5. Which is the vertex of the quadratic function f(x) = 2x² - 4x - 6?
(-1,8)
O (1,8)
O (1,-8)
O(-1,-8)

The percentage of alcohol after an hour will be approximately 4.9%.

What is percentage?

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let p(t) be the percentage of alcohol at time t.

Where t is in minutes.

Amount of alcohol in vat = Volume of vat x p/100

Rate of change of alcohol in vat = Volume of vat x dp/dt time 1/100

Rate of change of alcohol in vat = 500 x dp/dt x 1/100

Rate of change of alcohol in vat = 5 x dp/dt

Net rate of change of alcohol = (Rate of inflow of alcohol) - (Rate of Outflow of alcohol)

Rate of Inflow of alcohol = 0.06 - 5 = -4.94 gal/min

Rate of outflow of alcohol = p(t)/100 x 5 = 0.05p(t) gal/min

Therefore, the rate of change of alcohol is 0.03 - 0.05 p(t) gal/min

Finally we can write

5 x dp/dt = 0.3 - 0.05 p

Divide both sides by 5

dp/dt = 0.06 - 0.01p

Integrate both sides

\(\int {dp} / 0.06 -0.01p = \int dt\)

-100ln (0.06 - 0.01p) = t + C

At t=0, p=4, therefore

-100ln (0.06 - 0.04) = 0 + C

391.2 = C

Substitute the value of C, to get

-100ln (0.06 - 0.01p) = t + 391.2

Substitute t = 60 and solve for p

-100ln (0.06 - 0.01p) = 60 + 391.2

-100ln (0.06 - 0.01p) = 451.2

ln (0.06 - 0.01p) = -4.512

\(p = \frac{0.06 - e^{-4.512} }{0.01}\) ≈ 4.9%

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Thus, we have \(r = 2πr2 + 8πr\), which can be written as \(2πr2 + 8πr - r = 0\).

Factor out r to get r(2πr + 8π - 1) = 0. We can then use the quadratic formula

to solve for \(r:r(A) = (-8π ± sqrt(64π2 - 8π)) / 4π= (-2 ± sqrt(16π2 - 2π)) / π= (-2 ± 2π√15) / π\)Thus, \(r(A) = (-2 + 2π√15) / π or r(A) = (-2 - 2π√15) / π.\)

Part a:Domain of the function A(r)The expression for the total surface area of a cylinder is 2πr2 + 2πrh, where r is the radius of the circular base of the cylinder and h is the height of the cylinder. However, in this question, the cylinder is defined as having a height of 4 inches, and the area expression A(r) is given as A(r) = 2πr2 + 8πr.  

To determine the domain of this function, we must look at the values of r that are permitted in the expression. A(r) = 2πr2 + 8πrThe domain of this function A(r) is all real numbers greater than or equal to zero

.Part b:Inverse function of A(r)Write the radius r as a function of AInverse functions are functions that undo each other's operations. In other words, given a function f(x), its inverse function g(x) undoes the effects of f(x).To find the inverse function of A(r), we must first switch the roles of A and r.

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Answer:

Step-by-step explanation:

We have been given that,

Level of significance,

α

=

0.05

Standard deviation,

σ

=

160

Margin of error, {eq}ME =...

See full answer below.

The system of equations has exactly one real solution , Option A is the correct answer.

The missing point of the line is (13,1)

An Equation is defined as the mathematical statement that is formed when algebraic expression is linked with an equal sign .

The lines are plot on the graph , The lines intersect at only one point which means

The system of equations has exactly one real solution

Option A is the correct answer.

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Answer:

Step-by-step explanation:

First we replace the original 'x' with 'x + 4,' which causes translation of the original parabolic graph 4 units to the left.  Next, reflect this translated graph about the x-axis (which is the effect of multiplying by -1/2 as shown).  Finally, shift the entire graph (the most recent one) down 5 units.

Answer:

Yes

Step-by-step explanation:

The numbers both multiplied by 10

3 -6

30-60

Here's a complete diagram of a normal distribution using the provided information:

 +3         +2         +1         0         -1         -2         -3

0.1%      2.1%     13.6%    34.1%   34.1%    13.6%     2.1%     0.1%

A normal distribution is a probability distribution that is symmetric around the mean and has a bell-shaped curve. In a normal distribution, the majority of the data falls close to the mean, with fewer and fewer data points further away from the mean. The mean, median, and mode are all the same in a normal distribution, and the shape of the curve is determined by the mean and the standard deviation.

Here,

The normal distribution is a bell-shaped curve that is symmetric around the mean. The mean is at the center of the distribution (0 in this case) and the standard deviation determines the spread of the curve. The numbers on the x-axis represent the number of standard deviations away from the mean. The percentages represent the proportion of the total area under the curve that falls within each range of standard deviations.

For example, approximately 34.1% of the area under the curve falls within one standard deviation above or below the mean, and another 34.1% falls within two standard deviations above or below the mean. The area between two and three standard deviations above or below the mean is 13.6%. The area to the right of three standard deviations above the mean is approximately 0.1%.

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Answer:

\(x = 8\frac{1}{12}\)

Step-by-step explanation:

\(\frac{17}{15} =\frac{10}{2x-2}\)

\(17 ( 2x - 2 ) = 150\)

\(34x - 34 = 150\)

\(34x = 184\)

\(x = \frac{97}{12} = 8\frac{1}{12}\)

Answer:

Step-by-step explanation:

\(\frac{17}{15}= \frac{10}{2x-2}\)

\((2x-2 )*\frac{17}{15} =\frac{10}{2x-2} *(2x-2)\)

\(\frac{34x-34}{15} = 10\)

\(15*\frac{34x-34}{15} = 10*15\)

\(34x-34=150\)

\(34x=150+34\)

\(34x=184\)

\(x=\frac{92}{17}\)

Answer:

y = 4x - 12

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

x= 4

Step-by-step explanation:

Please see the attached pictures for the full solution.

Answer:

\(\dfrac{7}{10}\)

Step-by-step explanation:

Given that

Number of batteries that do not have a charge = 14

Total number of batteries = 20

To find:

Experimental probability that the next battery checked does not have a charge = ?

Solution:

First of all, let us learn about the definition of experimental probability.

Probability is the chances of happening of an event.

Formula for probability of happening of an event E is given as:

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)

Here we have to find the probability of checking a battery that has no charge.

So, number of favorable cases = Number of batteries that do not have a charge = 14

AND

Total Number of cases = Total number of batteries to be checked = 20

So, the required probability is:

\(\dfrac{14}{20} = \bold{\dfrac{7}{10}}\)

Answer:

9x=2

Step-by-step explanation:

4 - 6(3 - 2x) = 3(x -4)

4 - 18 + 12x = 3x - 12

12x - 14 = 3x - 12

12x - 3x = 14 - 12

9x = 2

hope you are happy with the answer ;)

Answer:

Step-by-step explanation:

I'm pretty sure it's the first answer, translating left 4, up 5.

False. When conducting a cluster sample, it is typically preferable to have more heterogeneous clusters with fewer individuals.

This is due to the fact that when clusters are diverse, it is crucial to appropriately represent the population by capturing its diversity.

In such situations, the danger of sampling bias is increased by having fewer clusters with more individuals because a larger number of people from a single heterogeneous cluster would not fairly represent the overall community. Incorrect estimates and conclusions may result from this.

Having fewer clusters with more individuals, on the other hand, can assist raise the precision of the estimates when clusters are homogeneous by lowering the variance associated with sampling from a single cluster. In general, to achieve a precise representation of the population and to lessen the chance of sampling bias, the number of clusters and the size of each cluster should be balanced.

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The​ chi-squared statistic measures which of the "goods of fit". Therefore option B is correct.

The chi-squared statistic is a statistical measure that is used to test the goodness of fit between an observed frequency distribution and an expected frequency distribution. It measures how well the observed values fit the expected values and quantifies the differences between them.

The calculation of the chi-squared statistic involves comparing the observed and expected frequencies for each category and computing a sum of squared differences between them, divided by the expected frequency. The resulting value indicates the degree to which the observed frequencies differ from the expected frequencies.

In summary, it can be sais that the chi-squared statistic is used to assess whether the observed frequencies are consistent with the expected frequencies or not , and it is commonly used in hypothesis testing, particularly in testing for independence in contingency tables or testing the fit of a model to observed data.

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\(\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=8\pi \\ r=2 \end{cases}\implies 8\pi =\cfrac{\pi (2)^2 h}{3}\implies 8\pi =\cfrac{4h\pi }{3} \\\\\\ 24\pi =4h\pi \implies \cfrac{24\pi }{4\pi }=h\implies 6=h\)

The percent of pizzas that are less than 12.04 inches is 56.36%

Given the following:

Mean, μ=12

Standard deviation, σ=0.25

Percent of pizzas less than 12.04:

Let P(X<12.04) be percent of pizzas less than 12.04

P(X<12.04)=P(Z<(x-μ)/σ)

               =P(Z<(12.04-12)/0.25)

               =P(Z<0.16)

Z-value of 0.16 from cumulative standardized normal distribution is 0.5636

Given that P(X<12.04)=P(Z<0.16), and P(Z<0.16) from normal distribution table is 0.5636,

P(X<12.04)=P(Z<0.16)=0.5636

P(X<12.04)=0.5636

                 =56.36%

Hence, the correct choice is 56.36%

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Answer:

When the bottom of the fraction equals zero

Step-by-step explanation:

2/(x-3) the VA would be at x=3 because when x does x=3 the bottom is 0

Answer:

400h=mi

Step-by-step explanation: 400 hours = miles which is an equation above.

Hence the average rate of change, in simplest form is -10 .

What is average rate of change?

Using the coordinate points from the table  ( 4,53) ( 8, 13 )

Substitute the coordinate into the expression

Average rate of change  = y₂ - y₁/x₂ - x₁

                                         = 13 - 53/8 - 4                    

                                         = -  4 0/4 ⇒ -10

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Answer:

No

Step-by-step explanation:

Counting numbers are considered to be whole numbers greater than zero. Whole numbers are positive numbers without decimals or fractions, so 12, 15, and 124 can be classified as counting numbers, but not 0.1.

hope this helps!!!

Answer:

Step-by-step explanation:

Answer: Y = 1/3x^2 - 4x + 12

Step-by-step explanation:

Hope this helps, sorry I don't have an explanation...

Based on the survey results, a 99 percent confidence interval for the proportion of vaccine-eligible people who received the flu vaccine is calculated to be approximately 0.391 to 0.442. This means that we can be 99 percent confident that the true proportion of vaccine-eligible people who received the flu vaccine falls within this interval.

To construct the confidence interval, we can use the formula for the standard error, which is the square root of [(p-hat * (1 - p-hat)) / n], where p-hat is the sample proportion and n is the sample size. In this case, p-hat is 978/2350 = 0.4166 (rounded to four decimal places), and n is 2350.

Using this information, we can calculate the standard error as:

Standard Error = sqrt((0.4166 * (1 - 0.4166)) / 2350) ≈ 0.0113 (rounded to four decimal places).

Next, we can calculate the margin of error by multiplying the standard error by the critical value corresponding to a 99 percent confidence level. For a large sample size like this, we can use the standard normal distribution, and the critical value is approximately 2.58.

Margin of Error = 2.58 * 0.0113 ≈ 0.0292 (rounded to four decimal places).

Finally, we can construct the confidence interval by subtracting and adding the margin of error from the sample proportion:

Confidence Interval = 0.4166 ± 0.0292 = (0.3874, 0.4458).

Therefore, we can be 99 percent confident that the true proportion of vaccine-eligible people who received the flu vaccine lies between approximately 0.391 and 0.442.

Based on this confidence interval, we can comment on the belief that 45 percent of vaccine-eligible people received the flu vaccine. Since the lower bound of the confidence interval is 0.391 (or 39.1 percent) and does not include 45 percent, we can conclude that there is evidence to suggest that the belief of 45 percent may be higher than the true proportion. However, we need to note that the true proportion could still be close to 45 percent, as the upper bound of the confidence interval is 0.442 (or 44.2 percent).

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a percent using the form % to represent the following word problem is x=12

What do u mean by percent?

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage. Related Topics: mathematics percentile.

60 % of 20

60/100 = x/20

cross product

60 * 20 = 100x

divide by 100

1200/100 =x

12=x

60/100 = x/20    x= 12

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The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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Answer:

$74.55

Step-by-step explanation:

420 divided by 20 =21

21 times 3.55= 74.55

Hope this helps!

Below is a MATLAB program that evaluates the mathematical expression

% Prompt the user to enter the value of x

x = input('Enter the value of x: ');

% Evaluate the expression A

A = (x^2 - 3*x + 2) / (2*x - 5);

% Display the result

fprintf('The value of A is: %.2f\n', A);

Answer:

\(x^{2} -xz-xy+yz\)

Step-by-step explanation:

To answer this question we have to multiply each value of a bracket by every value from the other bracket!

It is super important to make sure that we take in consideration the operations of each value

Firstly, we are going to multiply the x in the first bracket by every value in the other bracket...

Now we are going to multiply the \(-y\) by everything in the other bracket...

This leaves us with \(x^{2} -xz-xy+yz\)

Hope this helps, have a lovely day! :)

The probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item is 0.68.

Given data ,

According to store records, approximately  1/ 4 of all customers who go to the service department ask for help finding an item.

All the  customers who go to the service department will not ask for help.

Now, the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item is

P(X>=1)   = 1 - P(X<1)

               = 1 - (1/4)⁰ (3/4)⁴

               = 1 - (3/4)⁴

               = 0.68

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced to predict how likely events are to happen.

The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment.

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