Which graph shows how the Student distance from home changed over time

Therefore, the answer is A. {5, 5√3, 10}.

The set of values {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

In a 30-60-90 triangle, the sides are in a specific ratio. The ratio is 1 : √3 : 2, where the shortest side (opposite the 30-degree angle) has length x, the side opposite the 60-degree angle has length x√3, and the hypotenuse (opposite the 90-degree angle) has length 2x.

Let's check if the given set of values satisfies this ratio:

   If x= 5, then the side opposite the 60-degree angle should be 5√3, and the hypotenuse should be 10. These values match the ratio, so the set {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

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Step-by-step explanation:

850 calls

1000:100=10

1%=10

10×85=850

Discount is the reduction in value. The total number of calls not answered this is 150 calls

Given the following

Total number of calls = 1000 calls

If 15% of those calls were not answered, the total calls that were not answered is given as:

Total call not answered . = 0.15 * 1000

Total call not answered = 150 calls

Hence the total number of calls not answered this is 150 calls

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In one- half table the patient take 900 mcg colchicine.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Example: If the cost of 6 cans of juice is 300, then what will be the cost of 4 cans of juice?

cost of 4 cans of juice = 50 × 4 = 200.

1 mg= 1000 mcg

0.6 mg= 0.6* 1000 = 600 mcg

In one tablet = 600 mcg

in half tablet = 300 mcg

So, in one- half table the patient take 900 mcg colchicine.

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Answer:

17

Step-by-step explanation:

15^2 + 8^2 = 225 + 64 = 289

=17

Given the trigonometry equation below

If two numbers multiplies themselves and the result is zero, it implies that one of them is zero or both are zero

For instance:

Thus,

For

In radian,

Hence, the solutions in radians of the equation in the interval [0, 2π) is

Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


hope it helped u dear...........

Answer:

\(f(x) = \frac{2x}{2x + 3}\)

Step-by-step explanation:

Given

\(h(x) = \frac{2x + 3}{x}\)

\(g(x) = \frac{2}{x}\)

\(g(f(x)) = h(x)\)

Required

Find f(x)

\(g(x) = \frac{2}{x}\)

Substitute x for f(x)

\(g(f(x)) = \frac{2}{f(x)}\)

Recall that

\(g(f(x)) = h(x)\)

This gives

\(\frac{2}{f(x)} = \frac{2x + 3}{x}\)

Cross Multiply

\(f(x) * (2x + 3) = 2 * x\)

\(f(x) * (2x + 3) = 2 x\)

Make f(x) the subject of formula

\(f(x) = \frac{2x}{2x + 3}\)

Answer:

x/x+3

Step-by-step explanation:

Answer:

x = 25°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°

The given triangle is a right triangle which means one of its angle has a measure of 90°

since thd other angle is given as 65 to calculate x we just add the given measures and subtract it from 180

90° + 65 + x = 180

155 + x = 180 subtract 155 from both sides

x = 25°

Answer:

9 times 11 equals 99

99

if you are satisfied with my answer, please mark brainliest :D

Step-by-step explanation:

Answer: 99

Step-by-step explanation:

The given proportion of triangle ABC as AE/AD = EB/DC is; Not Accurate

This theorem states that If a line is drawn parallel to one side of a triangle, then it cuts other two sides proportionally.

Thus, In ΔABC, DE || BC

By Thales theorem, we can say that;

AD/DB = AE/EC

Rearranging we can arrive at;

AE/AD = EC/DB

When we simplify further by adding 1 to both sides, we will get;

AD/AB = AE/AC

Thus, the given proportion is not accurate

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Answer:

2000000000 ants would equal 1 elephant.

Step-by-step explanation:

8 x 10^6 = 8000000

4 x 10^-3 = 0.004

8000000 ÷ 0.004 = 2000000000

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

175.5in

Step-by-step explanation:

12 x 9 + 67.5

If this answer is incorrect (Which it should not be) than try 243

Answer:

9 + 3 + 3 = 15

15 x 12 x 1/2(basically just dividing by 2) = 90

9 x 12 = 108

108 + 90 = 198 in^2 for a

7 x 7 = 49

7 x 7 = 49, 49 divided by 2 ( x 1/2) = 24.5

49 + 24.5 = 73.5 ft^2 for b

Answer: 135

Step-by-step explanation:

Since the expression gives you that n = 5, you'll plug 5 into every "n" within the original equation.

6n^2 -15 = 6(5)^2-15

You'll then square 5

= 6(5*5)-15

= 6(25)-15

= 150-15

= 135

Answer:

Step-by-step explanation:

it is true

We reject the null hypothesis and come to the conclusion that there is adequate evidence at the 0.02 level.

The rejection of a correct null hypothesis during hypothesis testing is referred to as a Type I mistake. As a result, we get the incorrect conclusion that there is a large difference between two groups or variables. A false positive is another name for a Type I mistake.

Failure to reject a faulty null hypothesis is a Type II mistake. This means that we get the incorrect conclusion that there is no difference between two groups or variables when there actually is one. False negative is another name for a Type II mistake.

The valve generates a mean pressure of 4.7 lbs/square inch, which is the null hypothesis:

H0: μ = 4.7

The other possibility is that the valve does not generate 4.7 lbs/square inch of mean pressure:

Ha: μ ≠ 4.7

Since we are comparing the single sample mean to a known population mean and we are aware of the population variance, we can test this hypothesis using a one-sample t-test. The test statistic is determined by dividing the sample mean (x) by the population mean, the sample size (n), and the population standard deviation (s).

We obtain the following by plugging in the values:

t = (4.6 - 4.7) / (0.9 / √(240))

t = -4.15

Using a two-tailed test and a t-distribution table with 239 degrees of freedom (240 - 1), we can get the crucial t-value as follows:

T critical equals 2.571

We reject the null hypothesis and come to the conclusion that there is adequate evidence at the 0.02 level that the valve does not operate in accordance with specifications since our computed t-value (-4.15), which is in the rejection area (t -2.571 or t > 2.571), falls within this range.

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Answer:

The answer is D.

Step-by-step explanation:

The phrase "20 decreased by the sum of 6 and b." means that since the word sum is the word for the result of two numbers being added together, it would make sense if you look at ( 6 + b ), and since you're also decreasing the result by 20, that would mean subtracting it by 20, so you get 20 - ( 6 + b ).

I hope this helps you :D

Step-by-step explanation:

that kind of wording is always misleading.

please give my regards and comments to your teacher.

a square root has ALWAYS 2 solutions : a positive AND a negative one.

in that sense the negative solution to a square root is NOT an extraneous solution.

only any value of x < -10 (to make the argument of the square root negative) as solution would be extraneous.

so, if your teacher wants to say that only the positive solutions of a square root are allowed, it has to be said as an extra definition or by applying the "+" sign to the square root.

so,

x + 4 = sqrt(x + 10)

since the 2 solutions are already given to us, we only need to use them in the equation and see what happens.

x = -1

-1 + 4 = sqrt(-1 + 10)

3 = sqrt(9) = 3 (actually, it is ±3)

so, x = -1 is a real solution.

x = -6

-6 + 4 = sqrt(-6 + 10)

-2 = sqrt(4) = 2 (actually, it is ±2)

so, based on your teacher's expectation of only positive results of the square root (even though it was not stated),

x = -6 is an extraneous solution.

therefore, the third answer (c) is the "correct" answer.

but actually, formally, the second answer (b) is the truly correct answer.

Answer:

35

Step-by-step explanation:

A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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The equivalenet expression is 54\(n^{-11}\)

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

(\(6n^-5\))(\(3n^-3\))²

We can simplify as follows:

(\(6n^-5\))(\(9n^-6\))

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

\(n^-5 * n^-6 = n^-11\)

So the simplified expression is:

\(54n^-11\)

Therefore, the expression \((6n^-5)(3n^-3)^2\) is equivalent to \(54n^-11.\)

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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Step-by-step explanation:

70 ÷ 3 = 23  1/3

The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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1.) a. From the standpoint of the Audio Division, the lowest acceptable transfer price for speakers sold to the Hi-Fi Division would be the variable cost per unit, which is $122. This is because the Audio Division would at least want to cover its variable costs for each unit sold to the Hi-Fi Division.

   b. From the standpoint of the Hi-Fi Division, the highest acceptable transfer price for speakers acquired from the Audio Division would be the quote from the other manufacturer, which is $137. This is because the Hi-Fi Division would want to pay a price that is equal to or less than what it would pay to the other manufacturer.

   c. The range of acceptable transfer prices between the two divisions would be $122 to $137. If left free to negotiate without interference, it is possible that the division managers would voluntarily agree to a transfer price within this range, as it would be mutually beneficial for both divisions.

   d. From the standpoint of the entire company, the transfer should take place if the transfer price is equal to or less than the selling price per unit on the intermediate market, which is $140. This is because the company would be able to cover its variable and fixed costs and make a profit on the transfer.

2)a. From the standpoint of the Audio Division, the lowest acceptable transfer price for speakers sold to the Hi-Fi Division would still be the variable cost per unit, which is $122.

  b. From the standpoint of the Hi-Fi Division, the highest acceptable transfer price for speakers acquired from the Audio Division would still be the quote from the other manufacturer, which is $137.

   c. The range of acceptable transfer prices between the two divisions would still be $122 to $137. If left free to negotiate without interference, it is possible that the division managers would still voluntarily agree to a transfer price within this range.

   d. From the standpoint of the entire company, the transfer should still take place if the transfer price is equal to or less than the selling price per unit on the intermediate market, which is $140.

 3) a. From the standpoint of the Audio Division, the lowest acceptable transfer price for speakers sold to the Hi-Fi Division would still be the variable cost per unit, which is $122.

   b. From the standpoint of the Hi-Fi Division, the highest acceptable transfer price for speakers acquired from the Audio Division would still be the quote from the other manufacturer, which is $137.

   c. The range of acceptable transfer prices between the two divisions would still be $122 to $137. If left free to negotiate without interference, it is possible that the division managers would still voluntarily agree to a transfer price within this range.

   d. From the standpoint of the entire company, the transfer should still take place if the transfer price is equal to or less than the selling price per unit on the intermediate market, which is $140. However, if the Audio Division is already selling its full capacity of 25,000 units to outside customers, it may not have the capacity to produce an additional 5,000 units for the Hi-Fi Division. In this case, the company may need to consider other options, such as increasing production capacity or finding another supplier for the Hi-Fi Division.

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