A person uses a screwdriver to turn a screw and insert it into a piece of wood. The person applies a force of 20 newtons to the screwdriver and turns the handle of the screwdriver a total distance of 0. 5 meter. How would these numbers be different with a hammer and a nail instead of a screwdriver and a screw

Answer:

\(x =3\) or \(x = 7\)

Step-by-step explanation:

Given

\(x^2 - 10x = -21\)

Required

Solve by factoring & quadratic formula

By Factoring:

\(x^2 - 10x = -21\)

Equate to 0

\(x^2 - 10x +21 = 0\)

Expand:

\(x^2 - 7x -3x+21 = 0\)

Factorize:

\(x(x-7)-3(x-7) = 0\)

\((x-3)(x-7) = 0\)

\(x -3 = 0\) or \(x - 7 = 0\)

\(x =3\) or \(x = 7\)

By quadratic

\(x^2 - 10x = -21\)

Equate to 0

\(x^2 - 10x +21 = 0\)

For

\(ax^2 + bx + c = 0\)

x is solved using:

\(x = \frac{-b\±\sqrt{b^2-4ac}}{2a}\)

where

\(a = 1\); \(b = -10\); \(c = 21\)

So:

\(x = \frac{-(-10)\±\sqrt{(-10)^2-4*1*21}}{2*1}\)

\(x = \frac{10\±\sqrt{100-84}}{2}\)

\(x = \frac{10\±\sqrt{16}}{2}\)

\(x = \frac{10\±4}{2}\)

Split

\(x = \frac{10+4}{2}\) or \(x = \frac{10-4}{2}\)

\(x = \frac{14}{2}\) or \(x = \frac{6}{2}\)

\(x = 7\) or \(x =3\)

Answer:

ML=8.8

sin(66)= 8/x

LK=3.6

tan(66)= 8/x

The dimensions of the room will be 12m x 6m.

So, now calculate the dimensions of the room as follows:

Solve as shown:

Therefore, 12m x 6m will be the dimensions of the room.

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Primarily, horizontal lines mean zero slope. Therefore the equation is y= 3 because you are only left with the y-intercept at this point. The rate of change is another way of saying slope. Function 2's slope is 5 and function 1's slope is 0. Therefore, the rate of change of function 2 is greater than the rate of change of function 1 by 5.  

5 is the answer.

hope this helps :)

Approximate an x-value in which the quadratic function exceeds the exponential function, we need to graph both functions and find the intersection point.

To graph the functions, we can plot points on a graph or use a graphing calculator. The graph shows that the exponential function grows faster than the quadratic function at first, but eventually, the quadratic function surpasses the exponential function. We can find the intersection point by setting the two equations equal to each other and solving for x:

4x = 7x^2 + 4x - 2

0 = 7x^2 - 2

x = ±sqrt(2/7)

The positive value of x, approximately 0.53, is the x-value in which the quadratic function exceeds the exponential function. Therefore, at x > 0.53, the quadratic function will be greater than the exponential function.

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Answer: The dot over a number signifies that it is a repeater which would go on for ever, as when we endeavor to describe 1/3 decimally as 0.33333 . . . . (etc) With a series of numbers we place the dot over the first and last, as with 0.97979797979 . . . (etc) The remarkable feature being that a proper fraction divided by 9s e.g. 46/99 is exactly equal to the numerator with the repeater sign followed by the decimal.

Step-by-step explanation: Hope This Helps, Have A Nice Day.

Answer:

\(a_n=100 \left(\dfrac15\right)^{n-1}\)

Step-by-step explanation:

General equation of geometric sequence:  \(a_n=ar^{n-1}\)

Given:

\(\implies a_1=a=100\)

\(\implies a_2=100 \cdot r=20\)

\(\implies a_3=100 \cdot r^2=4\)

Common ratio:

\(r=\dfrac{a_3}{a_2}=\dfrac{4}{20}=\dfrac15\)

Therefore:

\(a_n=100 \left(\dfrac15\right)^{n-1}\)

a) The average selling price in Bloomington is $301,596.27.

b) The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively.

c) There are 98 houses made primarily of brick and 102 not.

d) There is a positive moderate relationship between selling price and square footage of houses in Bloomington.

e) On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

The descriptive analysis in Bloomington has given the following insights: The average selling price in Bloomington is $301,596.27. The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively. There are 98 houses made primarily of brick and 102 not. There is a positive moderate relationship between selling price and square footage of houses in Bloomington. On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

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Answer:yes, additional training is necessary because if the employee does not have training they will mess up and ur stores reputation will be ruined

Step-by-step explanation:

That would be x+4=2x+3, so we must use substitution. Making x=1, hope that helps.

Square root of 15.625 is 3.906

What in mathematics is a square root?

A number can be generated by multiplying the square root of that number by itself. The word" square root" is represented by the symbol" sqrt" square root of, end square root. The reverse of squaring a number is chancing the square root.

How is the square root calculated?

The result of multiplying a number by itself yields its square value, while the square root of a number can be set up by looking for a number that, when squared, yields the original value. It follows that a a = b if" a" is the square root of"b."

Find the nearest perfect square, in this case 16 .

Subtract 4 from the number (15.625) (the square root of 16). The outcome is around 3.906

Calculate 3.953 by averaging 4 and 3.906. This approximate value represents the square root of 15.625.

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The vector expressions are:

Vectors are objects that have both magnitudes and directions.

The expressions are illustrations of vectors, and the given parameters are:

Also, we have:

u = i + j.

u = i + j means that:

\(u = (5,-6) + (-7,3)\)

\(u = (5+ (-7) , -6 + 3 )\)

\(u = (5-7 , -6 + 3 )\)

\(u = (-2 , -3 )\)

Also, we have:

v = -11i + 3j

This becomes

\(v = -11 \times (-7,3) + 3 \times (5,-6)\)

\(v = (77,-33) + (15,-18)\)

Rewrite as:

\(v = (77+ 15,-33-18)\)

\(v = (92,-51)\)

Also, we have:

2u − v = i + j

and

u = i + j

Substitute i + j for u

\(2u - v = u\)

Substitute (-2, -3) for u

\(2u - v = (-2,-3)\)

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The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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Answer:

2/3+1/9 =7/9

Step-by-step explanation:

u are looking for the lcm of 3 and 9 and then u divide the denominator and mutiply the numerator to get the answer

The system of equations [x - 3y = -1 and -6x + 19y = 6] can be solved, resulting in x = -1 and y = 0.

To solve the system of equations [x - 3y = -1 and -6x + 19y = 6], we can use the method of substitution or elimination.

Let's solve it using the method of elimination.

First, we can multiply the first equation by 6 and the second equation by -1 to eliminate the x terms.

This gives us [6x - 18y = -6 and 6x - 19y = -6].

Now, subtracting the first equation from the second eliminates the x terms, leaving us with -y = 0. Solving for y, we find y = 0.

Substituting this value back into the first equation, we get x - 3(0) = -1, which simplifies to x = -1.

Therefore, the solution to the system of equations is x = -1 and y = 0.

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The inequality expression of the volume of the balloon is V < 4,400

From the question, we have the following statement:

The initial volume of the balloon is 4,400 cubic centimeters

Also, we understand that:

The balloon leaks out over time

This means that the volume of air in the balloon decreases over time.

So, we have the following representation

V = Less than the initial volume

Rewrite as

V < 4400

Hence, the volume of the balloon at any time after it starts leaking is V < 4,400

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Answer:

11 mushrooms

Step-by-step explanation:

If Colin has 22 more mushrooms than Sophie, then Sofie has 22 less. Half of 22 is 11, so Colin should have 11 less, and Sophie should have 11 more. If you plug a random value into Sophie's mushrooms, this should still work. For example, if Sophie has 2 mushrooms and Colin has 24, they'll both have 13.

in general, to perform a hypothesis test comparing the means of two independent samples using the critical value method, you would follow these steps:

State the null and alternative hypotheses. For example, the null hypothesis could be that there is no difference in means between the two populations (i.e., H0: µ1 - µ2 = 0), and the alternative hypothesis could be that there is a significant difference in means (i.e., Ha: µ1 - µ2 ≠ 0).

Determine the level of significance, α, which represents the probability of rejecting the null hypothesis when it is actually true. For example, if α = 0.05, then there is a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).

Calculate the test statistic. The most common test statistic for comparing the means of two independent samples is the t-test. The formula for the t-test is:

t = (x1 - x2) / [s^2pooled/n1 + s^2pooled/n2]^0.5

where x1 and x2 are the sample means, s^2pooled is the pooled variance (calculated using the two sample variances and sample sizes), and n1 and n2 are the sample sizes.

Determine the critical value(s) from the t-distribution table based on the degrees of freedom (df) and level of significance (α). The degrees of freedom for a two-sample t-test is calculated as:

df = n1 + n2 - 2

Compare the test statistic to the critical value(s). If the absolute value of the test statistic is greater than the critical value(s), then reject the null hypothesis; otherwise, fail to reject the null hypothesis.

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Answer: the answer is d

Step-by-step explanation:

Answer:

0.91

30.4

850

Step-by-step explanation:

In a chi-square test for the equality of population proportions, you need at least two categories or populations to be able to perform the analysis.

A chi-square test for the equality of population proportions is used to determine if there is a significant difference between the proportion of observations in different categories or populations. In order to perform this test, you need at least two categories or populations to compare the proportions. If you only had one category or population, there would be no basis for comparison and the test would not be meaningful.

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QR has a length of 2√3. According to the given question

HOW TO CALCULATE THE SIDE OF THE SQUARE ?

In order to solve for QR, we need to use the information given to us in the problem and apply some basic geometry concepts.

First, we know that the diagonals of a square are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other in half. This tells us that the length of the diagonal is equal to the square root of two times the length of one of the sides of the square, or d = s√2.

Next, we are given that the midpoint of one of the diagonals is point U, and that US has a length of 3. Because U is the midpoint of the diagonal, we know that SU and UR are equal in length. Let's call this length x.

Now we can use the Pythagorean theorem to solve for x:

(US)²+ (UR)² = (SR)²

3²+  x= (s√2)²

9 + x² = 2s²

We also know that SU and UR are each equal to x, so:

2x² = s²

We can substitute 2x² for s² in the previous equation:

9 + x² = 2(2x²)

9 + x²= 4x²

3x² = 9

x² = 3

x = √3

Now we can use x to solve for the length of QR:

QR = 2x = 2√3

Therefore, QR has a length of 2√3.

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Answer:

A, C, E, F

Step-by-step explanation:

when you multiply the numbers with 7 the answer is greater than 42

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population. If for some reasons, the sample does not represent the population, the variation is called a sampling error.

Researchers often start with a simple random sample. This allows them to statistically measure a subset of individuals selected from a larger group or population to approximate a response from the entire group.

1. Lack of Bias :

The use of simple random sampling removes all hints of bias—or at least it should. Because individuals who make up the subset of the larger group are chosen at random, each individual in the large population set has the same probability of being selected. In most cases, this creates a balanced subset that carries the greatest potential for representing the larger group as a whole.

Here's a simple way to show how a researcher can remove bias when conducting simple random sampling. Let's say there are 100 bingo balls in a bowl, from which the researcher must choose 10. In order to remove any bias, the individual must close their eyes or look away when choosing the balls.

2. Simplicity : -

As its name implies, producing a simple random sample is much less complicated than other methods. There are no special skills involved in using this method, which can result in a fairly reliable outcome. This is in contrast to other sampling methods like stratified random sampling. This method involves dividing larger groups into smaller subgroups that are called strata. Members are divided up into these groups based on any attributes they share. As mentioned, individuals in the subset are selected randomly and there are no additional steps.

3. Less Knowledge Required : -

We've already established that simple random sampling is a very simple sampling method to execute. But there's also another, similar benefit: It requires little to no special knowledge. This means that the individual conducting the research doesn't need to have any information or knowledge about the larger population in order to effectively do their job. Be sure that the sample subset from the larger group is inclusive enough. A sample that doesn't adequately reflect the population as a whole will result in a skewed result.

1.  Difficulty Accessing Lists of the Full Population : -

An accurate statistical measure of a large population can only be obtained in simple random sampling when a full list of the entire population to be studied is available. Think of a list of students at a university or a group of employees at a specific company. The problem lies in the accessibility of these lists. As such, getting access to the whole list can present challenges. Some universities or colleges may not want to provide a complete list of students or faculty for research. Similarly, specific companies may not be willing or able to hand over information about employee groups due to privacy policies.

2. Time Consuming : -

When a full list of a larger population is not available, individuals attempting to conduct simple random sampling must gather information from other sources. If publicly available, smaller subset lists can be used to recreate a full list of a larger population, but this strategy takes time to complete.

Organizations that keep data on students, employees, and individual consumers often impose lengthy retrieval processes that can stall a researcher's ability to obtain the most accurate information on the entire population set.

3. Costs :

In addition to the time it takes to gather information from various sources, the process may cost a company or individual a substantial amount of capital. Retrieving a full list of a population or smaller subset lists from a third-party data provider may require payment each time data is provided.

If the sample is not large enough to represent the views of the entire population during the first round of simple random sampling, purchasing additional lists or databases to avoid a sampling error can be prohibitive.

4. Sample Selection Bias : -

Although simple random sampling is intended to be an unbiased approach to surveying, sample selection bias can occur. When a sample set of the larger population is not inclusive enough, representation of the full population is skewed and requires additional sampling techniques.

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Answer: If event A and event B cannot occur at the same time, then events A and B are said to be _________

Answer:  a) mutually exclusive

Mutually exclusive events are those events that do not occur at the same time. For example, when a coin is tossed, the result will be either head or tail, but we cannot get both effects. Such events are also called disjoint events since they do not happen simultaneously.

If event A and event B cannot occur at the same time, then events A and B are said to be mutually exclusive

Step-by-step explanation:

Answer: A_a^3

B_c^1

Step-by-step explanation:they work like integers therefore vlby sharing the same base and Having the division sign u just subtract the powers