The sum of the first three terms of a sequence is 6 and the fourth term is 16

A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Answer:

38.667°

Step-by-step explanation:

the total sum of 3 angles in a triangle is 180

in triangle PQR this means:

P+Q+R = 180

so:

64+x+2x=180

64+3x=180

3x=116

x=116/3=38.667

So Q=X=38.667

Answer:her for ppoints

Step-by-step explanation:

Answer

domain (-inf,inf) range (-inf, 7)

Step-by-step explanation:

I think

Answer:

\(\frac{11}{2}\)

Step-by-step explanation:

To obtain the inverse of f(x)

let y = f(x) and rearrange making x the subject, that is

y = 2x - 1 ( add 1 to both sides )

y + 1 = 2x ( divide both sides by 2 )

\(\frac{y+1}{2}\) = x

Change y back into terms of x with x = \(f^{-1}\)(x) , thus

\(f^{-1}\)(x) = \(\frac{x+1}{2}\)

Evaluate g(3) and substitute the value obtained into \(f^{-1}\)(x)

g(3) = 3² + 1 = 9 + 1 = 10, then

\(f^{-1}\) (10) = \(\frac{10+1}{2}\) = \(\frac{11}{2}\)

Answer: 45

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

(-4, 4) & (-1, -2)

(y₂ - y₁) / (x₂ - x₁)

(-2 - 4) / (-1 + 4)

-6/3 = -2

slope = -2

set : {31, 76, 34, 35, 39, 49, 55}

arrange ascending to descending:

{ 31, 34, 35, 39, 49, 55, 76 }

given,

I.Q.R:

Answer:

21

Step-by-step explanation:

Place the numbers in order from smallest to largest:

31, 34, 35, 39, 49, 55, 76

The median (Q2) is the middle value = 39

Q1 is the middle value of the numbers smaller than the median = 34

Q3 is the middle value of the numbers larger than the median = 55

IQR = Q3 - Q1

      = 55 - 34

      = 21

Answer:

8.1822x10^8

Step-by-step explanation:

The Median of the data shown on the line plot is 6.5.

The median of a line plot The median is the central value in a data set that is arranged in numerical order from least to greatest. In other words, the median is the middle number of a set of data. To find the median of a set of data on a line plot, follow the steps below:

Step 1: Arrange the data in numerical order from least to greatest. In the line plot provided above, the data is already arranged in order from least to greatest. It ranges from 4 to 12.

Step 2: Determine the total number of data points. In this case, there are 8 data points.

Step 3: Identify the middle value in the data set. This is done by dividing the total number of data points by 2 (the middle point). If the number of data points is even, the median is the average of the two middle values. If the number of data points is odd, the median is the middle value itself. Since there are 8 data points in the line plot above, we have an even number of data points. The two middle values are 6 and 7, so the median is the average of these two values.

Step 4: Calculate the median. Add the two middle values (6 and 7) together and divide by 2:6 + 7 = 13 13/2 = 6.5

Therefore, the median of the data shown on the line plot is 6.5.

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The given probability of having six girls in a six-child family is 0.015625. To determine the method used to compute this probability, we need to analyze the information provided.

The Classical method is based on theoretical assumptions and probabilities calculated using mathematical principles. It assumes equally likely outcomes and relies on counting favorable outcomes over the total number of possible outcomes.

The Empirical method involves gathering data from observations or experiments to estimate probabilities. It relies on observed frequencies and relative frequencies to compute probabilities. However, the given probability does not suggest a sample or data collection, making it unlikely that the Empirical method was used.

The Subjective method involves assigning probabilities based on personal judgment or opinions. Individuals subjectively evaluate the likelihood of an event based on their own beliefs or knowledge.

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The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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12 - 8x = 3(x + 4)

12 - 8x = 3x + 12

-8x - 3x = 12 - 12

-11x = 0

x = 0

Answer:

The answer is 9/5

Step-by-step explanation:

7/5 + 4/10

Now, Cross Multiply

7 × 10 + 5 × 4/5 × 10

70 + 20/50

90/50 = 9/5

Thus, The answer is 9/5

-TheUnknownScientist 72

Answer:

The last figure.

Answer:

Figure 1, 3 and 6

Point symmetry is when two figures or (equal) parts of a figure lies at a same distance but in opposite direction from a certain point.

Answer:

26

Step-by-step explanation:

complementary means same. so A and B are 26.

There are some differences in the process of constructing a inscribed square and a hexagon inside a circle.

When constructing a square, we start with a circle. Then draw its diameter through the center of the circle. Now putting compass on end points of this diameter, measuring more than half the length of diameter on the compass, draw 4 arcs above and below the diameter. So we get a perpendicular bisector of the diameter. In total, we get 4 points on the circle. Joining the adjacent points, we get the inscribed square.

When constructing the regular hexagon, start drawing a circle. Put the compass on a point on the circle and measure the radius on it. Now draw an arc on the circle. Putting compass on this new point on the circle draw another arc. Continuing like this, we get a total of  6 arcs giving 6 points on the circle. Join the adjacent points to get an inscribed regular hexagon.

So the differences in constructing the square and the regular hexagon are:

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Answer:

El tiempo le llevara a Mariano es 2 horas y el tiempo que le llevara a Alberto es de una hora

Step-by-step explanation:

Para calcular el tiempo que le llevará a cada uno si juntos pueden hacer el trabajo en 3h, tenemos que primero segun los datos considerar lo siguiente:

Segun los datos tenemos que Mariano puede despachar periódicos 2 veces el tiempo que le toma a Alberto, por lo tanto:

2X=Mariano puede despachar periódicos 2 veces el tiempo que le toma a Alberto

X=El tiempo que le toma a Alberto.

Por lo tanto calculando la siguiente ecuacion, podremos hallar el valor de X:

2X+X=3 horas

3X=3 horas

X=1 hora

Entonces, tenemos que el tiempo le llevara a Mariano es 2 horas y el tiempo que le llevara a Alberto es de una hora

To find the value of c2 in the given differential equation, we can use the initial conditions x(0) = 5 and x'(0) = 6.

The general solution of the differential equation d^2x/dt^2 - 4x = 0 is given by x(t) = c1e^(-2t) + c2e^(2t), where c1 and c2 are arbitrary constant and real numbers.

Applying the initial condition x(0) = 5, we substitute t = 0 into the equation:

x(0) = c1e^(-2(0)) + c2e^(2(0)) = c1 + c2 = 5.

Next, we apply the initial condition x'(0) = 6. Taking the derivative of the general solution, we have:

x'(t) = -2c1e^(-2t) + 2c2e^(2t).

Substituting t = 0 and x'(0) = 6 into the equation:

x'(0) = -2c1e^(-2(0)) + 2c2e^(2(0)) = -2c1 + 2c2 = 6.

We now have a system of equations:

c1 + c2 = 5,

-2c1 + 2c2 = 6.

Solving this system of equations, we find that c1 = -1 and c2 = 6.

Therefore, the value of c2 is 6, which satisfies the given conditions x(0) = 5 and x'(0) = 6 in the differential equation.

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Step-by-step explanation:

I hope this answers your problem

Answer:

x = 20

Step-by-step explanation:

To solve this problem we first observe the Pythagoras equation. If a= 16 and b=12 are the lengths of the legs of a right triangle and c=x is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.  

This relationship is represented by the formula: a*a + b*b = c*c

\(\sqrt{16^2 + 12^2}\) = x  

Answer:

  9:50

Step-by-step explanation:

It appears the sequence has 0:51 as the first difference, and those differences increase by 0:01 in each interval. That means ? must be chosen so that ...

  ? - 8:58 = 0:52   ⇒   ? = 8:58 +0:52 = 9:50

  10:43 -? = 0:53   ⇒   ? = 10:43 -0:53 = 9:50

The missing time is 9:50.

Answer:

rational function is the correct answer

Given information:Position of a particle moving along the x-axis varies in time according to the expression x = 3t², where x is in meters and t is in seconds.

To determine the position at the following times. a. t = 3.30 s, b. t = 3.30 s + Δt xf and c. Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 3.30 s. a. To find the position when t = 3.30 s, substitute t = 3.30 s in x = 3t².x = 3t² = 3(3.30)² = 32.67 metersTherefore, the position at t = 3.30 s is 32.67 meters.

b. To find the position when t = 3.30 s + Δt, substitute t = 3.30 s + Δt in x = 3t².x = 3t² = 3(3.30 s + Δt)² = 3(10.89 + 6.6Δt + Δt²) = 32.67 + 19.8Δt + 3Δt²Therefore, the position when t = 3.30 s + Δt is 32.67 + 19.8Δt + 3Δt².c. Velocity is given by Δx/Δt.Δx/Δt = [x(t + Δt) - x(t)]/ΔtBy substituting the given values, we have;Δx/Δt = [x(3.30 + Δt) - x(3.30)]/Δt= [3(3.30 + Δt)² - 3(3.30)²]/Δt= 19.8 + 6ΔtTaking the limit of Δx/Δt as Δt → 0, we have;Δx/Δt = 19.8 + 6(0)Δt = 19.8Therefore, the velocity at t = 3.30 s is 19.8 m/s.

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Answer:

B=Cd,A

C=DA,B

D=Ab,c

Step-by-step explanation:

(A,b)

(7,8)

=-1

These measurements are not identical due to confounding;

When the effects of two or more explanatory variables on a response variable cannot be distinguished from one another, confounding occurs in an experiment.

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To compute the z-score for each observation, we need to standardize the data using the formula z = (x - μ) / σ, where x is the individual observation, μ is the mean of the sample, and σ is the standard deviation of the sample.

Given the sample observations: 16, 11, 13, 22, 15, and 19, we can calculate the z-score for each observation as follows:

Calculate the mean (μ) of the sample:

μ = (16 + 11 + 13 + 22 + 15 + 19) / 6 = 16

Calculate the standard deviation (σ) of the sample:

Step 1: Calculate the squared deviations from the mean for each observation:

(16 - 16)², (11 - 16)², (13 - 16)², (22 - 16)², (15 - 16)², (19 - 16)²

0, 25, 9, 36, 1, 9

Step 2: Calculate the variance:

Variance = (0 + 25 + 9 + 36 + 1 + 9) / 6 = 80 / 6 ≈ 13.33

Step 3: Calculate the standard deviation:

σ = √(Variance) = √13.33 ≈ 3.65

Calculate the z-score for each observation:

z = (x - μ) / σ

For 16: z = (16 - 16) / 3.65 = 0 / 3.65 = 0

For 11: z = (11 - 16) / 3.65 = -5 / 3.65 ≈ -1.37

For 13: z = (13 - 16) / 3.65 = -3 / 3.65 ≈ -0.82

For 22: z = (22 - 16) / 3.65 = 6 / 3.65 ≈ 1.64

For 15: z = (15 - 16) / 3.65 = -1 / 3.65 ≈ -0.27

For 19: z = (19 - 16) / 3.65 = 3 / 3.65 ≈ 0.82

The z-scores for the given sample observations are: 0, -1.37, -0.82, 1.64, -0.27, and 0.82.

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Answer:

y + 5 = x

Step-by-step explanation:

y= 15 * 3x

Subtract 15 on both sides

y - 15 = 3x

Divide 3 on both sides

y + 5 = x

(I hope this helps and sorry if i'm wrong)