. A 12-foot ladder leans 10 feet up a wall.
How far from the wall is the base of ladder?

Answer:

x=7y/6

Step-by-step explanation:

The value of x by using Division Property of Equality is (7/6)y so option (A) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given the equation,

6x = 7y

6x = 6(7/6)y

Division Property of Equality states that we need to divide by a common factor.

Since 6 is a common factor so,

6x/6 = 6/6(7/6)y

x = (7/6)y

Hence "The value of x by using Division Property of Equality is (7/6)y".

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The corrected statement should look like this:
```java
int[] hours = {8, 12, 16};
```

It looks like you are trying to create an integer array in Java called "hours" and initialize it with the values 8, 12, and 16. The given statement has incorrect syntax.
Declare the integer array using "int[]" followed by the variable name "hours".

This tells the Java compiler that you want to create an array of integers called "hours".
Use the assignment operator "=" to assign values to the array.
Enclose the values you want to assign to the array within curly braces "{" and "}" and separate each value with a comma.
The corrected statement should look like this:
```java
int[] hours = {8, 12, 16};
```
Now, the "hours" integer array is initialized correctly with the given values.

The syntax for declaring and initializing an integer array in Java is:

```java
data Type[] array

Name = {value1, value2, value3, ...};
```
In this case, "data Type" is "int", "array

Name" is "hours", and the values are 8, 12, and 16.
Remember to keep your code clean and concise to avoid syntax errors and make it easier for others to understand.

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The length of the entire tunnel is 127.88 meters by using cosine law or formulae.

Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.

\(c^{2} =a^{2} +b^{2} -2ab cos (\alpha )\)

Let us take surveyor as point A

one end of the tunnel denoted by point B

other end of the tunnel denoted by point C.

The length of AB is 101 meters

length of AC is 120 meters.

Measure of angle at point A = 42° + 28° =70°

Now lets find the length of tunnel

=\(\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }\)

=\(\sqrt{14400+10201-24240(0.34)}\)

=\(\sqrt{24601-8246}\)

\(\sqrt{16355}\)

=127.88 meters.

Hence the length of the entire tunnel is 127.88 meters.

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If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

Height of cylinder = 12 cm

Step-by-step explanation:

Given:

Radius of cylinder = 6 cm

Curved surface area of cylinder = [2/3][Total surface area of cylinder]

Find:

Height of cylinder

Computation:

Curved surface area of cylinder = [2/3][Total surface area of cylinder]

2πrh = [2/3][2πr(h + r)]

h = 2h/3 +[2/3][6]

h - 2h/3 = 4

[3h - 2h] / 3 = 4

h = 12

Height of cylinder = 12 cm

Answer: -10,30

Step-by-step explanation: I drew the graph, and it lined with 30 and interCepted -10

The solution of the system of equation is x = -1 and y=10/3.

The correct option is A.

Given

The given system of equation is;

\(\rm x + 3y = 9\\\\3x - 3y = -13\)

A system of linear equations is a collection of two or more linear equations.

From equation 1

\(\rm x+3y=9\\\\x=9-3y\)

Substitute the value of x in equation 2

\(\rm 3x-3y=-13\\\\3(9-3y)-3y=-13\\\\27-9y-3y=-13\\\\-12y=-13-27\\\\-12y=-40\\\\12y=40\\\\y = \dfrac{40}{12}\\\\y=\dfrac{10}{3}\)

Substitute the value of y in equation 1

\(\rm x+3y=9\\\\ x + 3\dfrac{10}{3}=9\\\\x+10=9\\\\x=9-10\\\\x=-1\)

Hence, the solution of the system of equation is x = -1 and y=10/3.

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Answer:

A

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Given

- 2x + 4 = 18

note the inverse of - 2 is - \(\frac{1}{2}\) not - 2

However , the first step is to isolate the term in x by subtracting 4 from both sides.

- 2x = 18 - 4 = 14 ( divide both sides by - 2 )

x = - 7

Answer: 1 solution I think

Step-by-step explanation:

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly can be calculated as follows:

Given, Principal = Rs 1200Time = 1.5 yearsInterest rate = 40% per annum, compounded quarterly

Let r be the quarterly rate of interest. Then we can convert the annual interest rate to quarterly interest rate using the following formula: \text{Annual interest rate} = (1 + \text{Quarterly rate})^4 - 1$$

Substituting the values, we get:0.40 = (1 + r)^4 - 1 Solving for r, we get:r = 0.095 or 9.5% per quarter

Now, we can use the formula for the amount of money after time t, compounded quarterly: $A = P \left( 1 + \frac{r}{4} \right)^{4t}

Substituting the values, we get:A = Rs 1200 x $\left(1 + \frac{0.095}{4} \right)^{4 \times 1.5}= Rs 1893.09

Therefore, the amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

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Yes, the true mean of 33 is within the margin of error of the sample mean, we can conclude that the confidence interval does contain the true mean.

To determine whether the confidence interval contains the true mean of 33, we need to calculate the margin of error for the confidence interval. The margin of error is a measure of the precision of the estimate, and it is calculated using the sample size, the standard deviation of the population, and the desired level of confidence.

For a 95% confidence interval, the margin of error can be calculated using the following formula:

The margin of error = 1.96 * (standard deviation / √sample size)

Plugging in the values, we get:

Margin of error = 1.96 * (14 / √42)

Performing the calculation, we find that the margin of error is 3.39. This means that the sample mean of 31 is likely to be within 3.39 units of the true mean, with a confidence level of 95%.

Since the true mean of 33 is within the margin of error of the sample mean, we can conclude that the confidence interval does contain the true mean. This means that our estimate of the population mean, based on the sample size 42, is likely to be accurate.

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Answer:

10.2

Step-by-step explanation:

-3.2+(16.4)-3=

13.2-3

10.2

Answer:

\(A=60m^2\)

Step-by-step explanation:

formula for area of a parallelogram is \(A=bh\) where \(b\) stands for base and \(h\) stands for height.

\(A=12(5)\)

\(A=60\)

17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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Step-by-step explanation:

Hey there!

f(x) = 7/x

~ Simply keep the "7" in the place where "x" is there.

\(f(7) = \frac{7}{7} \)

Therefore, X= 1.

Hope it helps....

Answer:

After evaluating the function \(f(x)=\frac{x}{7}\) by putting x = 7, we get f(7)= 1

Step-by-step explanation:

We need to evaluate the function \(f(x)=\frac{x}{7}\) and find f(7)

For finding f(7) we will put x = 7 in the given function \(f(x)=\frac{x}{7}\)

So, putting x= 7 and finding f(7)

\(f(x)=\frac{x}{7}\\Put\:x=7\\f(7)=\frac{7}{7}\\f(7)=1\)

So, after evaluating the function \(f(x)=\frac{x}{7}\) by putting x = 7, we get f(7)= 1

The dominant strategy of Farmer Jones is to buy 10 cows.

To determine the dominant strategy of Farmer Jones, we need to compare the outcomes of his two options:

buying either 10 cows or 20 cows.

Let's analyze the potential outcomes for each case:

Buying 10 cows:

If Farmer Smith buys 10 cows:  

The total number of cows in the field would be 30, resulting in each cow producing $3000 of milk.

If Farmer Smith buys 20 cows:

The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.

Buying 20 cows:

If Farmer Smith buys 10 cows:

The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.

If Farmer Smith buys 20 cows:

The total number of cows in the field would be 50, resulting in each cow producing less than $2000 of milk (exact value unknown).

From the given information, we can observe that regardless of the strategy chosen by Farmer Smith, Farmer Jones is better off buying 10 cows.

In all scenarios, the milk production per cow is higher when Farmer Jones buys 10 cows compared to buying 20 cows.

Therefore, the dominant strategy for Farmer Jones is to buy 10 cows.

Formally, we can express this as follows:

For Farmer Jones, no matter the strategy chosen by Farmer Smith, buying 10 cows yields a higher milk production per cow compared to buying 20 cows.

Hence, Farmer Jones' dominant strategy is to buy 10 cows.

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Answer:

Step-by-step explanation:

49.4 degrees

Step-by-step explanation:

In Triangle AXY,

We want to determine the angle of elevation from the point  is standing to the top of the flagpole, which is the angle at V in the diagram.

In Triangle XVY

|VY|=36 feet

Therefore, the angle of elevation from the point  is standing to the top of the flagpole is 49.4 degree to the nearest tenth of a degree.

I think i might of clicked on gthe wrong question sorry

The sample mean of the weight of the loaves in the bakery is 797.3 grams.

Given data:Number of loaves of bread = 10Weights of loaves in grams = {790, 680, 900, 855, 745, 740, 874, 903, 876, 800}

Mean or average weight of the loaves in the bakery can be calculated using the formula;

Mean = (Sum of weights of all loaves) / Number of loavesTherefore,Mean = (790 + 680 + 900 + 855 + 745 + 740 + 874 + 903 + 876 + 800) / 10 = 797.3

So, the sample mean of the weight of the loaves in the bakery is 797.3 grams.

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By using first principle, the value of Dy/Dx is,

⇒ Dy/Dx = - 7 / x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = 7 / x

Now, Differentiate the function with respect to x, we get;

⇒ y = 7 / x

⇒ Dy/ Dx = D / Dx (7 / x)

                = 7 D/Dx (1/x)

                = 7 (- 1 × x⁻¹⁻¹ )

                = 7 (- x⁻²)

                = - 7 / x²

⇒ Dy/Dx = - 7 / x²

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The domain of  the composition function fog(x) when f(x)= √6x and g(x)= 1/ (x-6) is equal to  (-∞, 6) U (6, ∞).

Function f(x) = √6x

And g(x)= 1/ (x-6

Composition function fog is ,

fog(x) = f(g(x))

Domain of fog(x),

First, find the domain of g(x),

Here,

g(x) = 1/(x-6)

The denominator of g(x) cannot be equal to zero,

So we must exclude x = 6 from the domain of g(x).

The domain of g(x) is equal to ,

domain of g(x) = {x | x ≠ 6}

The range of g(x) is,

As x approaches 6 from the left, g(x) approaches negative infinity,

And as x approaches 6 from the right, g(x) approaches positive infinity.

Range of g(x) = (-∞, 0) U (0, ∞)

Now, the domain of fog(x),

fog(x)

= f(g(x))

= √6g(x)

=√ 6 (1 /(x - 6 ) )

Square root sign must be non-negative.

Since the range of g(x) does not include zero,

Exclude the part of the range that is less than zero.

The domain of fog(x) is,

domain of fog(x)

= {x | g(x) > 0}

= {x | x < 6} U {x | x > 6}

The domain of fog(x) consists of all real numbers except x = 6.

Therefore, the domain of fog(x) is (-∞, 6) U (6, ∞).

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The above question is incomplete, the complete question is :

Given f(x)= √6x and g(x)= 1/ (x-6) Which value is in the domain of fog.

Answer:

b = 5

Step-by-step explanation:

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

12^2 + b^2 = 13^2

144+b^2 =169

Subtract 144 from each side

144-144+b^2 = 169-144

b^2 = 25

Take the square root on each side

sqrt(b^2) = sqrt(25)

b = 5

Answer:

B= 5

Step-by-step explanation:

The total number of votes cast in the city was 7864.

Given that there were 2949 no votes, which corresponds to 3 parts of the ratio.

Assume that the total number of votes as x. According to the given information, the ratio of yes votes to no votes is 5 to 3. This means that for every 5 yes votes, there are 3 no votes.

Set up the equation as given:

3 parts = 2949 votes

1 part = 2949 votes / 3

1 part = 983 votes

Now, since the ratio of yes votes to no votes is 5 to 3,  a total of 5 + 3 = 8 parts.

Total number of votes = 8 parts × 983 votes per part

Total number of votes = 7864 votes

Therefore, the total number of votes cast was 7864.

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A line plot can be used as a data display for the distribution of test scores in math class. Thus, the option to choose is TRUE.

A line plot is a graph that shows data as checkmarks or dots across a number line, indicating the frequency of each value.

The test score in the math test will be discrete data with repeating frequencies. The score of every individual will moreover be a whole number.

The line plot, as we know, marks the dots across the number line, indicating frequency.

Thus, the scores in the math test can be displayed using a line plot, by indicating each type of mark on the line, and dots above those marks for the number of times the same marks occur.

Thus, the option to choose is true.

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Answer:No it can not

Step-by-step explanation:

1,275 divided by 12 is 106.25

The requried Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR. Option A is correct.

A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value.

Here,
Burger Quick is able to estimate its wait time more consistently because it has a smaller interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The smaller the IQR, the more consistent the data is around the median, which is represented by the line within the box in the box plot.

In this case, Burger Quick has a smaller IQR (8.0) compared to Super Fast Food (7.0), indicating that the wait times at Burger Quick are more consistent around the median. The range, which is the difference between the maximum and minimum values, is not a good measure of consistency as it is affected by outliers.

Therefore, based on the given information, Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR.

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Answer: I think the answer is 5.3x + 1.7

The standard deviation of the investment is option (d) 8.43%

To calculate the standard deviation of this investment, we need to first calculate the expected rate of return

Expected rate of return = (0.4 x 15%) + (0.5 x 10%) + (0.1 x -3%)

= 6% + 5% - 0.3%

= 10.7%

Next, we need to calculate the variance of the investment:

Variance = (0.4 x (15% - 10.7%)^2) + (0.5 x (10% - 10.7%)^2) + (0.1 x (-3% - 10.7%)^2)

= 0.00744

Finally, we can calculate the standard deviation by taking the square root of the variance

Standard deviation = √(0.00744)

= 0.08626

= 8.43%

Therefore, the correct option is (d) 8.43%

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