4. How do you solve x2 + 9x - 3 = 0 using the completing-the-square method?

Answer:

The first derivative of \(r(t) = 5\cdot t^{-2}\) (r(t)=5*t^{-2}) with respect to t is \(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3}).

Step-by-step explanation:

Let be \(r(t) = \frac{5}{t^{2}}\), which can be rewritten as \(r(t) = 5\cdot t^{-2}\). The rule of differentiation for a potential function multiplied by a constant is:

\(\frac{d}{dt}(c \cdot t^{n}) = n\cdot c \cdot t^{n-1}\), \(\forall \,n\neq 0\)

Then,

\(r'(t) = (-2)\cdot 5\cdot t^{-3}\)

\(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3})

The first derivative of \(r(t) = 5\cdot t^{-2}\) (r(t)=5*t^{-2}) with respect to t is \(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3}).

Answer:

\({ \tt{x + 4 = {x}^{2} }} \\ { \tt{ \sqrt{(x + 4)} } = \sqrt{ {x}^{2} } } \\ { \tt{ \sqrt{(x + 4) } = x}}\)

Answer:

If the number gets bigger to the right.

The number gets less if it moves to the left.

Step-by-step explanation:

Answer:

You move the decimal points the amount at which the number that is next to the 10 is, or you could find 10^3, which is 1000, and move the decimal to the right 3 times (or places)... Resulting in 4,580... Do you understand?

Answer: The answer is 780, Option C.

Step-by-step explanation: Substitute 70 for N, you should get 500+4(70). That simplifies to 780.

To calculate probability of at least 6 graduates out of 11 ,we use binomial distribution formula. P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) by substituting values we get answer.

Let's denote the probability of a graduate having a summer job as p, which is given as 0.45, and the total number of graduates selected as n, which is 11. To find the probability of at least 6 graduates having a summer job, we need to sum up the probabilities of exactly 6, 7, 8, 9, 10, and 11 graduates having a summer job. This can be expressed as:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11)

Using the binomial distribution formula, the probability of exactly x successes in n trials is given by:

P(X = x) = C(n, x) * p^x * (1 - p)^(n - x)  where C(n, x) represents the number of combinations of n items taken x at a time.

Substituting the given values, we can calculate the probability as:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11)  Once the calculations are performed, the resulting probability represents the likelihood that at least 6 out of 11 randomly selected graduates have a summer job.

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If the \(z\)-score is \(z_1 < 0\), find the area under the curve to the right of \(-z_1\) and subtract that from 1.

If the z-score is z<0 , find the area under the curve to the right of -z  and subtract that from 1.

what is z-score?

z-score is a statistical measurement that describes a value's relationship to the mean of a group of values and the formula for the z-score is

z = (x - μ)/σ

x = data point

μ = mean

σ = standard deviation

Mean:- The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

Now,

As we know the area is just the space according to given condition

and if we find the area to the right of -z and substract it from 1 (as for z-score whole area is 1 square unit) then we get the area for z<0.

Hence,

             If the z-score is z<0 , find the area under the curve to the right of -z  and subtract that from 1.

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The appropriate family of distributions to approximate the probability of rolling a 6 on a fair die is the discrete uniform distribution, which assumes equal probabilities for each outcome. In this case, the probability of rolling a 6 would be approximately 1/6 based on the assumption of fairness.

For the problem of approximating the probability of rolling a 6 on a fair die, an appropriate family of distributions to consider is the discrete uniform distribution.

The discrete uniform distribution is commonly used to model situations where each outcome has an equal probability of occurring. In the case of rolling a fair die, the die has six equally likely outcomes (numbers 1 to 6).

Each outcome has a probability of 1/6 of occurring, making the discrete uniform distribution a suitable choice.

By assuming a discrete uniform distribution, we can assign equal probabilities to each outcome (1/6 for rolling a 6) and approximate the probability of rolling a 6 based on the assumption of fairness.

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Answer:

Carl can type 450 words in 5 minutes at that rate.

Step-by-step explanation:

Every two minutes, carl can type 180 words. To find out how many words he can type in 1 minute, all we have to to is divide 180 by 2 to get 90wpm (words per minute)

if we multiply 90wpm by 5 Minutes, we get 450 words per minute

Answer:

3/7 divided by 2 1/2 = 6/35

Explanation:

3/7 ÷ 2 1/2

= 3/7 ÷ 5/2

= 3/7 × 2/5

= (3 × 2)/(7 × 5)

= 6/35

Answer:

I think it's A

Step-by-step explanation:

225x + 400 ≥ 2200

225x ≥ 1800

x ≥ 8

Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.

The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.

Identify the null and alternative hypotheses.

As well as the sample size, specify.

Choose a suitable statistical test.

Gather information (note that the previous steps should be done prior to collecting data)

Based on the sample data, compute the test statistic.

Examine the null hypothesis, usually indicated by H0.

Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).

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Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.

Here,

Given:

Mean = 2

Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.

We can determine that at least

100 (1-1k2)% = 100 (1-1/4)% = 75%

is within 2 standard deviations of the mean using Chebyshev's Rule with

k = 2.

The percentage times the sample size yields the equivalent number of households:

=> 75% x 40 = 30

Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

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The derivatives for x, y, and dy/dx are dx/dt = 15t² + 3, dy/dt = 4 - 12t, and dy/dx = (4 - 12t) / (15t² + 3), respectively.

To find dx/dt, we need to take the derivative of x with respect to t:

dx/dt = d/dt (5t³ + 3t) = 15t² + 3

To find dy/dt, we need to take the derivative of y with respect to t:

dy/dt = d/dt (4t - 6t²) = 4 - 12t

To find dy/dx, we need to take the derivative of y with respect to x:

dy/dx = (dy/dt) / (dx/dt)

Substituting the expressions we found above, we get:

dy/dx = (4 - 12t) / (15t² + 3)

Note that dy/dx is a function of t, so its value depends on the value of t at a particular point.

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

Explanation:

Perfect square trinomials are in the form (a+b)^2 = a^2+2ab+b^2

So the first and last terms must be perfect squares. The middle term is twice that of the square roots of each first and last term.

Choice D fits the description because 4x^2 = (2x)^2 is the first term, so a = 2x and 25 = 5^2 is the last term meaning b = 5. Note how 2ab = 2*2x*5 = 20x is the middle term.

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

(a+b)^2 = a^2+2ab+b^2

(2x+5)^2 = (2x)^2+2*2x*5+5^2

(2x+5)^2 = 4x^2 + 20x + 25

Answer:

(2x+5)² or (2x+5)(2x+5)

Step-by-step explanation:

4x²+ 20x + 25

(2x       ) (2x      )     first step 2x*2x=4x²

(2x  +  5   )(2x  +   5  )  the constant sign is plus so it can be ( minus × minus=plus OR plus×plus=plus) look at the middle value it is positive so the two signs are positive or plus sign.

(2x+5)²

Answer:

y = -3/4x + 9

Step-by-step explanation:

first, find the slope by taking the difference of the y-values / difference of the x-values

(-3-12) / (16-(-4)) which equals -15/20 or -3/4

now use that value to represent the 'm' in the formula in order to find 'b'

y = mx + b

-3 = -3/4(16) + b

-3 = -12 + b

9 = b

y = -3/4x + 9

Answer:

3(1-7x) is first step

Step-by-step explanation:

Answer:

BIDMAS

Step-by-step explanation:

brackets

indices

division

multiplication

addition

subtraction

so.. do everything inside the brackets and then use the square

hope this helps! :)

The given statement is false because In programming, the break and continue statements serve different purposes and can be used independently or together within nested loops.

The break statement is used to exit the current loop prematurely. When encountered, it terminates the loop and continues with the next statement after the loop. This can be useful when a specific condition is met, and you want to stop the execution of the loop immediately.

The continue statement, on the other hand, is used to skip the current iteration of a loop and move on to the next iteration. It allows you to skip certain iterations based on a specific condition without terminating the entire loop.

Both break and continue statements can be used within nested loops. In such cases, the break statement will exit only the innermost loop it is placed in, while the continue statement will skip to the next iteration of the innermost loop.

By using break and continue strategically within nested loops, you can control the flow of execution based on specific conditions. This flexibility allows you to fine-tune the behavior of your program and optimize its efficiency.

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Note : This is a computer science question

Answer:

1. 0.6 (continues)

2. 1.3 (continues)

3. 2

4.  2.7

The correct check digit for the UPC code 6-73419-23216- is "3".

The check digit is used to verify the accuracy of the UPC code when it's scanned. It's the last digit of a UPC code and is calculated using a formula based on the first 11 digits.

The formula involves adding up the digits in the odd-numbered positions and multiplying the sum by three, then adding up the digits in the even-numbered positions, and subtracting the second sum from the first sum.

The check digit is then calculated by taking the difference and finding the smallest number that, when added to the difference, is a multiple of 10. The result of this calculation is the check digit.

In this case, the correct check digit is "3".

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Answer: only 2 (y = -1/2x - 3)

Step-by-step explanation: so first find the gradient by doing y minus x and dividing

-4-0/2--6 which equals -1/2 so you know that -1/2 is your gradient. 2 is the only one with a gradient of -1/2x.

Hope this made sense. If not I'll explain again

Answer:

hope it helps

Step-by-step explanation:

angle < EDG = 90°

5x + 4x = 90

9x = 90

x = 90/9

x = 10°

which means

5x = 50°

4x = 40°

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

sice EF and DG are parallel lines

EHD = 40°

DHG is 90°

then HGD = 50°

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

ED = 64 x2 (2 sides) = 128 inches

DG = 84 x2 (2 sides) = 168 inches

total perimeter = 128 + 168 = 296 inches

and yes. theres enough room for all 3 to cuddle

Answer: 2cm

Step-by-step explanation:

Answer:

x=53°

(x+2)=55°

Step-by-step explanation:

Add all the angles up to equal 180, because all triangles equal 180.

(x+2)+x+72=180

Simplify and solve for x.

2x+74=180

-74=-74

2x=106

2 = 2

x=53.

Plug x in to the inequalities. Hope this helps.

The first 3 terms of the sequence are 21, 24 and 29

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

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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Answer:

9?

Step-by-step explanation:

The solution is, 76,000 mg chlorine is in the pool.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The pool has 2.5 milligrams of chlorine per liter of water.

There are 8000 gallons of water in the swimming pool.

we know,

1 gallon = 3.785 liters

Water in pool = 8000 x 3.785

Water in pool = 30,280 liters

so, we get,

Chlorine dosage = 2.5 mg / liter

Chlorine = 2.5 x 30,280

Chlorine = 75,700 mg

To the nearest thousand milligram:

Chlorine = 76,000 mg

Hence, The solution is, 76,000 mg chlorine is in the pool.

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The statement 'Revenue management methodology was originally developed for the banking industry.' is False.

The revenue Management is an analytics technique.

This technique is used to predict consumer behavior at the micro-level, which is ultimately useful in optimizing the product availability and pricing and maximize revenue growth.

This methodology is used by companies in certain industries, particularly those with fixed costs and capacity and products or services that expire.

It is the operational procedures and practices that maximize revenues without creating additional products or services.

Therefore, The statement 'Revenue management methodology was originally developed for the banking industry.' is False.

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Answer:

please see analysis

step by step explanation

\(if \: y \: varies \: inversely \: as \: \: as \: x \ \: meanc \\ y = \frac{k}{x} \\ where \: y = 1 \: \: x = 3 \\ 1 = \frac{k}{3} \\ k = 3 \times 1 = 3 \\ equation \: connecting \: x \: and \: y \\ y = \frac{3}{x} \\ finding \: y \: when \: x = 9 \\ y = \frac{3}{9} \\ y = \frac{1}{3} \)

Answer:

when adding 3

6+3=9

when subtracting 2

9-2=7

7,8,9,10,11,12,13,