Solve for x. Figures are not necessarily drawn to scale.
M
X
9
N
7
Q
10.5
9

Part (a)

The error happens on the 2nd step.

The student multiplied both sides by the LCD (x+3)(x-3) to clear out the fractions, but forgot about the first "1" at the very left.

=================================================

Part (b)

[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\(x+3)(x-3)*1 - (x+3)(x-3)*\frac{2}{x+3} = (x+3)(x-3)*\frac{x+1}{x-3}\\\\(x+3)(x-3) - 2(x-3) = (x+1)(x+3)\\\\x^2-9 - 2x+6 = x^2+4x+3\\\\x^2-2x-3 = x^2+4x+3\\\\x^2-2x-3-x^2-4x-3=0\\\\-6x-6=0\\\\-6x=6\\\\x = 6/(-6)\\\\x = -1[/tex]

Check:

[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\1 - \frac{2}{-1+3} = \frac{-1+1}{-1-3}\\\\1 - \frac{2}{2} = \frac{0}{-4}\\\\1 - 1 = 0\\\\0 = 0\\\\[/tex]

The answer is fully confirmed.

You can use a graphing tool like GeoGebra to visually confirm the answer.

The measure of angle m is,

⇒ m = 43°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle PQR is shown in figure.

Now, We know that;

An exterior angle of a triangle is sum of two opposite angle of that triangle.

⇒ m + 68° = 111°

Solve for m;

⇒ m = 111° - 68°

⇒ m = 43°

Thus, The measure of angle m is,

⇒ m = 43°

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Answer:

kg = gal × 3.7854 × density.

Step-by-step explanation:

the shape is bimodal and symmetric and  histogram have 38 to 40 and 44 to 46.

If the two peaks are mirror reflections of one another, the bimodal distribution may be symmetrical. symmetrical Cauchy distributions exist. These are not likely to be found in basic statistics. These distributions belong to a family where the anticipated value is hypothetical. the long tails of the logistic distribution. If the data is symmetric but contains more extreme values than one would anticipate from a normal distribution, the logistic and Cauchy distributions are utilized. these different distribution types. It is symmetric for the uniform distribution. Since the odds are same at every location, the distribution is essentially a straight line. The distribution is bimodal and nearly symmetric. There are two modes in the distribution, from 38 to 40 and 44 to 46. The existence of data for both men and women may account for this. Women may prefer the lower mode, whereas males may prefer the upper.

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The amount of time in which the simple interest on Rs7560 be Rs1102.50 at 25/4% per annum, 5 years

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

To find the time it takes for the simple interest on Rs. 7560 to be Rs. 1102.50 at 25/4% per annum, we can use the formula for simple interest:

We are given I = 1102.50 and P = 7560, and the interest rate is 25/4% per annum, which we can convert to a decimal:

r = 25/4% ÷ 100

 = 0.25/4

 = 0.0625

Now, we can substitute the known values into the formula and solve for t:

1102.50 = 7560 x r x t

1102.50 / 7560 = r x t

t = 1102.50 / (7560 x 0.0625)

t = 5 years

So, it will take 5 years for the simple interest on Rs. 7560 to be Rs. 1102.50 at 25/4% per annum.

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Answer: 4

Step-by-step explanation:

1+1=2 but  if it is 2+2 then it would = 4

Answer:

Step-by-step explanation:

Continuous variables are variables that can take on any value within a specified range. Some common examples of continuous variables include:

Height: Height can be measured in inches, centimeters, or any other unit of length and can take on any value within the range of human heights.

Weight: Weight can be measured in pounds, kilograms, or any other unit of weight and can take on any value within the range of human weights.

Age: Age can be measured in years, months, or days and can take on any value within the range of human ages.

Time: Time can be measured in seconds, minutes, or hours and can take on any value within the range of time that can be measured.

Temperature: Temperature can be measured in degrees Celsius, Fahrenheit, or any other unit of temperature and can take on any value within the range of temperatures that can be measured.

Income: Income can be measured in dollars, euros, or any other currency and can take on any value within the range of human incomes.

These are just a few examples of continuous variables. In general, any variable that can take on an infinite number of values within a specified range can be considered a continuous variable.

Answer:

192

Step-by-step explanation:

2x9=18

18x12=192

The approximate measure of the slide is 20 feet.

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Given that, a slide is 15 feet high and the slides makes a 50° angle with the ground.

Let the length of the slide be x.

Now, sin50° =15/x

0.766=15/x

x=15/0.766

x=19.58

≈ 20 feet

Therefore, the approximate measure of the slide is 20 feet.

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The t-test assuming equal variances means Pooled t-test in which variances of the two sample populations are equal.

The pooled t-test is the statistical procedure that assumes that population variances are equal. Finding a weighted average of the two independent sample variances is referred to as pooling. By combining data from samples from populations 1 and 2, we may estimate the common variance when there is solid evidence that population 1's variance is equal to population 2's variance.

Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be compared as: S1/S2. The ratio would be 1, or, in the event that the two are equal.

However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some errors. Thus, the pooled t-test implies whether the null-hypothesis should be accepted or rejected.

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The point 3/4th of the way from point A to point B is (3.25, -1.25).

What is the coordinate geometry?

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements

To determine the point 3/4th of the way from point A to point B, we can use the midpoint formula to find the coordinates of the midpoint M of the line segment AB, and then use those coordinates to find the point 3/4th of the way from point A to point B.

The midpoint M of the line segment AB can be found using the midpoint formula:

M = ((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.

Substituting the given coordinates, we get:

M = ((3 + 4)/2, (2 - 3)/2) = (3.5, -0.5)

Now we can find the point 3/4th of the way from point A to point B by starting at point A and moving 3/4th of the way towards point B. To do this, we can use the following formula:

P = ((1 - 3/4)*x1 + (3/4)*x2, (1 - 3/4)*y1 + (3/4)*y2)

Substituting the coordinates of points A and B, we get:

P = ((1 - 3/4)*3 + (3/4)*4, (1 - 3/4)2 + (3/4)(-3)) = (3.25, -1.25)

Hence, the point 3/4th of the way from point A to point B is (3.25, -1.25).

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The true response would be 15,488/7 square centimeters based on the information provided.

Square offers businesses a range of goods and services to help them complete sales transactions, use marketing strategies, and control their finances, inventory, and workforce.

The lateral surface (the curved portion of the cylinder) is added to the areas of a round top and bottom to figure out the surface surface of the cylindrical cheese wheel. The perimeter of the base (2πr, where r is the radius) as well as the height can be used to compute the lateral surface area. Each round top and bottom's surface area is πr².

Hence, the cheese wheel's overall surface area is:

(2πr × h) + (2πr²)

Inputting the values provided yields:

(2 × 22/7 × 22 × 16) + (2 × 22/7 × 22 × 22)

When we simplify and find the total area of the surface, we obtain:

15,488/7 square centimeters

As a result, 15,488/7 square centimeter of the cheese wheel are covered by the label.

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A procedure for using sample data to find the estimated regression equation is (c) the least squares method.

The least squares method is a commonly used statistical procedure for finding the estimated regression equation by minimizing the sum of the squared differences between the observed and predicted values.

The goal of this method is to find the line of best fit that closely represents the relationship between the independent and dependent variables in the sample data. The regression equation obtained from the least squares method can be used to make predictions about the dependent variable based on the values of the independent variable.

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Answer: The measure of RST is 124 degrees.

Step-by-step explanation:

If HJK and RST are supplementary angles, it means that their sum is equal to 180 degrees. So we can use this information to find the measure of RST.

HJK + RST = 180

Substituting HJK = 56, we get:

56 + RST = 180

Subtracting 56 from both sides, we get:

RST = 180 - 56

RST = 124

Therefore, the measure of RST is 124 degrees.

The angle of elevation is 61.34°.

An angle of elevation is defined as an angle between the horizontal plane and line of sight from the observer's eye to some object above.

here, we have,

Given here, ramp 18 ft long rises to a platform.

The bottom of the platform is 13 ft from the foot of the ramp.

Let the angle be x then angle of elevation is

      tanx =22/12

     x   = tan⁻¹(22/12)

    x   =61.34°

Hence, the angle of elevation is  61.34°

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Answer:

C

Step-by-step explanation:

It makes the most sense.

Answer:

= 43.

Step-by-step explanation:

[tex] \frac{5}{18} + \frac{11}{12} \\ = 36 \times \frac{5}{18} + 36 \times \frac{11}{12} \\ = 2(5) + 3(11) \\ = 10 + 33 \\ = 43[/tex]

Note// the LCM for 18 and 12 is 36.

Since segment AD bisects angle BAC, the value of x is equal to 14.6.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to this triangle (ΔABC), we have:

AB/BD = AC/DC

19/x = 17/(20 - x)

17x = 19(20 - x)

17x = 380 - 19x

19x + 17x = 380

26x = 380

x = 380/26

x = 14.6.

In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.

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C. The probability of the type I error best defines the notion of the significance position of a thesis test.

The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.

Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.

Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.

Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.

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The surfing increased by 50% from the first week to the second. His method is correct.

The amount of any product is given as if it were a percentage of a hundred. The ratio is one-quarter of one hundred. % is an abbreviation for one hundred percent. It is represented by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The Surfing 6 seconds to reach 9 seconds. Then the percentage is given as,

P = [(9 - 6) / 6] x 100

P = (3 / 6) x 100

P = 0.50 x 100

P = 50%

The surfing increased by 50% from the first week to the second. His method is correct.

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An algebraic expression to represent how much Xavier will have in his savings account after w weeks is; y = 15w + 43

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given that Xavier has $43 in his savings account. Thus;

y-intercept = $43

He plans to save $15 each week. Thus;

Slope = $15

Now, after w weeks, the total savings is expressed as;

y = 15w + 43

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Answer:

Therefore, the height of the pole is approximately 20.79 feet.

Step-by-step explanation:

the person is standing at point A, which is 36 ft away from the base of the telephone pole. The angle of elevation from the ground to the top of the pole is 30 degrees. We want to find the height of the pole, which is represented by "h" in the diagram.

To solve for "h", we can use the tangent function, which relates the opposite side (height) to the adjacent side (distance from the pole to the person) of a right triangle:

tan(30°) = h / 36

We can solve for "h" by multiplying both sides by 36 and taking the tangent of 30 degrees:

h = 36 * tan(30°)

h = 36 * 0.5774 (rounded to four decimal places)

h ≈ 20.79

Therefore, the height of the pole is approximately 20.79 feet.

Answer:

20.78460969082652752232935609807

Step-by-step explanation:

;)

Yall are some cheaters. Quit looking it up on this website like, dang....

1. a. The graph for the g(x) = -4x - 5 is mentioned in the image below.

1. b. The graph for the h(x) = - 4x - 12 is mentioned in the image below.

1. c. The graph for the j(x)= -4x -15 is mentioned in the image below.

2. The equation for the linear function with a gradient of - 4 and an unknown y-intercept of k is y = -4x + k.

A slope-intercept form is an equation that represents a straight line and is written as y = mx + c, where m is the gradient and c is the y-intercept. If c becomes zero, it passes through the origin.

1. a.

The function g(x) = -4x - 5 represents a straight line that has a slope of -4 and a y-intercept of -5.

When x = 0, g(x) = -5. The point is (0,-5).

When x = 1, g(x) = -9. The point is (1,-9).

When x = -1, g(x) = -1. The point is (-1,-1).

The graph of the function is given below.

1. b.

The function h(x) = -4x - 12 represents a straight line that has a slope of -4 and a y-intercept of -12.

When x = 0, h(x) = -12. The point is (0,-12).

When x = 1, h(x) = -16. The point is (1,-16).

When x = -1, h(x) = -8. The point is (-1,-8).

The graph of the function is given below.

1. c.

The function j(x) = -4x - 15 represents a straight line that has a slope of -4 and a y-intercept of -15.

When x = 0, j(x) = -15. The point is (0,-15).

When x = 1, j(x) = -15. The point is (1,-19).

When x = -1, j(x) = -11. The point is (-1,-1).

The graph of the function is given below.

2.

The slope-intercept form of a line is y = mx + c. On substituting m = -4 and c = k into the equation, it gets reduced to y = -4x + k.

Therefore, the obtained answer is y = -4x +k.

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The requried, each month receives 1/12 of the calendar or about 8.33% of the total space.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

Here,
Anita can start by drawing a large rectangle on the paper to represent the entire year. Then, she can divide the rectangle into 12 equal parts, each representing a month. One way to do this is to draw four vertical lines to divide the rectangle into five equal columns, and then draw three horizontal lines to divide each column into four equal rows.

Each of the 12 parts represents 1/12 or one-twelfth of the calendar. Therefore, each month receives 1/12 of the calendar, or about 8.33% of the total space.

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Integer: 12

Irrational numbers: -2√10 and √20

Rational numbers: 17/4, 0.25, and -77/11.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

There are rational and irrational numbers in the image.

The numbers can be written in the form of p/q, where q is never zero is rational numbers.

And rest of the numbers are irrational numbers.

So, the solutions are given in the image below.

√144 = 12

0.25 = 25/100 = 1/4

Therefore, the solutions are given in the image below.

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The value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and 5g is equal to 5 times that amount, or 5000mg.

When converting between different metric units of mass, the prefixes are used to denote the multiple of the base unit. In this case, the base unit is the gram, and the prefix we are using is 'milli', which is equal to one thousandth of the base unit. Therefore, in order to convert 5g to mg, the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.When converting between metric units, it is important to remember that the decimal point moves right by a number of places equal to the number of zeroes in the prefix. For example, if we were converting 5g to kg, the prefix 'kilo' has three zeroes, so the decimal point would move three places to the right, resulting in a value of 0.005kg.When converting from a larger unit to a smaller unit, the numerical value will increase, and when converting from a smaller unit to a larger unit, the numerical value will decrease. In this case, we are converting 5g to mg, which is a smaller unit, so the numerical value of 5g increases to 5000mg.

Overall, the value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.

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Answer:

Step-by-step explanation:

a + 2a + 6 = 180

3a = 174

a = 58

2(58) + 6 = 122

Answer:92

Step-by-step explanation:

[tex]\frac{64+88+92+89+81+92+x}{7} =85[/tex]

85 x 7 = 595

595 - 64 - 88 - 92 - 89 - 81 - 92 = 92

Answer:

Naomi needs to score a 92 on her seventh test to raise her mean to an 85.

Step-by-step explanation:

Let's call the score Naomi needs to get on her seventh test "x".

To find out what score she needs to raise her mean to 85, we can set up an equation:

(64 + 88 + 92 + 86 + 81 + 92 + x) / 7 = 85

We add up all her scores so far (64 + 88 + 92 + 86 + 81 + 92) and add the score she needs to get on her seventh test (x). We divide the sum by the total number of tests (7) to get the mean score of 85.

Simplifying the equation, we get:

503 + x = 595

Subtracting 503 from both sides, we get:

x = 92

Answer:

[tex]\frac{4}{90}[/tex]

Step-by-step explanation:

[tex]\frac{4}{9}[/tex]  - [tex]\frac{4}{10}[/tex]

to subtract the fractions we require them to have a common denominator

the LCM of 9 and 10 is 90

= = [tex]\frac{4(10)}{9(10)}[/tex] - [tex]\frac{4(9)}{10(9)}[/tex]

= [tex]\frac{40}{90}[/tex] - [tex]\frac{36}{90}[/tex]

= [tex]\frac{40-36}{90}[/tex]

= [tex]\frac{4}{90}[/tex]