A 14ft ladder leans against the side of a house the angle of elevation of the ladder is 74 how high is the top of the ladder from the ground round to the nearest tenth

In exponential function f(x), the ratio of outputs for any two inputs that are one value apart is

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,

x: -3, -2, -1, 0, 1, 2, 3

f(x): 1/256, 1/64, 1/16, 1/4, 1, 4, 16

the ratio of outputs for any two inputs that are one value apart

= 1/64 / 1/256

= 4

Therefore the ratio is 4

Learn more about exponential function here:

https://brainly.com/question/29716012

#SPJ1

Answer:

,.........................................

the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. pastels salary in dollars for a week when his sales were 0$ is $700.

Pastels weekly salary includes base pay plus commission of his sales.

the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars.

find pastels salary in dollars for a week when his sales were 0$

the model is given as

s=700+0.07c

let us solve for c, the sales made

s =700 +0.07c given sales is 0$

then s=700

Hence , the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. pastels salary in dollars for a week when his sales were 0$ is $700.

learn more about of equation here

https://brainly.com/question/19297414

#SPJ4

The 4th degree Taylor polynomial for \( \ln(x) \) centered at \( x = 1 \) is:

\[ T_4(x) = (x - 1) - \frac{1}{2}(x - 1)^2 + \frac{1}{3}(x - 1)^3 - \frac{1}{4}(x - 1)^4 \]

The 4th degree Taylor polynomial for \( \ln(x) \) centered at \( x = 1 \) can be found by taking the derivatives of \( \ln(x) \) and evaluating them at \( x = 1 \). The general form of the Taylor polynomial is:

\[ T_n(x) = f(c) + f'(c)(x - c) + \frac{f''(c)}{2!}(x - c)^2 + \frac{f'''(c)}{3!}(x - c)^3 + \frac{f^{(4)}(c)}{4!}(x - c)^4 \]

where \( c \) is the center of the approximation. In this case, \( c = 1 \). Let's go through the steps to find the 4th degree Taylor polynomial:

Step 1: Find the derivatives of \( \ln(x) \).

\[ f(x) = \ln(x) \]

\[ f'(x) = \frac{1}{x} \]

\[ f''(x) = -\frac{1}{x^2} \]

\[ f'''(x) = \frac{2}{x^3} \]

\[ f^{(4)}(x) = -\frac{6}{x^4} \]

Step 2: Evaluate the derivatives at \( x = 1 \).

\[ f(1) = \ln(1) = 0 \]

\[ f'(1) = \frac{1}{1} = 1 \]

\[ f''(1) = -\frac{1}{1^2} = -1 \]

\[ f'''(1) = \frac{2}{1^3} = 2 \]

\[ f^{(4)}(1) = -\frac{6}{1^4} = -6 \]

Step 3: Plug the values into the general form of the Taylor polynomial.

\[ T_4(x) = 0 + 1(x - 1) + \frac{-1}{2!}(x - 1)^2 + \frac{2}{3!}(x - 1)^3 + \frac{-6}{4!}(x - 1)^4 \]

Simplifying, we get:

\[ T_4(x) = (x - 1) - \frac{1}{2}(x - 1)^2 + \frac{1}{3}(x - 1)^3 - \frac{1}{4}(x - 1)^4 \]

Therefore, the 4th degree Taylor polynomial for \( \ln(x) \) centered at \( x = 1 \) is:

\[ T_4(x) = (x - 1) - \frac{1}{2}(x - 1)^2 + \frac{1}{3}(x - 1)^3 - \frac{1}{4}(x - 1)^4 \]

This polynomial provides an approximation of \( \ln(x) \) near \( x = 1 \) up to the 4th degree term.

To learn more about 4th degree Taylor polynomial click here:

brainly.com/question/32769264

#SPJ11

Answer:

72m

Step-by-step explanation:

since 5cm is 6m, just take 5 and make it 6, so 10cm is 12m and 5cm is 6m

multiply, and you get the answer

If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to widen.

This is because the standard deviation is a measure of the spread of the data, so if it increases, the data points are more spread out from the mean. As a result, the range of values that could reasonably contain the true population parameter (i.e., the confidence interval) needs to be wider to account for the increased variability in the sample.
If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to become wider.
When standard deviation increases, it indicates more variability in the data. As a result, the confidence interval, which is a range of values that estimates the true population parameter with a certain level of confidence, needs to be wider to account for the increased variability. This ensures that the true population parameter is still captured within the interval with the same level of confidence.

Visit here to learn more about standard deviation:

brainly.com/question/23907081

#SPJ11

Hi! The answer is going for be D (400)

Step-by-step explanation:

Out of 100 women, 8 were married 2 or more times which is 8% or 0.08

So out of 5000 women, the number of women married 2 or more times is: 0.08*5000 = 400

x/5000 = 8/100

x/50=8/1

x=400

Hope this helps! Have a good day!

The statement 2(1 / 2 x - 5), when x = 20 is justified by the property of substitution.

Substitution property in mathematics is a property that helps in substituting the value of a variable into an algebraic expression to solve a given problem.

Therefore, by substituting the value of x in the algebraic expression, the expression will be solved.

Hence,

2(1 / 2 x - 5) , when x = 20

Therefore,

2(1 / 2 (20) - 5)

2(10 - 5)

2(5) = 10

Hence, the property is substitution property.  

learn more on expression here: https://brainly.com/question/5217895

#SPJ1

The measurements of <a is 105^o, and <b is 75^o.

Two or more angles are said to be supplementary if their measures add up to 180^o.

In the given diagram, we have;

a. To find the measure of <a;

m<a + 40 + 35 = 180

m<a + 75 = 180

m<a = 180 - 75

       = 105

m<a = 105^o

b. To find the measure of <b;

m<b + m<a = 180

m<b + 105 = 180

m<b = 180 - 105

       = 75

m<b = 75^o

Learn more about supplementary angles at https://brainly.com/question/26760105

#SPJ1

Answer:

use google  

Step-by-step explanation:

Let the random variable p represent a randomly selected prize amount the expected value of p is $3.90  by using probability.

Prize                $1          $5            $10            $20              $50

Probability     0.60      0.30         0.05           0.04              0.01

It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.

The expected value is defined as the the sum of each outcome is multiplied by its probability.

p=x1p1+x2p2+x3p3+x4p4

p=1.0.60+5.0.30+10.0.05+20.0.04

p=3.90

Therefore, the correct option is A, i.e. $ 3.90 is the expected value of P.

Three Types of Probability

Classical: (equally probable outcomes) Let S=sample space (set of all possible distinct outcomes).

Relative Frequency Definition.

Subjective Probability.

Learn more about probability here:-

https://brainly.com/question/11234923

#SPJ4

Answer:

There is no Shape

Step-by-step explanation:

Give more information

Answer:

Option 1 and 5 will be your answer :)

Step-by-step explanation:

Let the equation representing number of sold is,

y - y' = m(x - x')

Where m = number of condo sold per month  

(x', y') is a point from the given table,

Slope of line passing through two points  and  =

Slope of the passing through (1, 8) and (0, 11) will be,

m =  = -3

Therefore, equation of the line passing through (3, 2) and slope (-3),

y - 2 = (-3)(x - 3)

y - 2 = -3(x - 3)

Similarly, equation of the line passing through (0, 1) and slope (-3),

y - 11 = -3(x - 0)

Therefore, Option (1) and (5) will be the answer.

Answer:

not 24 i got an 80 its not 24 though

Step-by-step explanation:

i dont know  how this helps but there you go

We are given that the inside diameter of a piston ring is a random variable with mean value 10 cm and standard deviation 0.07 cm.

We are asked to find the sampling distribution of the sample mean diameter for two different random samples of n=16 and n=64 piston rings, respectively, and to calculate the standard deviation of each sampling distribution.

The sampling distribution of the sample mean diameter is the distribution of all possible sample means that could be obtained from a given sample size n.

The central limit theorem tells us that for large enough sample sizes (typically n ≥ 30), the sampling distribution of the sample mean is approximately normal, regardless of the shape of the underlying population distribution.

The mean of the sampling distribution of the sample mean is equal to the population mean, and the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size.

For the first random sample of n=16 piston rings, the center of the sampling distribution of the sample mean diameter is still 10 cm, as this is the population mean.

However, the standard deviation of the sampling distribution is equal to the population standard deviation of 0.07 cm divided by the square root of 16, which is 0.0175 cm. Therefore, the standard deviation of the sampling distribution of the sample mean diameter for the first random sample is 0.0175 cm.

For the second random sample of n=64 piston rings, the center of the sampling distribution of the sample mean diameter is still 10 cm, but the standard deviation of the sampling distribution is equal to the population standard deviation of 0.07 cm divided by the square root of 64, which is 0.00875 cm.

Therefore, the standard deviation of the sampling distribution of the sample mean diameter for the second random sample is 0.00875 cm.

Finally, we are asked which of the two random samples is more likely to have a sample mean diameter within 0.01 cm of 10 cm. Since the standard deviation of the sampling distribution of the sample mean decreases as the sample size increases, the second random sample of n=64 piston rings is more likely to have a sample mean diameter within 0.01 cm of 10 cm.

This is because the decreased variability of the sampling distribution means that the sample means are more tightly clustered around the population mean of 10 cm. Therefore, we can conclude that the second random sample is more precise than the first random sample.

In statistics, a random sample is a subset of a larger population that is selected in such a way that each member of the population has an equal chance of being included in the sample.

Random sampling is a crucial tool for drawing conclusions about a population based on a smaller subset of data. In this problem, we will explore the sampling distribution of the sample mean for two different random samples of piston rings.

To know mare about random sample refer here:

https://brainly.com/question/29852583#

#SPJ11

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 7}(x-\stackrel{x_1}{8}) \\\\\\ y-6=7x-56\implies {\Large \begin{array}{llll} y=7x-50 \end{array}}\)

The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

for similar questions on sandbox.

https://brainly.com/question/31290675

#SPJ8

In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.

The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.

Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.

Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.

By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.

To learn more about economy click here: brainly.com/question/30131108

#SPJ11

Given

One fourth as a decimal value is

To determine how much 3/4 is equivalent to, multiply 0.25 by 3

add the decimal value to 4

The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer:

AAS

Step-by-step explanation:

The given expression 7x - y = -9 in the slope intercept form can be represented as y = 7x + 9.

The expression given to us is -

7x - y = -9

We have to represent this in the slope intercept form.

The slope intercept form can be represented as -

y = mx + c

where, y = y coordinate of the line

           m = slope of the line

            x = x coordinate of the line

            c = y intercept of the line

Thus, representing the given expression in the slope intercept form, we have

7x - y = -9

=> -y = -7x - 9

=> y = 7x + 9

Thus, the given expression in the slope intercept form can be represented as y = 7x + 9.

To learn more about slope intercept form visit https://brainly.com/question/9682526

#SPJ1

Answer:

A

Step-by-step explanation:

Group like-terms, that is move the numbers to one side of the sign.

Then, divide both sides by 2

Answer:

each member's lunch costs $3.62

Step-by-step explanation:

$209.96 is the total cost of all the members' lunches.  To find the price of 1 lunch, divide 209.96 by 58. You will get 3.62.

Answer:

A- 200+25x

B- 200+25×4=300

Continued for question B: The input of 4 into "x" indicates how many cans of paint you have bought

Step-by-step explanation:

The total number of hours Josh worked during the week is 44.7 hours.

We first need to calculate his regular pay by dividing his weekly gross earnings by his hourly rate:

$487.29 / $10.95 = 44.7 hours

Since the company pays time-and-a-half for any hours worked exceeding 40 in one week, we need to determine if Josh worked more than 40 hours during the week. If he did, we'll calculate his overtime pay by multiplying his regular pay by 1.5.

If Josh worked 44.7 hours, then he worked 44.7 - 40 = 4.7 hours of overtime.

His overtime pay would be 4.7 hours * $10.95 * 1.5 = $81.48

His regular pay would be 40 hours * $10.95 = $438.00

So his total weekly pay would be $438.00 + $81.48 = $519.48

The total number of hours Josh worked during the week is 44.7 hours.

Learn more about multiplying here: brainly.com/question/1135170

#SPJ1

Answer:

x-intercept = (3/4,0)

y'intercept = (0,-3)

Step-by-step explanation:

Not sure what conversion you need but here are the intercepts

Answer:

a = 18.8

Step-by-step explanation:

With it being a right angle, you can use the pythagorean theorem equation.

\(a^{2} + b^{2} =c^{2} \\a^{2} + 18^{2} =26^{2} \\a^{2} +324 = 676\\a^{2} = 676 - 324 \\a^{2} = 352\\a = \sqrt{352} \\a = 18.76 = 18.8\)