = 17

To construct a CI  95 %

significance level is    α  = 5 %   α = 0.05      α/2  =  0.025

z critical for α/2 from z- table is :   z (c) = 1.96

CI  95 %  =  (  x  ±  z(c) * s/√n )

CI  95 %  =  (  35 ± 1.96 * 17/√30 )

CI  95 %  =  (  35 ±  6.08 )

CI  95 %  =  (  28.92  ;  41.08 )

Answer:

it is (4,120)

hope this helps you

Answer: (3, -3)

Step-by-step explanation:

You substitute each point into the function and see if it fits:

(-2, -1) ⇒ -2(-2) + 3 = 4 + 3 = 7 ≠ -1

(3, -3) ⇒ -2(3) + 3 = -6 + 3 = -3

(3, 3) ⇒ -2(3) + 3 = -6 + 3 = -3 ≠ 3

(-3, -9) ⇒ -2(-3) + 3 = 6 + 3 = 9 ≠ -9

Answer:

b

Step-by-step explanation:

im doing it on edge right now

Step-by-step explanation:

here is the answer. Feel free to ask for more.

Answer:

The answer is b

Step-by-step explanation:

Step-by-step explanation:

hope it helps you..........

Answer:

nine 9 classes in the histogram

Answer:

0.1587

Step-by-step explanation:

Applying,

P(μ>40) = P(μ-(x-μ)/σ)............. Equation 1

Where P(μ>40) =  probability of the age of the random subscriber more than 40 years   μ = mean, σ = standard deviation, x = random subscriber

From the question,

Given: μ = 35 years, σ = 5 years, x = 40 years.

Therefore,

P(μ>40) = P(35-(40-35)/5) = P(35-(5/5)

P(μ>40) = 1-φ(1)

From the norminal probabilty table,

P(μ>40) = 1-0.8413

P(μ>40) = 0.1587

9514 1404 393

Answer:

  B  2/6

Step-by-step explanation:

2 of the 6 possible outcomes are ones that are of interest. A "fair" die means the mutually-exclusive outcomes have equal probability, so ...

  P(4 or 5) = P(4) +P(5) = 1/6 + 1/6 = 2/6

Answer:

Just A and C

Step-by-step explanation:

B doesn't count because you would not be looking at the 9. Only the 4.

You only look at one number to the right.

Answer:

A and C are correct, but not B

Step-by-step explanation:

When you round, you only look at the number behind the place you are rounding.

6.04 doesn't round to 6.1, so that is not correct

Answer:

?

Step-by-step explanation:

Answer:

26.59 minutes

Step-by-step explanation:

Let's say the time needed to do the driveway combined is x. Sue does y parts of the driveway, and Tom does z parts of the driveway. Combined, y + z = 100% = 1, as they finish the whole driveway.

Next, Tom will take 45 * z minutes to do his part of the driveway. For example, if he did 50% = 0.5 of the driveway, he would take 45 * 0.5 = 22.5 minutes to do it. Similarly, Sue will take 65 *y minutes to do her part of the driveway. Since they will finish at the same time, we can say

45 * z = 65 * y

y + z = 1

Therefore, if we subtract y from both sides of the second equation, we have

z = 1-y

We can then plug 1-y in for z in the first equation to get

45 * (1-y) = 65 * y

45 - 45*y = 65*y

add both sides by 45 * y to separate the y values and their coefficients

45 = 110 * y

divide both sides by 110 to find y

y = 45/110 = 0.409

Use 1-y=z to get z = 1-0.409 = 0.59

Therefore, 45*z = 26.59 = 65*y

Answer:

Option A. -1/20x

Step-by-step explanation:

[tex] \frac{5x + 1}{5x} - \frac{4x + 1}{4x} [/tex]

[tex] = \frac{20x + 4x - 20x - 5x}{20x^{2} } [/tex]

[tex] = \frac{ - x}{20x^{2} } [/tex]

[tex] - \frac{1}{20x} [/tex]

Answered by GAUTHMATH

Answer:

The answer is true

Step-by-step explanation:

Answer:

0.260

Step-by-step explanation:

According to the Question,

And, it found that ​P(D)=0.740​, where D is directly in person.

⇒P(D) is the probability flirting of directly in person.

⇒P( D ) represents the probability of flirting other than in person.  

P(D)=0.740    &   P( D )=1 - P(D)

P( D ) = 1 - 0.740.

P( D ) = 0.260

Hence the value of Upper P left parenthesis Upper D overbar right parenthesis is 0.260.

Answer:

I think it would be 3/4

Step-by-step explanation:

Answer:

happy person in the village

Answer:

128 for 4.99

64 for 2.99 times 2 is more than 4.99.

12 oz. for 0.99 is also more than 4.99.

Answer:

The critical value that should be used in constructing the confidence interval is T = 1.316.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 26 - 1 = 25

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.8}{2} = 0.9[/tex]. So we have T = 1.316

The critical value that should be used in constructing the confidence interval is T = 1.316.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.059 = 2.741 pounds

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

Answer:

y=(2/3)x+10

Hope it helps!

My graph isn't really clear

The slope-intercept of the line that passes through the point (-9, 4) and has a slope of 2/3 will be y = (2/3)x + 10.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A line is given as y = mx + c

Here m is the slope,

Put m = 2/3 and  (-9, 4)

4 = (2/3)(-9) + c

c = 10

Thus equation will be y = (2/3)x + 10.

Hence "Y = (2/3)x + 10 is the slope-intercept of the line passing through the point (-9, 4), which has a slope of 2/3".

For more about the linear function,

brainly.com/question/21107621

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