Given the function g defined by the formula g(x) =x − 5/2x-5 find the following:

db/dt = 40/12 = 10/3 Feet per second, or approximately 3.33 feet per second. So the foot of the ladder is being pulled away from the wall at a rate of about 3.33 feet per second when it is 8 feet away from the wall and the top of the ladder is sliding down at 4 feet per second.

We can use the Pythagorean theorem to relate the length of the ladder, the distance of its foot from the wall, and the height it reaches on the wall:

\(a^2 + b^2 = c^2\)

where c is the length of the ladder, a is the distance of its foot from the wall, and b is the height it reaches on the wall. Differentiating with respect to time, we get:

2a da/dt + 2b db/dt = 2c dc/dt

We are interested in finding db/dt when a = 8 feet and dc/dt = -4 feet per second (negative because the top of the ladder is sliding down). We also know that c = 10 feet, so we can plug in these values and solve for db/dt:

2(8) da/dt + 2b db/dt = 2(10) (-4)

Simplifying:

16 da/dt + b db/dt = -40

We also know that when a = 8 feet and b = 6 feet (from the Pythagorean theorem), the ladder is at a height of 6 feet on the wall. Therefore, we can plug in these values and solve for da/dt:

8 da/dt + 6 db/dt = 0

Simplifying:

da/dt = -(3/4) db/dt

Now we can substitute this expression for da/dt in the first equation, and solve for db/dt:

2(8) (-(3/4) db/dt) + 2(6) db/dt = -40

Simplifying:

-12 db/dt = -40

for such more question on word problem

https://brainly.com/question/13818690

#SPJ11

Answer:

x = 45°

y = 90°

Step-by-step explanation:

    The 135° is on a line, so 180° - 135° = 45°

Since this is an isosceles triangle, x will be equal to 45° as well.

    The sum of a triangle's angles is 180°, so if we add them all together and subtract from 180° we will get our y.

180° - (45 + 45) = y

180° - 90° = y

90° = y

(a triangle can be both an isosceles and a right-triangle!)

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

y= mx+c

-4= -3/5(-5) + c

-4= -3/5 *-5+ c

-4=3+c

-4-3=c

-7=c

therefore the equation of the line is y=-3/5x-7

Step-by-step explanation:

the equation of a line is

y=mx +c

where y is the y coordinate

where m is the slope

where x is the x coordinate

where c is the y- intercept

Answer:

you leave the decimal point In the answer.

Answer:

Option A, \(3\frac{3}{8}\ in\)

Step-by-step explanation:

Step 1:  Remove the excess from the total

\(Total - Excess\)

\(19\frac{1}{8}\ in - 2\frac{1}{4}\ in\)

\(18\frac{9}{8}\ in - 2\frac{2}{8}\ in\)

\(16\frac{7}{8}\ in\)

Step 2:  Split the remaining into 5 pieces

\(\frac{16\frac{7}{8}\ in}{5\ pieces}\)

\(\frac{\frac{135}{8}\ in}{5\ pieces}\)

\(\frac{135\5}{8\ in}\)

\(\frac{27}{8\ in}\)

\(3\frac{3}{8}\ in\)

Answer:  Option A, \(3\frac{3}{8}\ in\)

Answer: g = w² - 14w + 49

\(w=7-\sqrt{g}\\\\=> \sqrt{g} =7-w \\\\<=>g=(7-w)^{2}=49-14w+w^{2}\)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

From the graph, the lines intersect at (3, 1) so that is the answer.

Answer:

$24

Step-by-step explanation:

Inversely proportional means that the two variables (price and weight in this case) will always have the same product. Therefore, we can write the following equation:

25 * x = 20 * 30 (where x is the price of a 25 oz. racquet)

25x = 600

x = $24

The probability that no one in the United States will be struck and killed by lightning tomorrow is approximately 0.835, or 83.5%.

To find the probability that no one in the United States will be struck and killed by lightning tomorrow, we can use the Poisson distribution, which models the number of rare events occurring in a fixed period of time, given the average rate of occurrence.

The Poisson distribution has the following probability mass function:

P(X = k) = (e^(-λ) * λ^k) / k!

where:

X is the random variable representing the number of events (in this case, the number of people struck and killed by lightning)

λ is the average rate of events per unit of time (in this case, the average number of people struck and killed by lightning per day)

We can use the data given in the problem to estimate the value of λ:

λ = (2457 deaths) / (36 years * 365 days/year) ≈ 0.18 deaths/day

Now we can use the Poisson distribution to find the probability that no one in the United States will be struck and killed by lightning tomorrow:

P(X = 0) = (e^(-0.18) * 0.18^0) / 0! ≈ 0.835

This means that there is a high likelihood that no one will be killed by lightning tomorrow, given the historical average rate of lightning deaths.

To learn more about probability click on,

https://brainly.com/question/30666048

#SPJ4

The relationship between the height of the pole and the shadow cast by the pole is a proportional relationship, from which the height of the pole can be calculated

The height of the pole is 11.\(\overline 6\) feet

A proportional relationship is one in which the ratio between the elements of an ordered pair is a constant.

The example values for the lengths of the shadows and Sam's height are as follows;

Let the length of the shadow cast by the pole = 3.5 feet

Let the shadow cast by Sam = 1.5 feet

Let Sam's height = 5 feet

Sam's height and the height of the pole and their shadows have proportional relationship.

The constant of proportionality is therefore;

\(K = \dfrac{1.5}{5} =\dfrac{3.5 }{Height \, of \, the \, pole}\)

Therefore;

Height of the pole = 5 × 3.5 ÷ 1.5 = 11.\(\overline 6\)

Learn more about proportional relationships in mathematics here:

https://brainly.com/question/28761566

#SPJ1

To compute the 99% confidence interval for the population mean, you need to determine the appropriate sample size to ensure that the sample mean does not deviate from the population mean by more than 1.3. The key terms involved in this process are the confidence interval, sample size, population mean, and sample mean.

The confidence interval represents the range within which the population parameter (in this case, the population mean) is likely to fall, given a certain level of confidence. A 99% confidence interval means that you are 99% confident that the true population mean falls within the specified range.

To calculate the required sample size, you will need to use the formula for the margin of error (E), which is E = (Zα/2 * σ) / √n, where Zα/2 is the critical value associated with the desired level of confidence (99%), σ is the population standard deviation, and n is the sample size.

Since you want the sample mean to not deviate from the population mean by more than 1.3, you will need to set E = 1.3 and solve for n. After finding the critical value for a 99% confidence interval (which is approximately 2.576) and assuming you know the population standard deviation, you can plug these values into the formula and solve for n.

By doing this, you will be able to determine the appropriate sample size to ensure that the 99% confidence interval for the population mean is within 1.3 units of the sample mean.

To learn more about confidence interval click here

brainly.com/question/22851322

#SPJ11

the answer will be 5,427 because we need to round the six and since 8 is greater that 5, we aproximate 6 to 7

The standard deviation of a set of values can be calculated using the formula:

σ = √((Σ(x - μ)²) / N)

Where: σ is the standard deviation Σ represents the sum x is each value in the set μ is the mean of the set N is the number of values in the set

Given the set of values (13.6, 5.9), we can calculate the standard deviation.

Step 1: Calculate the mean (μ) μ = (13.6 + 5.9) / 2 = 19.5 / 2 = 9.75

Step 2: Calculate the sum of squared differences from the mean Σ(x - μ)² = (13.6 - 9.75)² + (5.9 - 9.75)² = 3.85² + (-3.85)² = 14.8225 + 14.8225 = 29.645

Step 3: Calculate the standard deviation (σ) σ = √(29.645 / 2) ≈ √14.8225 ≈ 3.85

Therefore, the standard deviation of the set (13.6, 5.9) is approximately 3.85 (rounded to three significant figures).

To know more about standard deviation, visit

https://brainly.com/question/29115611

#SPJ11

There are two terms in the given expression 5xy²+ 35xy².

What is meant by term?

Terms comprise expressions. A term may be a constant, a variable, or a combination of variables and constants.

What is an example of a term?

It could be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase. Single-word examples: A single phrase is 3x.

There are two terms in the equation 5xyA ^2 + 35xyA^2 that is separated by an arithmetic operator +.

To learn more about term visit the link:

https://brainly.com/question/12786767

#SPJ4

Answer:

15°

Step-by-step explanation:

120° and 8x are vertically opposite angles, which are always equal.

=> 8x = 120°

=> x = 120/8

=> x = 15°

Each dot in a graph that is built when building a sampling distribution represents a sample mean.

The sample mean can be defined as the average of the values in a particular sample.

A sampling distribution is a theoretical distribution of the sample statistics that are derived from multiple samples of the same population.

The distribution demonstrates how the statistic varies across numerous samples.

In other words, a sampling distribution refers to the distribution of values derived from all possible samples with a given sample size that can be drawn from the population.

Suppose we are building a sampling distribution through a simulation.

In that case, we randomly draw numerous samples from the population and then calculate the sample mean of each sample.

The sample means are then used to build a distribution, with each dot in the graph representing a sample mean.

The resulting sampling distribution will be approximately normal when the sample size is large enough.

Learn more about sampling distribution here:

https://brainly.com/question/15713806

#SPJ11

The main difference in calculations for the independent samples t-test when the variances are equal and the variances are unequal is the method used to calculate the pooled variance, the t-value, and the degrees of freedom.

1. When variances are equal (also called pooled variance):
- Calculate the pooled variance using the formula:

\(Sp^2 = [(n1-1) × s1^2 + (n2-1) × s2^2] / (n1 + n2 - 2)\)
- Calculate the t-value using the formula:

\(t = (M1 - M2) / sqrt(Sp^2 × (1/n1 + 1/n2))\)
- Determine the degrees of freedom using the formula:

df = n1 + n2 - 2
2. When variances are unequal (also called Welch's t-test):
- Calculate the t-value using the formula:

\(t = (M1 - M2) / sqrt((s1^2 / n1) + (s2^2 / n2))\)
- Determine the degrees of freedom using the formula:

\(df = [(s1^2 / n1 + s2^2 / n2)^2] / [(s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1)]\)
In summary, the main difference in calculations for the independent samples t-test when the variances are equal and the variances are unequal is the method used to calculate the pooled variance, the t-value, and the degrees of freedom.

for such more question on t-test

https://brainly.com/question/6589776

#SPJ11

The test hypothesis for the 2010 U. S. Census is H0 = Oregon < Latino.

In math the term called hypothesis is defined as an idea that is suggested as the possible explanation for something but has not yet been found to be true or correct.

Here we know that in 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino.

And here we have also know that random sample of 853 adults in Oregon and 110 of the people surveyed were Hispanic or Latino.

Then the sample proportion is calculated as,

=> sample proportion=113/853=0.1325

And the value of Test statistic is,

=> z = (0.1325-0.117)/√(0.117*(1-0.117)/853)

=> z = 1.41

So, the hypothesis is written as,

=> H0 = Oregon < Latino.

To know more about Hypothesis here,

https://brainly.com/question/29576929

#SPJ4

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

Answer:

mean= 12

median= 10

mode= 10

Step-by-step explanation:

mean: add up all values, then divide by how many values you have(84/7=12)

median: when sorted, value in middle(See pic)

mode: value that appears most

The inequality is

\( - 6 \geqslant x \leqslant 3\)

And please shade at the points of -6 and 3 to indicate the greater or equal sign.

The 9 is the spacing from -6 and 3.

Welcome to Brainly! All the best!:)

Answer: D’ (3, -6), E’ (4, -2), F’ (5, -5)

Step-by-step explanation:

If it’s reflected across the x-axis, the y coordinates become negative. Then move each coordinate 2 units to the right.

(x, y) — (x + 2, -y)

D (1, 6) — D’ (3, -6)

E (2, 2) — E’ (4, -2)

F (3, 5) — F’ (5, -5)

a. A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as

f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3), b) Two examples of functions that belong to this family are: f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)

f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3) and the equation for the member of the family that passes through the point (-2,25) is:

f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x.

a) A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as the product of linear factors with those zeroes:

f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3)

where "a" is a constant that determines the overall scaling of the function.

b) Two examples of functions that belong to this family are:

f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)

f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3)

Note that these functions differ only in the value of the constant "a".

c) To find the value of "a" that makes the graph of the function pass through the point (-2,25), we can substitute x = -2 and y = 25 into the equation for f(x):

25 = a(-2 + 5/2)(-2 + 1)(-2 - 7/2)(-2 - 3)

Simplifying this expression:

25 = a(5/2)(-1)(-11/2)(-5)

25 = a(6875/4)

a = 100/6875 = 4/275

Therefore, the equation for the member of the family that passes through the point (-2,25) is:

f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)

To learn more about quadratic equation from the given link:

brainly.com/question/30098550

#SPJ1

Answer:

0.5625

Step-by-step explanation:

3/4 as a decimal is 0.75

0.75×0.75=0.5625

Answer:

0.75 x 0.75 = 0.5625

Step-by-step explanation:

3/4=.75

The characteristics of the quadratic function f(x) = -0.25(x + 2)(x + 8) are given as follows:

The x-intercepts of a function are the values of x for which the function is zero, that is:

f(x) = 0.

Hence:

-0.25(x + 2)(x + 8) = 0.

The roots are already factored, as follows:

In expanded form, the function is:

f(x) = -0.25(x + 2)(x + 8)

f(x) = -0.25(x² + 10x + 16)

f(x) = -0.25x² -2.5x - 4

The coefficients are:

a = -0.25, b = -2.5, c = -4.

The x-coordinate of the vertex is given as follows:

\(x_v = -\frac{b}{2a} = -\frac{-2.5}{4(-0.25)} = -2.5\)

Which is also the axis of symmetry of the quadratic equation.

The y-coordinate of the vertex is:

\(y_v = -\frac{b^2 - 4ac}{4a} = -\frac{(-2.5)^2 - 4(-0.25)(-4)}{4(-0.25)} = -2.25\)

Hence the vertex is:

(-2.5, -2.25).

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ1

Answer:

A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, where n is the exponent and is greater than 0; for example, 106 is written 1,000,000.

Step-by-step explanation:

Answer:

Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.

Step-by-step explanation:

Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.

Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10 sec as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.

The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

To know more about t-value follow

https://brainly.com/question/22848147

#SPJ2