A ladder 17 m long reaches a window 8 m high on one side of the road. the ladder is then turned over to the opposite side of the road and is found to reach another window 15 m high. Find the width of the road.Please apply the pythgoras property .

The test has four degrees of freedom and a significance level of 0.05/2. The p-value for the left tail is 0.010, while the right tail is 0.015. The p-value is less than the level of significance, rejecting the null hypothesis and indicating a difference in the proportions of students transferring to at least one college.

Yes, we can determine that whether the proportions of college students that transfer to an in-state university are the same for different colleges using the given data and the chi-square homogeneity of proportions test. We are provided with the following data . Suppose the test statistic value for a chi-square homogeneity of proportions test for this data is x² = 9.722.

Using a = 0.95, we need to determine whether the proportions of students that transfer are the same for all five colleges.

The null hypothesis is that the proportions of students that transfer are the same for all five colleges.

H0: P1 = P2 = P3 = P4 = P5

The alternative hypothesis is that the proportions of students that transfer are not the same for all five colleges.H1: At least one Pi is different from the others where Pi is the proportion of students that transfer for the it h college.

There are five colleges, so there are four degrees of freedom.

The level of significance is a = 0.05/2

= 0.025,

where the significance level is divided by 2 since the test is a two-tailed test. The critical value for the test is 13.277.

Before calculating the test statistic, let us calculate the expected values for each cell. We calculate it by taking the row total times the column total and dividing it by the grand total. The calculations are shown below: content loadedUsing these expected values, we calculate the test statistic as:content loadedWe can use a chi-square distribution table with four degrees of freedom to find the p-value. Since the test is a two-tailed test, we need to find the p-value for both tails.

The p-value for the left tail is 0.010, and the p-value for the right tail is 0.015. The total p-value is 0.025, which is equal to the level of significance.Since the p-value is less than the level of significance, we reject the null hypothesis. There is sufficient evidence to suggest that the proportions of students that transfer are not the same for all five colleges. The researcher should conclude that there is a difference in the proportions of students that transfer for at least one college.

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Answer:

\(displacemnt \: = 4432.5m \: (left)\)

Step-by-step explanation:

\(velocity = \frac{displacemnt}{time} \\ - 98.5m {s}^{ - 1} = \frac{x}{45.0 \: s } \\ x = - 98.5 \times 45.0 \\ displacemnt \: = 4432.5m \: (left)\)

Answer:

-4432.5 m

Step-by-step explanation:

-98.5 × 45 = -4432.5 m

brainliest pls, it's for my next rank <:

The a = 0.01 critical value for the chi - square statistic with 13 degrees of freedom is given by 27.688.

Hence the correct option is (A).

Here given distribution is Chi - squared distribution.

two parameters of chi - squared distribution are given by ' a ' and ' d ' where d is degree of freedom.

The critical value against chi squared distribution changes according to the change of the values of a and d.

The table chi squared distribution is given by,

Here we have to find the critical value for the chi - squared statistic with 13 degrees of freedom when a = 0.01.

Therefore, a = 0.01 and d = 13

From the given table we can see that when a = 0.01 and d = 13 the critical value is given by 27.688.

Hence the correct option is (A).

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Answer:

the second one the third one and the last one

Step-by-step explanation:

Answer:

1,2,3 and 5 are right.

Step-by-step explanation:

Answer:

(4.25*H)+10

H=hours used

Step-by-step explanation:

samules age = (cousins age * 2) -2

Step-by-step explanation:

1) 10+4.25x

the variable represents the time so in this case it would be per a hour so we know the cost changes based on the hour

A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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Scott's statement that (13g + 1) + (-2 - 5g) and 8/3(3g + 9/8) are equivalent is wrong

From the question, we have the following parameters that can be used in our computation:

(13g + 1) + (-2 - 5g)

Remove the brackets

So, we have

13g + 1 - 2 - 5g

Evaluate the like terms

8g - 1

When factorized, we have

8/3(3g - 3/8)

This is not the same as Scott's expression

Hence, Scott is incorrect

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Given an angle α in quadrant 4 with cos α = -7/25, we can use the half-angle formula for cosine to find the exact value of cos(α/2) as √(15)/10.

In trigonometry, the half-angle formula for cosine states that cos(α/2) = ±√((1+cos α)/2), where α is an angle and cos α is the cosine of that angle. The sign of the formula depends on the quadrant in which the angle α lies.

In this case, we are given that α is an angle in quadrant 4 and that cos α = -7/25. Since cosine is negative in quadrant 4, we know that the half-angle formula for cosine must be negative. Using the half-angle formula for cosine, we have cos(α/2) = -√((1+cos α)/2) = -√((1-7/25)/2) = -√(18/50) = -√(9/25) * √(2/2) = -3/5 * √2.

However, we can simplify this answer further by rationalizing the denominator. Multiplying both the numerator and denominator by √2, we get cos(α/2) = -3√2/10.

Therefore, the exact value of cos(α/2) is -3√2/10 or equivalently, √(15)/10 in simplified radical form.

In conclusion, given an angle α in quadrant 4 with cos α = -7/25, we can use the half-angle formula for cosine to find the exact value of cos(α/2) as √(15)/10.

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Given an angle α in quadrant 4 with cos α = -7/25, we can use the half-angle formula for cosine to find the exact value of cos(α/2) as √(15)/10.

In trigonometry, the half-angle formula for cosine states that cos(α/2) = ±√((1+cos α)/2), where α is an angle and cos α is the cosine of that angle. The sign of the formula depends on the quadrant in which the angle α lies.

In this case, we are given that α is an angle in quadrant 4 and that cos α = -7/25. Since cosine is negative in quadrant 4, we know that the half-angle formula for cosine must be negative. Using the half-angle formula for cosine, we have cos(α/2) = -√((1+cos α)/2) = -√((1-7/25)/2) = -√(18/50) = -√(9/25) * √(2/2) = -3/5 * √2.

However, we can simplify this answer further by rationalizing the denominator. Multiplying both the numerator and denominator by √2, we get cos(α/2) = -3√2/10.

Therefore, the exact value of cos(α/2) is -3√2/10 or equivalently, √(15)/10 in simplified radical form.

In conclusion, given an angle α in quadrant 4 with cos α = -7/25, we can use the half-angle formula for cosine to find the exact value of cos(α/2) as √(15)/10.

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According to the given statement There are 2 rows and 3 columns in the matrix, resulting in a total of 6 categories (cells).

In a chi-square test for independence, the degrees of freedom (df) is calculated as (r-1)(c-1),

where r is the number of rows and c is the number of columns in the contingency table or matrix.

In this case, the df is given as 2.

To determine the total number of categories (cells) in the matrix, we need to solve the equation (r-1)(c-1) = 2.

Since the df is 2, we can set (r-1)(c-1) = 2 and solve for r and c.

One possible solution is r = 2 and c = 3, which means there are 2 rows and 3 columns in the matrix, resulting in a total of 6 categories (cells).

However, it is important to note that there may be other combinations of rows and columns that satisfy the equation, resulting in different numbers of categories.

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Answer:

Fraction form:       1/729

Decimal form:      0.00137174...

Exponent form:   3^-6

Answer:

k= -63 and equation answer is 7

Step-by-step explanation:

Answer: Solve for  

by simplifying both sides of the equation, then isolating the variable.  k= -63

:)

The total amount owed after 3 years with the given rate of interest compounded quarterly will be $2851.52.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

Given that,

Principle amount P = $2000

Rate of interest R = 12%

Compounded quarterly n = 4

Time period T = 3 years

Total amount = P{1 + R/n]^(nT)

Total amount = 2000[1 + 0.12/4]^(4×3)

Total amount = $2851.52

Hence "The total amount owed after 3 years with the given rate of interest compounded quarterly will be $2851.52".

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Answer:

±2\(\sqrt{2}\) - 2

Step-by-step explanation:

x² + 4x + 4 = 4 + 4

(x+2)² = 8

x+2 = \(\sqrt{8}\);  \(\sqrt{8}\) = 2\(\sqrt{2}\)

x = ±2\(\sqrt{2}\) - 2

In your given situation, the distribution of grades is left-skewed, which indicates that the majority of the students scored higher grades, with fewer students receiving lower grades.

If the distribution of grades was left-skewed, it means that there were more students who scored higher grades than those who scored lower grades. This would result in a longer tail on the left side of the distribution curve. However, despite the skewness, the mean, median, and mode were all the same. This suggests that the majority of the grades fell around the same value, which is the central tendency of the distribution. The fact that the mean and median are the same suggests that the skewness was not significant enough to pull the mean away from the median. Therefore, in this case, the mean and median can be considered as representative of the typical grade achieved by the students.
. However, the mean, median, and mode are all the same, suggesting that the central tendency of the grades is consistent, and the overall distribution might be only slightly skewed.

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Answer: 14

Step-by-step explanation:

Answer: 78.2

Step-by-step explanation:

You can figure out by making proportions so 5/17=23/x and then solve for x

\(\small\tt\red{Question : 2x + 3(5x - 7) = 47 } \\ \\ \small\tt\orange{solution : - } \\ \\ \small\tt\blue{2x + 3(15x - 7) = 47} \\ \\ \small\tt\blue{2x + 15 - 21 = 47} \\ \\ \small\tt\blue{17 = 47 + 21} \\ \\ \small\tt\blue{17x = 68} \\ \\\small\tt\blue{x = \cancel \frac{68}{17} } \\ \\\\\small\tt\green{\boxed{x = 4 \: \: is \: your \: answer}} \\ \\ \\\small\tt\pink{\boxed{\boxed{hope \: it \: help \: you \: dear}}}\)

The project variance and the standard deviation in the given table are shown below. Variance The variance is the difference between the minimum and maximum values.

For Activity A: Variance Variance \[V_{D} = \frac{(11-9)^{2}}{6}=0.33\]Standard deviationThe standard deviation is the square root of the variance.

Standard For Activity A: Standard deviation For Activity B: Standard deviation For Activity C: Standard deviation For Activity D: Standard deviation \[\sigma_{D}

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The graph of the exponential function 2(0.5)^x is given by the image presented at the end of the answer.

An exponential function is defined as follows:

y = ab^x.

In which:

The function for this problem is defined as follows:

y = 2(0.5)^x.

Meaning that when x = 0, y = 2, and for each increase of 1, the numeric values are halved, and hence the points are given as follows:

(0,2), (1,1), (2,0.5), (3, 0.25), (4, 0.125).

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Answer:

-3n-+21

Step-by-step explanation: 1. Get rid of the Parenthesis , so times -3 by what’s inside

2. If you multiply -3 by n you get -3n

3. if you multiply -3 by -7 you get 21 , you get a positive because a negative times a negative is a positive

4. so now you have -3n + 21 you don’t add these because -3n has a variable and 21 doesn’t have a variable , and if 21 did have a variable it would need to also be n

Answer:

−3n  +  21

Step-by-step explanation:

This is the answer because:

1) You have to distribute everything from outside of the parenthesis to the inside

2) -3 times n is -3n

3) -3 times -7 is 21

4) Therefore, the answer is −3n  +  21

Hope this helps!

The solution to the given system of equations using elimination method is (x, y) = (-3/2, 3/4).

Given system of equations is

4x+8y=-6

6x+12y=-9

To solve the given system of equations using elimination method, let's first multiply the first equation by 3 and second equation by 2 such that the coefficient of x in both the equations become equal. So, the system of equations becomes

12x + 24y = -18

6x + 12y = -18

Now, let's subtract the second equation from the first equation

12x + 24y - 6x - 12y = -18 - (-18)6x + 12y = 0

Dividing the above equation by 6, we get

x + 2y = 0=> x = -2y

Substituting x in any one of the given equation, we get

6x + 12y = -96(-2y) + 12y = -9-12y = -9y = 3/4

Substituting y in x = -2y, we get

x = -2(3/4) = -3/2

Therefore, the solution to the given system of equations is (x, y) = (-3/2, 3/4).

Hence, the correct option is option (D).

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A goniometer is a tool used to measure the range of motion of a joint. It helps determine the degrees of flexion and extension of the joint. By using this device, healthcare professionals can assess the mobility and flexibility of a joint.


A goniometer is a simple tool that consists of two arms and a protractor. It is used to measure the range of motion of a joint, such as the shoulder or knee. The arms of the goniometer are aligned with the bones on either side of the joint, and the protractor is used to measure the angle between the arms. This angle indicates the degrees of flexion and extension of the joint.

For example, if a physical therapist wants to assess a patient's knee mobility, they would place the goniometer on the patient's knee joint and measure the angle as the patient moves their leg. This measurement helps determine the extent of movement and any limitations or abnormalities in the joint.

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The efficiency of the Zumba class system is approximately 69.2%, and its utilization is approximately 54.5%.

To calculate the efficiency of the system, we can divide the actual output (number of employees trained) by the designed capacity (maximum number of employees that can be trained per month) and multiply by 100 to get a percentage.

Efficiency = (Actual Output / Designed Capacity) * 100

Efficiency = (600 / 850) * 100 = 70.6%

Therefore, the efficiency of the system is approximately 70.6%.

To calculate the utilization of the system, we can divide the actual output (number of employees trained) by the capacity (maximum number of students per month) and multiply by 100.

Utilization = (Actual Output / Capacity) * 100

Utilization = (600 / 1100) * 100 = 54.5%

Therefore, the utilization of the system is approximately 54.5%.

The Zumba class system at the local gym has an efficiency of approximately 69.2% and a utilization rate of approximately 54.5%. The efficiency indicates how well the system is performing relative to its designed capacity, and in this case, it suggests that the system is operating at a reasonably high level. The utilization rate, on the other hand, indicates how much of the available capacity is being utilized, and in this case, it suggests that the system is operating at around half of its maximum capacity. This information can be used by the gym to evaluate the performance of their Zumba class program and make informed decisions regarding resource allocation and potential improvements.

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Answer:

y = 3x - 6

Step-by-step explanation:

The line here is parallel

Equation of line

The equation of the line parallel to the given line passes through the point (-2, 4) is, y = 4x + 12.

What is slope - intercept form of the line?

y = mx + b, where m denotes the slope and b the y-intercept, is how the line's equation is expressed in the slope-intercept form.

Consider, the given equation of line

y = 4x - 9

We have to find the equation of line that parallel to the given line.

The point is (-2, 4).

First we have to find the slope of the line.

Since, slope of the parallel line, is same as the slope of the given line.

Here, the slope of the given line is 4.

So, the slope of the parallel line is also 4.

Now, consider the point - slope form of the line

\(y-y_1=m(x-x_1)\)

Plug \((x_1, y_1) = (-2, 4), m = 4\)

\(y-4=4(x-(-2))\\y-4=4(x+2)\\y-4=4x+8\\y=4x+8+4\\y=4x+12\)

Hence, the equation of line parallel to the given line in slope-intercept form is y = 4x + 12.

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Answer:

3/5

Step-by-step explanation:

4/5-1/5= 3/5

Answer:60

Step-by-step explanation: You are currently converting speed units from kilometers per hour to minute per kilometer 1 kph = 60 min/km

Answer:

(9-57i)

Step-by-step explanation:

We need to find the product of the given complex number i.e.

(3-9i)(6-i)

It can be solved as follows :

(3-9i)(6-i) = 3(6) +3(-i) +(-9i)(6) + 9i(i)

= 18-3i-54i+9i²

We know that, i² = -1

So,

= 18-3i-54i+9(-1)

= 18-57i-9

= 9-57i

So, the product of the given complex number is (9-57i).