Factor x² + 25x + 24 in standard form

Greetings from Brasil...

Here's our problem:

\(\large{\frac{12^{16}}{12^{4}}}\)

From potentiation properties:

Mᵃ ÷ Mᵇ = Mᵃ⁻ᵇ

division of power of the same base: I repeat the base and subtract the exponents

Bringing to our problem

12¹⁶ ÷ 12⁴

12¹⁶⁻⁴

Answer:

\(12^{12}\)

Step-by-step explanation:

The distance of the swing of a pendulum decreases by a constant amount each swing. To find the distance of the swing at the tenth swing, you can use the formula:

distance at nth swing = distance at first swing * (1 - decay factor)^(n-1)

Where decay factor is the fractional decrease in distance per swing. In this case, the decay factor is (80 - 76) / 80 = 0.05. Plugging this into the formula above, we get:

distance at 10th swing = 80 * (1 - 0.05)^9 = 53.78 cm

So the distance of the swing at the tenth swing is approximately 53.78 cm.

It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.

If the average student age is not substantially different from 24 years, then the null hypothesis is tested, which is:

\(H_{0}\) : μ = 24

If it differs from 24 years, the alternative premise is tested, so:

\(H_{1}\) :  μ ≠ 24

The z-distribution is utilized because we have the population's standard deviation. The test statistic comes from:

z = x -  μ÷ σ/\(\sqrt{n}\)

The parameters in this issue have the following values:

x(mean) = 25

μ = 24

σ = 2

n=16

As a result, the test statistic's value is:

z = 25-24÷ 2/\(\sqrt{16}\)

z = 2

The probability of a sample mean older than 25 years determines the test's p-value, which is 1 less than the p-value of z = 2.

The p-value for z = 2 in the z-table is 0.9772; 1 - 0.9772 = 0.0228.

Given that the test's p-value is 0.0228 0.05, we may say that:

It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.

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Answer:

I don't know if you are not be in this email

The graph approaches the vertical asymptote at x = 2/3 and the horizontal asymptote y = 1/3 as x approaches positive or negative infinity. The function intersects the x-axis at x = 2 and the y-axis at y = 1.

Holes:

Holes occur when a factor in the numerator cancels out with a factor in the denominator. In this case, the factor (x - 2) can cancel out with the factor (3x - 2). To find the value(s) of x where this occurs, we set the denominator equal to zero and solve:

3x - 2 = 0

3x = 2

x = 2/3

So, there is a hole at x = 2/3.

Vertical Asymptotes:

Vertical asymptotes occur when the denominator becomes zero and the numerator is nonzero. In this case, the denominator is 3x - 2. Setting it equal to zero:

3x - 2 = 0

3x = 2

x = 2/3

Therefore, there is a vertical asymptote at x = 2/3.

Horizontal Asymptotes:

To determine the horizontal asymptote(s), we compare the degrees of the numerator and denominator. In this case, the degree of the numerator is 1, and the degree of the denominator is also 1. Since the degrees are equal, we can find the horizontal asymptote by comparing the coefficients of the highest degree terms. The coefficient of x in the numerator is 1, and the coefficient of x in the denominator is 3. Thus, the horizontal asymptote is given by the ratio of the coefficients: y = 1/3.

x-Intercept:

To find the x-intercept, we set the numerator equal to zero and solve:

x - 2 = 0

x = 2

Therefore, there is an x-intercept at x = 2.

y-Intercept:

To find the y-intercept, we set x equal to zero and evaluate the function:

f(0) = (0 - 2)/(3 * 0 - 2) = -2/(-2) = 1

Therefore, there is a y-intercept at y = 1.

Now, let's graph the function f(x) = (x - 2)/(3x - 2):

There is a hole at x = 2/3, so we exclude this point from the graph.

There is a vertical asymptote at x = 2/3.

There is a horizontal asymptote at y = 1/3.

There is an x-intercept at x = 2.

There is a y-intercept at y = 1.

Based on these characteristics, we can plot the graph of f(x):

      |\

      | \

      |  \

      |   \

      |    \

_______|     \____

      |      \

      |       \

      |        \

      |         \

      |          \

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Answer:

2 4/5

Step-by-step explanation:

Put the whole number to the side and then make a fraction out of the remaining decimal. 8/10 can be simplified to 4/5

Answer:

2 4/5

Step-by-step explanation:

When you see the decimal the whole number is 2, so that doesnt change.

Next you see the 8 in the tenths place. Whatever place the digit is in is its  denominator. So 8 in the tenths place is 8/10.

Simplify and it becomes 4/5. Attatch to the whole number and your done.

Answer:

A: Decrease, y is 80% of x

B: Increase, y is 160%of x

Step-by-step explanation:

It sounds like it wants to know what percent Y is of X, so if y was 50% of x, that would mean y was half as much of x. so if x was 10 and y was 5

A:  x is 5 and y is 4  since y is less it is a decrease.  to find the percent do 100*y/x, so in this case that's 100*4/5 =80, so y is 80% of x.  and it makes sense it is less than 100% since x is less than y

B: x=5 and y=8  y is greater than x so it is an increase and will be more than 100%.  100*8/5 = 160 so y is 160% of x

Height of cylinder is 5 units

Define Cylinder

               ⇒ V = (π × radius²) × h

We have given,

Slant height of cylinder = √29

Radius is = 2 units

Now, we to have to calculate the height for that we have the formula

h = √l² - r²

where, l = slant height

            r = radius of the circular base

            h = height of the cylinder

Now, for the sake of simplicity

h = √l² - r²

h² =  l² - r²

Now, plug in the values

h² = (√29)² - 2²

h² = 29 - 4

h² = 25

h = 5

Hence, the height of cylinder is 5 units

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The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will  lighter, not darker.

The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.

Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.

After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.

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Riya earns $45 in commission for selling 15 newspaper ads at $50 each.

A commission is a charge or payment given to a person or group in exchange for a good or service. When selling goods or services on behalf of a corporation, sales representatives or agents are frequently compensated with commissions in the business world. For instance, a stockbroker may receive a fee for carrying out a trade on behalf of a customer, while a real estate agent may receive a commission depending on the sale price of a property they assist in selling.

Riya receives a 6% commission for selling newspaper ads, and if she sells 15 ads for $50 each, her total earnings can be calculated as follows:

Total earnings = Total sales x Commission rate

The total sales from selling 15 ads at $50 each are:

Total sales = 15 x $50 = $750

The commission rate is 6%, which can be written as 0.06 as a decimal.

Plugging these values into the formula, we get:

Total earnings = $750 x 0.06 = $45

Therefore, Riya earns $45 in commission for selling 15 newspaper ads at $50 each.

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Therefore the base of the triangle is 8 centimeters.

The area of the triangle is calculated by using the formula listed below,

Area of the triangle = \(\frac{1}{2} * base * height\)

From the given data area = 28.8 square centimeters

Height = 7.2 centimeters

Therefore to find the base,

\(28.8 = \frac{1}{2} * base * 7.2\)

base = \(\frac{28.8 * 2}{7.2}\)

base = 8 centimeters

Therefore the base of the triangle is 8 centimeters.

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Complete question:

The area of the triangle below is 28.8 square centimeters What is the length of the base? 7.2 cm

Answer:

Answer: There is 32in² more sand in the pyramid with greater volume.

step explanation:

Answer:

y = 2x + 5

Figure 505

Step-by-step explanation:

(3,11) ( 4,13)

Find the slope

Change in y over the change in x

\(\frac{13-11}{4-3}\) = \(\frac{2}{1}\) = 2

slope (m) is 2.

Part A

Find the y -intercept

m = 2

x = 3     from the point (3,11)

y = 11    from the point (3,11)

y = mx + b  Substitute what I know and solve for b

11 = (2)(3) + b

11 = 6 + b  Subtract 6 from both sides

11 - 6 = 6 -6 + b

5 = b

The y intercept (b) is 5

y = mx + b

y = 2x + 5

Part B

y =  2x + 5

1015 = 2x + 5  Subtract 5 from both sides

1015 - 5 = 2x + 5 - 5                                                    

1010 = 2x  Divide both sides by 2

505  

Answer:

\( \frac{3}{20} \)

Step-by-step explanation:

\(15\% = \frac{15}{100} \)

So,

\( \frac{15 \div 5}{100 \div 5} = \frac{3}{20} \)

hope this helps you.

The probability of at most six individuals in the sample having used a discount broker is calculated to be approximately 0.997.

To solve this problem, we need to use the binomial distribution formula. Let X be the number of individuals in the sample who have used a discount broker. Then, X follows a binomial distribution with parameters n = 9 and p = 0.3.

The probability of at most six individuals in the sample having used a discount broker can be calculated as follows:

P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 6)

Using a binomial probability table or calculator, we can find the individual probabilities and sum them up. Alternatively, we can use a normal approximation to the binomial distribution if the sample size is large enough (np and n(1-p) are both greater than 5).

Using the normal approximation, we have:

mean = np = 9 x 0.3 = 2.7

variance = np(1-p) = 9 x 0.3 x 0.7 = 1.89

standard deviation = √(variance) = 1.374

To standardize the distribution, we calculate the z-score:

z = (6.5 - 2.7) / 1.374 = 2.75

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than or equal to 2.75 is approximately 0.997.

Therefore, the probability of at most six individuals in the sample having used a discount broker is approximately 0.997.

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The complete question is :

What is the probability that in a random sample of nine individual investors, at most six have used a discount broker, given that the American Society of Investors survey found that 30% of individual investors have used a discount broker?

Answer:

65+5x=180

Step-by-step explanation:

Answer:

-7m(1.2m - 2) + (-6m) = -8.4m² + 8m

Step-by-step explanation:

Let us simplify the given expression

∵ The expression is -7m(1.2m - 2) + (-6m)

→ At first multiply the bracket by -7m

∵ -7m(1.2m - 2) = (-7m)(1.2m) - (-7m)(2)

∴ -7m(1.2m - 2) = -8.4m² - (-14m)

→ Remember (-)(-) = (+)

∴ -7m(1.2m - 2) = -8.4m² + 14m

→ Substitute it in the expression above

∵ -7m(1.2m - 2) + (-6m) = -8.4m² + 14m + (-6m)

→ Remember (+)(-) = (-)

∴ -7m(1.2m - 2) + (-6m) = -8.4m² + 14m - 6m

→ Add the like terms

∵ -7m(1.2m - 2) + (-6m) = -8.4m² + (14m - 6m)

∴ -7m(1.2m - 2) + (-6m) = -8.4m² + 8m

A sample size of at least 538 freshmen to estimate the proportion of freshmen who do not visit their advisors regularly with a margin of error of 4% and a confidence level of 95%.

To answer your question, we need to use the formula for sample size calculation for proportion:
n = [(Z-score)^2 * p(1-p)] / E^2

Where:
n = required sample size
Z-score = the critical value for the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)
p = the estimated population proportion (34% or 0.34)
1-p = the complement of p
E = the desired margin of error (4% or 0.04)

Plugging in the values:
n = [(1.96)^2 * 0.34(1-0.34)] / (0.04)^2
Simplifying the equation:
n = [(3.8416) * 0.2244] / 0.0016
n = 537.38

We need a sample size of at least 538 freshmen to estimate the proportion of freshmen who do not visit their advisors regularly with a margin of error of 4% and a confidence level of 95%. Keep in mind that this is just an estimate based on the historical data and assumes that the population proportion has not changed significantly.

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Answer:

3.14 + 3.14 × 3.14 + 3.14 ÷ 3.14 is equal to 13.9996

Step-by-step explanation:

In a pie chart, each section represents a proportion or percentage of the whole

To determine how many students said their favorite subject was math from the given pie chart, we need additional information such as the percentage or angle measure of the math section. Without specific values for each subject, we cannot accurately determine the number of students who chose math as their favorite subject.

To find the number of students who said math was their favorite subject, we would need to know the percentage or angle measure associated with the math section.

In this case, we know that the pie chart represents the results from a survey of 48 students about their favorite subject.

However, without information on the actual sizes of the slices or the percentages, we cannot determine the number of students who chose math as their favorite subject.

For example, if the math section in the pie chart represents 30% of the whole, we can calculate the number of students by multiplying the percentage by the total number of students surveyed (48):

Number of math students = 30% * 48 = 0.3 * 48 = 14.4

However, without the specific information about the math section, we cannot provide an exact number.

Please provide the necessary data, such as percentages or angle measures for each subject, to determine the number of students who chose math as their favorite subject accurately

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The three digit number is 727 while the one digit number is 4

Given data

The sum of a three-digit number and a one-digit number is 731.

The product of the numbers is 2,908

let three digit number be x, y, and z

let the one digit be w

The sum

xyz + w =731

xyz * w = 2,908

making xyz the subject of formula

xyz = 731 - w

plugging in xyz into xyz * w = 2,908

( 731 - w ) * w = 2908

731w - w^2 = 2908

w^2 - 731w + 2908 = 0

solving the quadratic equation gives

w = 727 or 4

since w is a one digit number then w = 4

plugging in w = 4 into xyz + w =731 we have

xyz + w =731

xyz + 4 =731

xyz =731 - 4

xyz  = 727

Hence the three digit number is 727 while the one digit number is 4

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Answer:

t = 63.897 years

Step-by-step explanation:

Simple interest rate formula: A = P(1 + r)^t

Simply plug in what we know and solve:

12502 = 1020(1 + 0.04)^t

6251/510 = 1.04^t

log base 1.04 of (6251.510) = 63.897

Answer:

Here they are unrounded

800 grams = 1.7637

700 grams = 1.54324

Step-by-step explanation:

Hope this helps

Answer:

私はあなたの言語を理解していなかった

Step-by-step explanation:

お邪魔して申し訳ありません

ところで、あなたが与えたポイントに感謝しますあなたは、あなたが、あなたのおかげで、あなたは、このビデオをありがとう

we can draw the Bode plot for the given transfer function L(s) = 2572/((s + 45.3)(s + 341)).

To draw the Bode plot for the transfer function L(s) = 2572/((s + 45.3)(s + 341)), we need to plot the magnitude and phase response as a function of frequency.

Step 1: Convert the transfer function to the standard form:

L(s) = K / ((s + z1)(s + z2))

where K = 2572, z1 = -45.3, and z2 = -341.

Step 2: Calculate the corner frequencies:

The corner frequencies are the values of s where the denominator of the transfer function becomes zero. In this case, the corner frequencies are z1 = -45.3 and z2 = -341.

Step 3: Draw the Bode plot:

a) Magnitude plot:

- At low frequencies (ω << corner frequencies), the magnitude is approximately constant (0 dB).

- At high frequencies (ω >> corner frequencies), the magnitude decreases at a rate of -20 dB/decade for each pole.

- At the corner frequencies, there will be a downward slope of -20 dB/decade for each pole starting from 0 dB.

b) Phase plot:

- At low frequencies (ω << corner frequencies), the phase is approximately 0 degrees.

- At high frequencies (ω >> corner frequencies), the phase decreases at a rate of -90 degrees/decade for each pole.

- At the corner frequencies, there will be a phase shift of -45 degrees for each pole.

Using the above information, we can draw the Bode plot for the given transfer function L(s) = 2572/((s + 45.3)(s + 341)).

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