for any triangle the sum of the measure of the three angles equals 180. In one triangle the largest angle is 14 less than 5 times the smallest angle. the middle angle is 5 more 3 times the smallest angle. what is the measure of the smallest angle?

9514 1404 393

Answer:

  (a) $2.857 million

  (b) vertical compression by 1/3; shift left by 6; shift up by 2

Step-by-step explanation:

(a) Find the year difference (2021-2010=11) and put that value where x is. Then do the arithmetic.

  g(11) = (∛(11+6))/3 +2 = (∛17)/3 +2 ≈ 2.57128/3 +2 ≈ 0.857 +2

  g(11) ≈ 2.857 . . . 2021 revenue in millions of dollars

__

(b) For parent function f(x), the transformation ...

  g(x) = a·f(x -h) +k

represents a vertical scaling by a factor of 'a', right shift by h units, and up shift by k units.

Comparing this form to the given g(x), we see ...

  a = 1/3 . . . vertical compression by a factor of 1/3

  h = -6 . . . .right shift 6 units

  k = 2 . . . . up shift 2 units

_____

Additional comment

The vertical scaling is called "compression" when the scale factor is less than 1, and "stretch" when the scale factor is greater than 1. Here, the scale factor of 1/3 means the graph is vertically compressed.

Answer:

the prime factor of 841 is 29

Step-by-step explanation:

841 divided by 29 gives back 29 without any remainder

The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

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Answer:

12 batches

Step-by-step explanation:

Total cups of flour = 1 1/2

Flour used per batch = 1/8 cups

What is the maximum number of times (batches) Steve can complete the recipe?

Maximum batches Steve can make = Total cups of flour / Flour used per batch

= 1 1/2 ÷ 1/8

= 3/2 ÷ 1/8

= 3/2 × 8/1

= (3*8) / (2*1)

= 24 / 2

= 12 batches

Maximum batches Steve can make = 12 batches

9514 1404 393

Answer:

  16 square units

Step-by-step explanation:

The area of the square base is ...

  A = s²

  A = 2² = 4

The area of each triangle is ...

  A = (1/2)bh

  A = (1/2)(2)(3) = 3

So, the area of the base and 4 triangles is ...

  total area = 4 + 4(3) = 16 . . . square units

Answer:

its 16

Step-by-step explanation:

Answer:

  a. a[1] = 3; a[n] = 2a[n-1]

  b. a[n] = 3·2^(n-1)

  c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

The recursive rule is ...

  a[1] = 3

  a[n] = 2×a[n-1]

__

The explicit rule is ...

  a[n] = a[1]×r^(n-1)

  a[n] = 3×2^(n-1)

__

The 15th term is ...

  a[15] = 3×2^(15-1) = 3×2^14

  a[15] = 49,152

Answer:

???

Step-by-step explanation:

L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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According to the question the best guess for the distribution's standard deviation is 32.

To determine the best guess for the standard deviation (SD) using the empirical rule, we can utilize the 68-95-99.7 rule. According to this rule, in a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% of the data falls within two standard deviations of the mean.

- Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the range between the lowest and highest accident rates is from 9 accidents per day to 105 accidents per day, encompassing the entire data range.

To estimate the standard deviation, we can calculate the range between the mean and the lowest/highest values:

Range = Highest Value - Lowest Value

      = 105 - 9

      = 96

Since the empirical rule states that approximately 99.7% of the data falls within three standard deviations, and we know that the data range spans from the lowest to the highest value, we can assume that three standard deviations encompass this range.

Therefore, we can estimate the standard deviation as follows:

Range = 3 * SD

Substituting the values:

96 = 3 * SD

Solving for SD:

SD = 96 / 3

SD = 32

So, the best guess for the distribution's standard deviation is 32.

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Answer:

c. non-linear and increasing

Step-by-step explanation:

Answer:

\( \rm t = \dfrac{5 - b}{2} \)

Step-by-step explanation:

Solve for t:

\( \longrightarrow \) 5 - b = 2t

5 - b = 2t is equivalent to 2t = 5 - b:

\( \longrightarrow \) 2t = 5 - b

Divide both sides by 2:

\( \longrightarrow \) \( \sf \dfrac{2t}{2} = \dfrac{5 - b}{2} \)

\( \sf \dfrac{2}{2} \) = 1:

\( \longrightarrow \) \( \sf t = \dfrac{5 - b}{2} \)

Answer:

x = -4

Step-by-step explanation:

Step 1: Write equation

-5x - 10 = 10

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

-5(-4) - 10 = 10

20 - 10 = 10

10 = 10

Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

The percentage of data that is roughly greater than 66, as displayed in the box plot, is 100%.

In a box plot, we have the following displayed five-number summary which tells what percentage of the data distribution for each part of the data distribution:

Upper quartile (Q3): This is the value at where the box in the box plot ends at the edge of the box. From this point to the left, all data values that fall within the bracket make up 75% of the data.

Lower quartile (Q3): This is the value at where the box in the box plot starts at the edge of the box. From this point to the left, all data values that fall within the bracket make up 25% of the data.

Median: this is the middle value at the point where the line divides the box and data below this point make up 50% of the data.

The other five-number summary are the maximum and the minimum values that are represented by the whiskers.

On the box plot given, 66 is at the extreme whisker at the left. This means that the percentage of data that is roughly greater than 66 is 100%.

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The solid is bounded below by the xy-plane, above by the plane x + y + 2z = 2, and by the elliptic cylinder x^2 + 2y^2 = 2 on the sides.

To find the volume of this solid, we can use a triple integral, integrating over the region of the xy-plane that is bounded by the ellipse x^2 + 2y^2 = 2.

We can express this region in polar coordinates, where x = r cos θ and y = r sin θ. Then, the equation of the ellipse becomes:

r^2 cos^2 θ + 2r^2 sin^2 θ = 2

Simplifying:

r^2 = 2/(cos^2 θ + 2sin^2 θ)

So the region of integration can be expressed as:

∫(0 to 2π) ∫(0 to √(2/(cos^2 θ + 2sin^2 θ))) ∫(0 to 2 - x - y)/2 dz dy dx

This gives us the iterated integral:

∫(0 to 2π) ∫(0 to √(2/(cos^2 θ + 2sin^2 θ))) ∫(0 to 2 - r(cos θ + sin θ))/2 dz r dr dθ

Note that the limits of integration for z and r depend on x and y, which depend on θ and r.

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Answer:

it is 24

Step-by-step explanation:

i did andn i got 1000

For a quadratic of the form px^2 + 40x + 16 to be a perfect square, it must be able to be written in the form (mx + n)^2 for some real numbers m and n.

Expanding (mx + n)^2 gives:

(mx + n)^2 = m^2x^2 + 2mnx + n^2

Comparing this to the given quadratic, we can see that:

m^2 = p

2mn = 40

n^2 = 16

Solving for m and n, we find that:

m = ±√p

n = ±4

Therefore, in order for the quadratic to be a perfect square, the square root of p must be rational, and the value of p must be one of the following:

p = 0, 1, 16

So the possible values of p that make the quadratic a perfect square are 0, 1, 16.

Answer:

8(h)=96

Step-by-step explanation:

Remember when you are writing a multiplication equation, it's a division backwards.

96/8=h

h×8=96

hope this helps you

goodluck

Answer: 8x=96

Step-by-step explanation:

8X = 96

X = 96/8

X = 12 hours

INSTANCE.

In my opinion a red mustang is an instance of the car class.

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Answer:

42/12

Step-by-step explanation:

3 1/2 in improper fraction form is 7/2. We can see the denominator in the equivalent fraction is 12. In order for that to happen, the common factor that must have been multiplied is 6. So the numerator of the equivalent fraction should be 42 because:

                         7            42

                       ___ =    ____

                         2            12

42/12

The answer is \(\frac{42}{12}\)

First, you must simplify both sides if the equation.

\(\frac{7}{2}=\frac{x}{12}\)

Then, multiply both sides by 12

\(42=x\)

\(x=42\)

Finally, substitute in 42 for x

\(3\frac{1}{2}=\frac{42}{12}\)

To describe the typical quiz scores of the students, a common measure used is the mean, or average, score. The mean is calculated by summing up all the scores and dividing by the total number of scores.

Given its simplicity and simplicity in interpretation, the mean was chosen as a proxy for normal quiz scores. It offers a solitary figure that encapsulates the scores' median. We can figure out the pupils' overall performance on the quiz scores by computing the mean.

It's crucial to keep in mind, though, that outliers or extremely high scores dividing might have an impact on the mean. The mean may not be an accurate representation of the normal results of the majority of students if there are a few students who severely underperform or do very well on the quizzes.

To get a more thorough picture of the distribution of quiz results in such circumstances, it might be beneficial to take into account additional metrics like the median or mode.

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The polynomial that represents the area of the rectangle is:
\(A = 2x^4 + x^3 - 15x^2 + 8x + 24\).

To find the polynomial that represents the area of the rectangle, we need to multiply the polynomials representing the length and width.
Length (L): \(2x^3 - 5x^2 + 8\)
Width (W): x + 3
Now, let's multiply these polynomials:
Area (A) \(= L \times W = (2x^3 - 5x^2 + 8)(x + 3)\)
To multiply, we'll use the distributive property and multiply each term in the first polynomial by each term in the second polynomial:
\(A = (2x^3 \times  x) + (2x^3 \times  3) + (-5x^2 \times x) + (-5x^2 \times  3) + (8 \times  x) + (8 \times  3)\)
Now, let's perform the multiplications:
\(A = 2x^4 + 6x^3 - 5x^3 - 15x^2 + 8x + 24\)
Next, we'll combine like terms:
\(A = 2x^4 + (6x^3 - 5x^3) - 15x^2 + 8x + 24\)
\(A = 2x^4 + x^3 - 15x^2 + 8x + 24\).

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Answer:

Step-by-step explanation:

Step-by-step explanation:

6x+2=9x-1

6x-9x=-2-1

-3x=-3

x=1

Answer:

Step-by-step explanation:

Here you go mate

Step 1

6x+2=9x-1  Equation/Question

Step 2

6x+2=9x-1  Simplify

6x+2=9x-1

Step 3

6x+2=9x-1  Subtract -9x

-3x+2=-1

Step 4

-3x+2=-1  Subtract

-3x=-3

Step 5

-3x=-3  Divide

;answer

x=1

Hope this helps

The probability that a student chosen at random dislikes at least one of them is 0.2. Probability is the likelihood of occurrence of an event.

Probability a student likes math's = 0.7

Probability a student dislikes maths = 1 - 0.7 = 0.3

Probability a student likes history = 0.2

Probability a student dislikes history = 1 - 0.2= 0.8

Probability a student likes maths and history = 0.1

Probability a student dislikes maths = 1 - 0.1= 0.9

Probability a student dislikes at least one of them = probability he dislikes math's + Probability a student dislikes history- Probability a student dislikes math's and history = 0.3+0.8-0.9 = 0.2

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Letter D is the correct choice also letter A is correct.

There are two correct answers A and D.

False. The statement you described is not an equivalent form for a conditional statement. The process you mentioned, which is reversing and negating the antecedent and consequent, is known as forming the contrapositive of the statement.

A conditional statement has the form "If P, then Q," where P is the antecedent and Q is the consequent. The contrapositive is formed by negating both the antecedent and consequent, and reversing their order: "If not Q, then not P." The contrapositive is equivalent to the original conditional statement.

However, simply reversing the antecedent and consequent without negating them gives you the converse, which is "If Q, then P." The converse is not equivalent to the original conditional statement.

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The probability of at least one is a Samsung in the purchase collection of two independent LED HDTV is equal to 0.376.

Percent of all LED display manufactured by Samsung = 21%

Probability that at least one purchase is Samsung

= 1 - Probability that both purchases are not Samsung

Probability that the first purchase is not Samsung is 1 - 0.21 = 0.79.

The probability that the second purchase is also not Samsung is also 0.79.

Since the purchases are independent,

Multiply these probabilities to get the probability that both purchases are not Samsung,

P(neither is Samsung)

= 0.79 x 0.79

= 0.6241

The probability that at least one purchase is Samsung is,

P(at least one is Samsung)

= 1 - P(neither is Samsung)

= 1 - 0.6241

= 0.3759

Rounding to 3 decimal places, we get,

P(at least one is Samsung) = 0.376

Therefore, the probability that in a collection of two independent LED HDTV purchases, at least one is a Samsung is 0.376.

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