write the numeral: Nine thousand nine hundred?

Answer: 236 inches

Step-by-step explanation:

To find the total length, all we have to do is add together the mixed fractions. First, let's change the mixed fractions to improper fractions.

\(98\frac{1}{4}=\frac{393}{4}\)

\(39\frac{1}{2}=\frac{79}{2}\)

\(\frac{393}{4} +\frac{393}{4} +\frac{79}{2}\)         [make sure denominator is the same]

\(\frac{393}{4} +\frac{393}{4} +\frac{158}{4}\)        [add]

\(\frac{944}{4}\)                           [divide]

\(236\)

Now, we know that the total length is 236 inches.

The parabola has an axis of symmetry x=22, vertex at (22, 2), and opens downward.

Given the focus (22, 3) and directrix y=1, we can determine the following:

a. Axis of symmetry: Since the parabola is vertical (directrix is horizontal), the axis of symmetry will be a vertical line passing through the focus. So, x=22 is the axis of symmetry.

b. Vertex: The vertex is the midpoint between the focus and the directrix. To find the vertex, average the y-coordinates of the focus and the directrix. Vertex = (22, (3+1)/2) = (22, 2).

c. Direction: If the focus is above the directrix, the parabola opens upward. If the focus is below the directrix, the parabola opens downward. In this case, the focus (22, 3) is above the directrix y=1, so the parabola opens downward.

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Answer:

The radius is 4

You have to do half what 8 it 4 an that your answer

Step-by-step explanation:

is there more to the question?

Answer: 412.5 ml

Step-by-step explanation:

500 ( 1 - 25%) ( 1 + 10%)

= 412.5 ml

Answer:

412.5 ml

Step-by-step explanation:

To decrease 500 ml by 25%, you would need to multiply 500 by 0.25 to find the amount of decrease:

Subtract that amount from the original value:

Therefore decreasing 500 ml by 25% would give us 375 ml.

To then increase this value by 10%, you would multiply it by 0.10 to find the amount of increase:

Now, add that amount to the previous value:

Therefore, if you decrease 500 ml by 25% and then increase it by 10%, the final result is 412.5 ml.

Answer:

-4

Step-by-step explanation:

12/-3=-4

The transformed tangent function is:

g(x) = -5*tan(x) - 3

We start with tangent function:

f(x) = tan(x).

First, we reflect our function over the x-axis, so we just have a change of sign as:

g(x) = -f(x).

Then, a horizontal stretch of scale factor of 5.

g(x) = -5*f(x)

Finally, a shift down of 3 units, this is:

g(x) = -5*f(x) - 3 = -5*tan(x) - 3

This is the transformed function.

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The intervals of concavity for f(x) = 3 cos x, with 0 < x < 21, are (0, π/2) and (3π/2, 2π).

To find the intervals of concavity for f(x) = 3 cos x, we need to analyze the second derivative of the function.

First, let's find the second derivative of f(x):

f'(x) = -3 sin x (derivative of cos x)

f''(x) = -3 cos x (derivative of -3 sin x)

Now, we can analyze the concavity of f(x) by considering the sign of the second derivative:

When x ∈ (0, π/2): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.

When x ∈ (π/2, 3π/2): In this interval, cos x < 0, so f''(x) > 0. The second derivative is positive, indicating concavity upwards.

When x ∈ (3π/2, 2π): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.

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The explicit formula for the given sequence is O_an = -3n + 12.

To determine the explicit formula for the given sequence, we need to analyze the relationship between the term numbers (n) and their corresponding values.

Looking at the values in the table, we can observe that the sequence seems to follow a pattern where each value is obtained by subtracting three times the term number from a constant.

Let's break down the pattern:

Term #1: Value 9

Term #2: Value 16

Term #3: Value 13

Term #4: Value -3

From Term #1 to Term #2, the value increases by 7 (16 - 9). From Term #2 to Term #3, the value decreases by 3 (13 - 16). Finally, from Term #3 to Term #4, the value decreases by 16 (−3 - 13). We notice that the change in the value depends on the term number.

By examining the pattern, we can determine that the explicit formula for the sequence is O_an = -3n + 12. This formula states that the nth term of the sequence is obtained by multiplying the term number (n) by -3 and then adding 12 to the result.

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This an be prove by SSS Congruence theorem.

Two triangles are congruent if the three sides of one triangle are equal to the corresponding three sides of the other triangle.

it is given that ,MQ = NQ; Q is the midpoint of LP; LM ≅ PN Triangles M L Q and N P Q are connected at point Q.

so ,

Comparing △MLQ and  △NPQ

ML = NP   ( as given LM ≅ PN )

LQ = PQ   (∵ Q is the midpoint of LP)

MQ = NQ  Given

=> △MLQ   ≅   △NPQ  using SSS criteria

SSS - Side Side Side

Corresponding sides of triangles are equal

SSS Congruence theorem can be used to prove △MLQ ≅ △NPQ.

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Answer:

32

Step-by-step explanation:

The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:

1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)

2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:

\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)

3. Simplify the equation:

\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)

4. Combine like terms:

  -x^3 - x^2 + 14x - 8 = 16x

5. Move all terms to one side of the equation:

\(-x^3 - x^2 - 2x - 8 = 0\)

6. Rearrange the equation in descending order:

  -x^3 - x^2 - 2x + 8 = 0

7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.

8. Divide the equation by (x - 2):

\(-(x - 2)(x^2 + x - 4) = 0\)

9. Apply the zero product property:

  x - 2 = 0 or x^2 + x - 4 = 0

10. Solve each equation separately:

   x = 2

11. Solve the quadratic equation:

   For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:

 \(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)

Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

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Solution: 60 ml

$ | The volume of the rock is calculated by subtracting the final volume from the initial volume. In this case, 125ml - 65ml = 60ml.

Answer:

A=False

B=True

C=True

Step-by-step explanation:

An inscribed circle is tangent to

all 3 sides of the triangle it is inscribed in.

The correct option is the second option

Explanation

A circle is inscribed in the triangle if the triangle's three sides are all tangents to a circle. In this situation, the circle is called an inscribed circle, and its center is called the inner center, or incenter.

Since the triangle's three sides are all tangents to the inscribed circle, the distances from the circle's center to the three sides are all equal to the circle's radius

The correct option is C, Prices have increased about 16-fold over the last 80 years, assuming an average annual U.S. inflation rate of 4 percent.

The inflation rate is a measure of the rate at which the general level of prices for goods and services is rising over a period of time, usually a year. It is typically expressed as a percentage increase or decrease in the average price level of a basket of goods and services over a certain period of time.

Here, the price index is a weighted average of the prices of a specific set of goods and services. The inflation rate is a key indicator of the overall health of an economy, as high inflation can erode purchasing power and reduce the standard of living for individuals, while low or negative inflation can lead to economic stagnation or deflation. Governments and central banks closely monitor inflation rates to ensure that they remain within a targeted range, typically around 2-3% per year, through the use of monetary and fiscal policies.

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Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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Step 1: Let's recall what is SAS:

"SAS" means "Side, Angle, Side"

Step 2: Let's use The Law of Cosines to calculate the unknown side of the triangles given:

Formula of The Law of Cosines is:

In the triangle ABC, we have:

b = 15, c = 21 and angle A is 75 degrees

Step 3: Substitute the values given in the formula

Step 4: Let's use The Law of Sines to find the smaller of the other two angles

Step 5: Find the last angle, recalling that the interior angles of a triangle add up to 180 degrees

Now, we have the sides and the angles of triangle ABC:

Sides = 15,21, 22.43

Angles = 75, 64.74, 40.26

The  valid license plates are possible = 676,000 possibilities

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The subset's components are given in a permutation in a certain order.

There is no prohibition on using the same letters or numbers more than once, therefore all 26 letters of the alphabet and all 10 numerals are permissible choices.

There are 26 options if the initial answer is A:

AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

There are 26 options if the initial answer is B:

BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

So,

The first letter can be one of 26 options, and the second letter can be one of 26 options. There are a variety of 2 letter combinations, including:

26 x 26 = 676

For the three digits, the same holds true.

The first, second, and third options each have ten options available:

10  × 10 × 10 = 1000

Thus, there are several options for a license plate with two letters and three digits:

26 x 26 x 10  × 10 × 10 =  676,000 possibilities.

The  valid license plates are possible = 676,000 possibilities.

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Point slope form of the line is y−9=−1/4(x+2) y-9 = -1/4 (x+2)

What do you mean by point slope form of the line?

The equation is useful when we know :

One point on the line: (x1, y1)

the slope  sof the line: m,

and want to find other points on the line.

The "point-slope" form of the equation of a straight line is:

y - \(y_{1}\) = m(x - \(x_{1}\))

Given passing point, (\(x_{1},x_{2}\)) = (-2,9)

Slope of the line, m = -1/4

Point slope form of the line ⇒ y - \(y_{1}\) = m(x - \(x_{1}\))

⇒ y - 9 = -1/4 (x - (-2))

⇒ y - 9 = -1/4(x + 2)

⇒ y - 9 = -x/4 - 1/2

⇒ y = -x/4 - 1/2 + 9

⇒ y = -x/4 + (-1/2 + 9)

⇒ y = -x/4 + 17/2

⇒ y = \(\frac{-x+34}{4}\)

⇒ 4y = -x+34

⇒ 4y + x = 34

It can also be written as y - 9 = -1/4(x + 2)

Therefore, point slope form of the line is y - 9 = -x/4 - 1/2 = -1/4(x + 2)

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Step-by-step explanation:

remember, the domain is the interval or set of all valid x values, the range is the interval or set of all valid y values (functional result values).

1.

domain : -infinity < x < +infinity

range : -1 <= y < +infinity

due to the x² term that part can never be negative. the minimum is 0, and then -1 gives us a overall minimum -1. and then up ... the sky is the limit ...

2.

domain : every value of x that does not turn (3x + 5) to 0 and therefore does not cause a 1/0 situation.

the only forbidden value of x is therefore

3x + 5 = 0

3x = -5

x = -5/3

so, (-infinity < x < -5/3) OR (-5/3 < x < +infinity)

range : -infinity < y < +infinity

3.

domain : -infinity < x < +infinity

range : 0 <= y < +infinity

due to the x⁴ term (even exponent) all results will be positive starting with 0. similar to 1.

4.

this is 1/(2x) as I understand it.

similar to 2. we must avoid at 1/0 situation.

so, x must not be 0. everything else is possible

domain : (-infinity < x < 0) OR (0 < x < +infinity)

range : -infinity < y < +infinity

5.

everything is allowed and possible.

domain : -infinity < x < +infinity

range : -infinity < y < +infinity

An insurance company experienced the following mobile home losses in 10,000's of dollars for 50 catas- trophic events: The answers are as follows:

(a) To find the five-number summary of the data, we arrange the losses in ascending order:

1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 7, 7, 9, 9, 10, 11, 12, 22, 24, 28, 29, 31, 33, 36, 38, 38, 38, 39, 41, 48, 49, 53, 74, 82, 117, 134, 192, 207, 224, 225, 236, 280, 301, 308, 351, 527

The five-number summary consists of the minimum value (1), the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value (527):

Minimum: 1

Q1: 5

Q2 (Median): 29

Q3: 74

Maximum: 527

Using these values, we can draw a box-and-whisker diagram.

(b) The Interquartile Range (IQR) is calculated by subtracting Q1 from Q3: IQR = Q3 - Q1 = 74 - 5 = 69

The inner fences are calculated as follows:

Lower Inner Fence (LIF) = Q1 - 1.5 * IQR

Upper Inner Fence (UIF) = Q3 + 1.5 * IQR

The outer fences are calculated as follows:

Lower Outer Fence (LOF) = Q1 - 3 * IQR

Upper Outer Fence (UOF) = Q3 + 3 * IQR

(c) The box plot can be drawn using the five-number summary, the fences, and identifying suspected outliers and outliers based on their position relative to the fences.

(d) Based on the distribution of losses, we can observe that there are some high values that significantly deviate from the majority of the data points, which are relatively lower. This indicates a right-skewed distribution, where the majority of losses are concentrated at the lower end, with a few extreme values at the higher end.

The presence of suspected outliers and outliers also suggests the presence of significant variability in the losses experienced by the insurance company.

Note: The specific values and the visual representation of the box-and-whisker diagram and box plot may vary based on the software or method used for analysis.

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Answer:

the second one i think

Step-by-step explanation:

I looked it up for you : )

Answer:

true

Step-by-step explanation:

if there is no y intercept then it is 0

Answer:

42c

Step-by-step explanation:

ANSWER

The percent error is 10.9 %

EXPLANATION

The percent error is:

In this problem, the approximate value is 16 and the exact value is 14.25:

Answer:

10.9%

Step-by-step explanation:

14.25/16 = 0.890625

0.890625 * 100 = 89.0625

1 - 89.0625 = 10.9375%

Answer: r=2.69. Calculate the radius of circle:Round the number: r=2.69Answer: r=2.69

Answer:

S

C

H

O

O

L

Step-by-step explanation:

Seven

Consecutive

Hours

Of

Our

Lives