Find the general solution to y'' + 5y' - 14y = 0|, Give your answer as y = ... |, in your answer, use c_1| and c_2| to denote arbitrary constants and the independent variable. Enter c_1| as c1 and c_2| as c2.

The number of blue fish in the aquarium is 0.8 or 80% of the total fish.

Let's use algebraic reasoning to solve the problem.

Let's assume the number of blue fish in the aquarium is represented by the variable 'B'.

According to the given information:

The number of red fish is 1 less than the number of blue fish, which can be represented as (B - 1).

60% of the fish in the aquarium are blue, so the total number of fish can be represented as 100% or 1 whole, which can be written as 1.

To set up an equation, we can write:

(B - 1) + B = 0.6 * 1

Now, let's solve the equation step by step:

(B - 1) + B = 0.6

Combining like terms:

2B - 1 = 0.6

Adding 1 to both sides:

2B = 0.6 + 1

2B = 1.6

Dividing both sides by 2:

B = 1.6 / 2

B = 0.8

Therefore, the number of blue fish in the aquarium is 0.8 or 80% of the total fish.

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The solutions to the right triangle in this problem are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle A is given as follows:

m < A + 50 + 90 = 180

m < A = 180 - 140

m < A = 40º.

Side b is opposite to the angle of 50º, while 21 is the adjacent side to the angle of 50º, hence:

tan(50º) = b/21

b = 21 x tangent of 50 degrees

b = 25.

The hypotenuse c is then obtained as follows:

sin(50º) = b/c

c = 25/sine of 50 degrees

c = 32.6.

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The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.

Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.

This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.

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Answer:

250 and 10

Step-by-step explanation:

substitute x = 10 into the expressions

a = \(\frac{5x^2}{2}\)

  = \(\frac{5(10)^2}{2}\)

  = \(\frac{5(100)}{2}\)

  = \(\frac{500}{2}\)

  = 250

-----------------------------------------------

b = \(\frac{2x^2(x-5)}{10x}\)

  = \(\frac{2(10)^2(10-5)}{10(10)}\)

  = \(\frac{2(100)(5)}{100}\) ( cancel 100 on numerator and denominator )

  = \(\frac{2(5)}{1}\)

  = 10

Answer:

D. 66

Hope this helps!!

Answer:

The equation has a maximum value with a y-coordinate of -21.

Step-by-step explanation:

Given

\(y =-3x^2 + 12x - 33\)

Required

The true statement about the extreme value

First, write out the leading coefficient

\(Leading = -3\)

\(-3 < 0\) means that the function would be a downward parabola;

Downward parabola always have their vertex on top of the parabola and as such, the function has a maximum value.

The maximum value is:

\(x = -\frac{b}{2a}\)

Where:

\(a= -3; b =12; c =-33\)

So, we have:

\(x = -\frac{12}{2 * -3}\)

\(x = -\frac{12}{-6}\)

\(x =2\)

Substitute \(x =2\) in \(y =-3x^2 + 12x - 33\)

\(y = -3*2^2 + 12 * 2 - 33\)

\(y = -21\)

Hence, the maximum is -21.

Answer:

The range is all values greater than or equal to -1

y : y≥-1

Step-by-step explanation:

f(x)=(x-4)(x-2)

This functions is an upwards facing parabola.  This means it has a minimum

The minimum is 1/2 way between the zeros

0=(x-4)(x-2)

x-4 =0   x-2 =0

The zeros are at 4 and 2

(4+2)/2 = 6/2 =3

The minimum is at x=3

The minimum value is at

f(3) = (3-4) (3-2) = -1 (1) =-1

The range is all values greater than or equal to -1

y : y≥-1

Answer:

Range: y 》-1

Step-by-step explanation:

f(x) = (x - 2)(x - 4)

f(x) = x² - 2x - 4x + 8

f(x) = x² - 6x + 8

f(x) = x² - 2(x)(3) + 3² - 3² + 8

f(x) = (x - 3)² - 1

Vertex: (3,-1)

Minimum value: -1

Range: y 》-1

A gradual upward or downward movement of data over time is called a trend. A trend indicates a consistent, long-term increase or decrease in data points, showing either an upward or downward movement over time.

A trend is a pattern in data that shows a gradual change in one direction over time. It can be identified by looking at the data over a long period and observing any consistent increase or decrease in the data points. A trend can be either upward or downward, indicating either an increase or a decrease in the data points over time.

For example, if we observe the sales data of a company over several years and notice a consistent increase in the sales figures, then we can say that there is an upward trend in the sales data. On the other hand, if we observe a consistent decrease in the sales figures over several years, then we can say that there is a downward trend in the sales data.

Trends can be helpful in making predictions about the future performance of a company or any other entity. They can be used to identify potential growth or decline in the future. However, it is important to note that trends are not always indicative of future performance as other factors can come into play and affect the data.

In summary, a trend is a gradual upward or downward movement of data over time. It indicates a consistent, long-term increase or decrease in data points, showing either an upward or downward movement over time.

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The domain and the range of the function are (-∝, ∝) and (-∝, 2), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an absolute function

The rule of this function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (-∝, 2)

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The original number of students scheduled to go on the field trip was 600.

Let the original number of buses be "x" and each bus having "y" students, we can use algebra to solve for the number of students on the field trip.

It is given that; x*y = 600, that is, the original number of students is 600. When the organizer increases the number of buses by 4, the number of buses will be (x + 4), and the number of students per bus decreases by 5. We can express this as y - 5.

Hence, the new number of students will be 600 since no new students were added. We can represent this using the equation (x + 4) * (y - 5) = 600.

Substituting x*y = 600, we get x*(y-5) = (x + 4) * (y - 5).

Expanding the equation above, we get; xy - 5x = xy - 5y + 20.

Rearranging, we have 5x - 5y = 20. Dividing both sides by 5, we get x - y = 4.

Substituting xy = 600, we get x * (x - 4) = 600. Solving this quadratic equation, we get x = 24 or x = - 25.

We discard the negative solution. Therefore, the original number of students scheduled to go on the field trip was

24 * 25 = 600 students.

Therefore, the conclusion is that the original number of students scheduled to go on the field trip was 600.

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Answer:

6 games and 2 rides

Step-by-step explanation:

Start with the equation 3*1.50x+3y=15

Then plug that equation into desmos graphing calculator

Then round up

This will tell you the number of games, and rides Adam went on

Answer:

The length of AC is 5.8 m

Step-by-step explanation:

In the kite, the longest diagonal is the axis of symmetry of the shortest diagonal which means the longest diagonal perpendicular to the shortest diagonal and bisects it (divide it into two equal parts)

In the given figure

∵ ABCD is a kite

∵ AC is the shortest diagonal

∵ BD is the longest diagonal

→ By using the fact above

∴ BD ⊥ AC

∴ BD bisects AC

∵ AC ∩ BD at the point N

→ That means N is the midpoint of AC

∴ N is the midpoint of AC

∴ AN = NC

∵ AN = 2.9 m

∴ NC = 2.9 m

∵ AC = AN + NC

∴ AC = 2.9 + 2.9

∴ AC = 5.8 m

∴ The length of AC is 5.8 m

Answer:

B) USA

Step-by-step explanation:

USA is in North America

The seismograph reading of the earthquake is approximately 1.99526.To determine the seismograph reading of the earthquake with a magnitude of 3.3 on the Richter scale, we can use the formula M(I) = log(I/0.001), where M(I) represents the magnitude and I represents the intensity of the earthquake.

In this case, we are given the magnitude of 3.3. Let's substitute this value into the formula and solve for I:

3.3 = log(I/0.001)

To isolate I, we need to convert the equation into exponential form:

10^(3.3) = I/0.001

Simplifying the equation, we have:

I = 10^(3.3) * 0.001

Using a calculator, we find that 10^(3.3) is approximately 1995.26.

So, the seismograph reading of the earthquake is:

I = 1995.26 * 0.001

≈ 1.99526.

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The  IRS form is provided at the end of the year by employers, so employees can use it to file taxes is Form W-2.

Form W-2 can be described as the form that is been offered from the  Internal Revenue Service which can be considered as the (IRS) tax form .

It should be noted that this form is been used in the United States so that the wages that is been paid to employees  as well as their taxes can be reported. withheld from them

It should be noted that the form is been provided  when the year is coming to an end by employers.

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Answer:

TRUE!

Step-by-step explanation:

1 liter (L) = 1000 milliliters (mL)

If you have 2 Liters, then you would DOUBLE the milliliters (2000)

It is true that the existence of two local maxima does not guarantee the presence of a local minimum. It is possible for a function to have multiple local maxima and no local minimum.

For example, consider the function f(x,y) = x^4 - 4x^2 + y^2. This function has two local maxima at (2,0) and (-2,0), but no local minimum. Therefore, the statement "if f(x,y) has two local maximal, then f must have a local minimum" is false. The presence or absence of local maxima and minima depends on the behavior of the function in the immediate vicinity of a point, and cannot be determined solely based on the number of local maxima. It is possible for a function to have an infinite number of local maxima and minima, or none at all. Therefore, it is important to carefully analyze the behavior of a function in order to determine the presence or absence of local extrema.

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Answer:

108

Step-by-step explanation:

for graph this equation,

we will calculate the point on this line,

the equation is

y = 1/2x-2

when x = 0

y = 1/2 (0) - 2

y = -2

thus, the point is (0, -2)

when x = 2

y = 1/2 (2) - 2

y = 1 - 2

y = -1

thus, the point is (2, -1)

when x = 4

y = 1/2(4) - 2

y = 2 - 2

y = 0

thus, the point is , (4, 0)

so we mark these points on the graph and join them to get a line on the graph.

A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.

In statistics, the analysis of variance (ANOVA) method is used to compare the means of two groups.

In an experiment with a completely randomized design, samples are at random assigned to either a treatment group or a placebo group.

For instance, if 40 persons are chosen to evaluate the effects of an analgesic,

four groups—Groups A, B, C, and D—could be created. Different dosages of the medication can be administered to Groups A, B, and C, while Group D receives a placebo. Due to the random grouping of the participants

, this is an illustration of a randomized design.

We assume that the sample populations are normally distributed and have the same variances in order for an ANOVA test to display completely randomized design.

Hence, A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.

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The exact forecasted number of customers to be served on each of the next five business days, rounded to one decimal place, are as follows:

Tuesday: 389.1

Wednesday: 368.7

Thursday: 326.5

Friday: 510.9

To forecast the number of customers served on each of the next five business days using Winters' method, we need to follow these steps:

Calculate the seasonal factor for each day by multiplying the seasonal index by the level.

Monday: 1.10 × 20 = 22

Tuesday: 0.95 × 20 = 19

Wednesday: 0.90 × 20 = 18

Thursday: 0.80 × 20 = 16

Friday: 1.25 × 20 = 25

Update the level and trend using the following formulas:

New Level = α × (Actual Value / Seasonal Factor) + (1 - α) × (Previous Level + Previous Trend)

New Trend = β × (New Level - Previous Level) + (1 - β) * Previous Trend

For Tuesday:

New Level = 0.2 × (30 / 22) + 0.8 × (20 + 1) = 20.3636

New Trend = 0.1 × (20.3636 - 20) + 0.9 × 1 = 0.0364

Forecast the number of customers served on each subsequent day using the formula:

Forecast = (New Level + Forecasted Trend) × Seasonal Factor

Tuesday Forecast = (20.3636 + 0.0364) × 19 = 389.0909

Wednesday Forecast = (20.3636 + 0.0364) × 18 = 368.7273

Thursday Forecast = (20.3636 + 0.0364) × 16 = 326.5455

Friday Forecast = (20.3636 + 0.0364) × 25 = 510.9091

Therefore, the forecasted number of customers to be served on each of the next five business days, rounded to one decimal place, are as follows:

Tuesday: 389.1

Wednesday: 368.7

Thursday: 326.5

Friday: 510.9

The question should be: A local bank is using Winters' method with α = 0.2, β= 0.1, and γ = 0.5 to forecast the number of customers served each day. The bank is open Monday through Friday. At the end of the previous week, the following seasonal indexes have been estimated: Monday, 1.10; Tuesday, 0.95; Wednesday, 0.90; Thursday, 0.80; Friday, 1.25. Also, the current estimates of level and trend are 20 and 1. After observing that 30 customers are served by the bank on this Monday, forecast the number of customers who will be served on each of the next five business days. Round your answers to one decimal place, if necessary.

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The distance between point A and B will be;

D = √72k² - 24k while the coordinates of the mid-point of the line joining A to B will be (4k + 1, -1).

Distance between two points is the length of the line that connects the two points on a plane.

The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

d=√((x2 – x1)² + (y2 – y1)²)

where x1 = 7k

x2 = 2+k

y1 = -3k

y2 = 3k - 2

d = √((2+k -7k)² + (3k -2 +3k)²

d = √((2 - 6k)² + (6k -2)²

d = √4 - 12k + 36k² + 36k²  - 12k - 4

d = √72k²  - 24k

Mid-points

X = (X1 + X2)/2

X = (7k + 2 + k)/2

X = (8k + 2) / 2

X = 4k + 1

Y = 3k - 2 + (-3k)

Y = -2/2

Y = -1

Midpoints (4k + 1, -1)

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Answer:

19

Step-by-step explanation:

A' represents everything out A

B' represents everything out B

C' represents everything out C

So only the outside is left hope this helps

Given:

The height of the girl is 5 ft and the length of the shadow is 2 ft., at the same time the shadow of the building is 50 ft .

Required:

To find the height of the building.

Explanation:

Let the height of the building is h ft.

Since triangle ABC is similar to the triangle DEF.

Thus by using the similarity condition.

Final Answer:

Thus the third option is the correct answer.

shld be either c or d I don't rlly know

Answer:

mC =mA

mC=57

FIRST OPTION IS THE ANSWER

Answer: The conversion of a raw score to a scaled LSAT score is a complex process that involves several steps. The Law School Admission Test (LSAT) is a standardized test used by law schools in the United States and Canada to assess applicants' critical thinking, reading comprehension, and analytical reasoning skills.

Here's a general overview of the process of converting a raw score to a scaled LSAT score:

- Raw score calculation: The raw score is the number of questions answered correctly on the LSAT. There is no penalty for incorrect answers, so it is in your best interest to answer every question, even if you are unsure of the correct answer.

- Equating: The LSAT is equated to account for differences in difficulty between test forms. This means that the raw scores of test-takers are adjusted so that the scaled scores are consistent across different test forms.

- Scaling: The raw scores are then scaled to a range of 120 to 180, with a median score of 150 and a standard deviation of 10. This scaling process allows for meaningful comparisons between test-takers, regardless of the difficulty of the specific test form they took.

It is important to note that the LSAT score is not based solely on the number of questions answered correctly, but also on the difficulty of the questions. This means that a high raw score on a particularly difficult test form may result in a lower scaled score than a lower raw score on a less difficult test form.

Step-by-step explanation:

Answer:

8÷(x+3)

Step-by-step explanation:

it doesnt specify what number you add with 3 so you substitute it with a variable such as x.

The sum is adding so x +3 and then divide by 8

Answer:

I. y = |x + 4|

Step-by-step explanation: