Let f(x) be the perimeter of a rectangle with an area 49units^2 and one side with length x.
f(x) =
What is the minimum perimeter of all rectangles with this area?
Perimeter =

Answer:

The sum of measures of angles in a triangle is 180. So if you take the three angles, add them, and set it to 180, you will get the answer. (39 + 3x + 7 + 5x - 2 = 180)

Step-by-step explanation:

Answer:

\(x = 17\)

Step-by-step explanation:

\(m < a + m < b + m < c = 180 \\ \\ 39 + (3x + 7) + (5x - 2) = 180 \\ 39 + 8x + 5 = 180 \\ 44 + 8x = 180 \\ 8x = 180 - 44 \\ 8x = 136 \\ x = \frac{136}{8} \\ \\ x = 17\)

Answer: 5

Step-by-step explanation:

The probability that x is less than 6 is 5/8.

If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.

To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:

p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)

Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:

p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)

Simplifying, we get:

p(x < 6) = 5/8

Therefore, the probability that x is less than 6 is 5/8.

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Answer:

The dimensions are thus 4 by 10 units

Step-by-step explanation:

Rewrite w(w + 6) = 40 in standard quadratic form ax^2 + bx + c = 0:

w^2 + 6w - 40 = 0

This factors as follows:

w^2 + 6w - 40 = 0  =>  (w + 10)(w - 4) = 0.

Solving for w, we get w = 4 (and also the unhelpful w = -10).

The width of the rectangle is 4 and the length is 4 + 6, or 10.

The dimensions are thus 4 by 10 units, with area = 40 units^2

Answer:

Step-by-step explanation:perp. 3/2

y + 8 = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14

nswer:

Terms in parentheses are handled first. If the parentheses are removed, it will change the answer.

Step-by-step explanation:

example:

(4-3)2 reduced would be 2     (because the 4-3 would be handled first.)

4-3x2 reduced would be -2     (because the multiplication would be handled first.)

The 90% confidence interval for the sample mean is (13.289, 16.711). This means that we can be 90% confident that the true population mean lies within this interval based on the given sample.

To calculate a 90% confidence interval for a sample mean, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

First, we need to determine the critical value for a 90% confidence level. Since we have a sample size of 25, we can use a t-distribution. Consulting a t-table or calculator, for a 90% confidence level and 24 degrees of freedom (sample size minus 1), the critical value is approximately 1.711.

Next, we calculate the standard error using the formula:

Standard Error = Sample Standard Deviation / √(Sample Size)

Plugging in the values, we get:

Standard Error = 5 / √(25) = 1

Now, we can calculate the confidence interval:

Confidence Interval = 15 ± (1.711 * 1) = (13.289, 16.711)

The 90% confidence interval for the sample mean is (13.289, 16.711). This means that we can be 90% confident that the true population mean lies within this interval based on the given sample.

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Answer:

C

Step-by-step explanation:

Plz give brainliest if this helped:)

Answer:

x=4 y=8

Step-by-step explanation:

Solution:

To determine the inequality that will have a shaded area below the boundary, we have to work through the given options below:

For option A, the graph is shown below:

For option B, the graph is shown below:

For option D, we have:

For option E, the graph is shown below:

From the above graphs, inequality which has its area below the boundary line is

i  think so is correct

After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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Answer:

Not much sure if this is a joke but 1+1 is 2 not 11.

Step-by-step explanation:

I hope I helped.

Have a great day ;)

Answer:13/8 and 7/4. 2/1 then 5/2 and 21/8

Step-by-step explanation: If you continue the pattern, you get 13/8 which is already simplified because 13 is a primw number. Then 14/8 which simplifies to 7/4 if divided by 2. Similar process for other ones

Answer:

64 R 0

Step-by-step explanation:

Here is a photo of the answer, it has all the steps!

Answer:

  (4, -8)

Step-by-step explanation:

The components of a vector are found by subtracting the tail from the head.

__

  Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)

⇒ The component form is (4, -8), or maybe 4i -8j.

_____

Additional comment

There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.

(4,-8) is the answer

Answer:

I think 15% im sorry if this is wrong

Answer:

14

Explanation:

To evaluate the expression, we need to replace x by 4. So, the expression is equal to:

3x + 2

3(4) + 2

12 + 2

14

Therefore, the value of the expression is 14

The sum can be used when sum gives the situations in which the probability of a union of events can be calculated by summing probabilities together. and product rule  If there are n(A) ways to do A and n(B) ways to do B, then the number of ways to do A and B is n(A) × n(B)

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Reason:

The probability rule of sum describes scenarios in which the probability of a union of events can be computed by adding probabilities. It is frequently used on mutually exclusive occurrences, which are events that cannot occur at the same moment.

If there are n(A) ways to perform A and n(B) ways to do B, then the total number of ways to accomplish A and B is n(A) n. (B). This is true if the number of possible ways to do A and B are independent; the number of options for doing B is the same regardless of the option you chose for A.

The probability product rule states that P(AnB) = P(A) * P (B)

This implies that the events must be distinct.

In contrast, for the probability sum rule.

P(A + B) = P(A) + P(B) (B)

This suggests that P(AnB) = 0, indicating that they are disjoint or mutually exclusive.

Box 2 states that the sum rule is used when events are independent, however this is not correct; it is employed when events are mutually exclusive.

Two events are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently. In other words, discontinuous events are those that are mutually exclusive. If two occurrences are regarded discontinuous, the likelihood of both occurring at the same time is zero.

If A and B are the two events, then the probability of their disjoint is stated as:

P (A and B) = 0 for the probability of a disjoint (or mutually exclusive) event.

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The sum can be used when sum gives the situations in which the probability of a union of events can be calculated by summing probabilities together. and product rule  If there are n(A) ways to do A and n(B) ways to do B, then the number of ways to do A and B is n(A) × n(B)

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Reason:

The probability rule of sum describes scenarios in which the probability of a union of events can be computed by adding probabilities. It is frequently used on mutually exclusive occurrences, which are events that cannot occur at the same moment.

If there are n(A) ways to perform A and n(B) ways to do B, then the total number of ways to accomplish A and B is n(A) n. (B). This is true if the number of possible ways to do A and B are independent; the number of options for doing B is the same regardless of the option you chose for A.

The probability product rule states that P(AnB) = P(A) * P (B)

This implies that the events must be distinct.

In contrast, for the probability sum rule.

P(A + B) = P(A) + P(B) (B)

This suggests that P(AnB) = 0, indicating that they are disjoint or mutually exclusive.

Box 2 states that the sum rule is used when events are independent, however this is not correct; it is employed when events are mutually exclusive.

Two events are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently. In other words, discontinuous events are those that are mutually exclusive. If two occurrences are regarded as discontinuous, the likelihood of both occurring at the same time is zero.

If A and B are the two events, then the probability of their disjoint is stated as:

P (A and B) = 0 for the probability of a disjoint (or mutually exclusive) event.

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Answer:quit

Step-by-step explanation:

Answer:

1/3

Steps:

The line rose 10 values (up) and went 30 values higher (to the right), so you divide 10/30 and end up with 1/3

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by y = e^2x, y = 0, x = -1, and x = 3 around the y-axis, we can use the method of cylindrical shells.

The height of each cylindrical shell will be the difference between the two functions: y = e^2x and y = 0. The radius of each cylindrical shell will be the x-coordinate of the corresponding point on the curve y = e^2x.Let's set up the integral to find the volume:\(V = ∫[a,b] 2πx * (f(x) - g(x)) dx\)

Where a and b are the x-values that define the region (in this case, -1 and 3), f(x) is the upper function (y = e^2x), and g(x) is the lower function (y = 0).V = ∫[-1,3] 2πx * (e^2x - 0) dxSimplifyingV = 2π ∫[-1,3] x * e^2x dxTo evaluate this integral, we can use integration by parts. Let's assume u = x and dv = e^2x dx. Then, du = dx and v = (1/2)e^2x.Applying the integration by parts formula

\(∫ x * e^2x dx = (1/2)xe^2x - ∫ (1/2)e^2x dx= (1/2)xe^2x - (1/4)e^2x + C\)Now, we can evaluate the definite integral:

\(V = 2π [(1/2)xe^2x - (1/4)e^2x] evaluated from -1 to 3V = 2π [(1/2)(3)e^2(3) - (1/4)e^2(3)] - [(1/2)(-1)e^2(-1) - (1/4)e^2(-1)]V = 2π [(3/2)e^6 - (1/4)e^6] - [(-1/2)e^(-2) - (1/4)e^(-2)]\)Simplifying further

\(V = 2π [(3/2)e^6 - (1/4)e^6] - [(-1/2)e^(-2) - (1/4)e^(-2)]V = 2π [(3/2 - 1/4)e^6] - [(-1/2 - 1/4)e^(-2)]V = 2π [(5/4)e^6] - [(-3/4)e^(-2)]V = (5/2)πe^6 + (3/4)πe^(-2)\)Therefore, the volume of the solid obtained by rotating the region bounded by y = e^2x, y = 0, x = -1, and x = 3 around the y-axis is (5/2)πe^6 + (3/4)πe^(-2) cubic units.

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The interval provides a range within which we estimate the population mean weight difference to lie with a 95% level of confidence.

To find a 95% confidence interval of the weight differences between the two methods of weighing trucks, you would typically need data from both methods of weighing. The data would consist of paired observations, where each truck's weight is measured using both the dynamic (driving across a plate) and static (traditional) methods.

Assuming you have the necessary data, you can follow these steps to calculate the confidence interval:

1. Calculate the difference in weights between the two methods for each paired observation.

2. Calculate the mean of the weight differences.

3. Calculate the standard deviation of the weight differences.

4. Determine the sample size, denoted by 'n'.

5. Use the t-distribution with (n-1) degrees of freedom to find the critical value, denoted by 't', for a 95% confidence level.

6. Calculate the margin of error by multiplying the critical value 't' with the standard deviation of the weight differences divided by the square root of 'n'.

7. Construct the confidence interval by subtracting the margin of error from the mean of the weight differences to obtain the lower bound and adding the margin of error to the mean to obtain the upper bound.

Once you have the confidence interval, you can interpret it in the context of the problem. For example, you can say, "Based on our sample data, we are 95% confident that the true difference in weights between the dynamic and static weighing methods for trucks falls between [lower bound] and [upper bound] yards." The interval provides a range within which we estimate the population mean weight difference to lie with a 95% level of confidence.

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Therefore, based on the inspection of the sample, it can be estimated that 8% of the articles in the original shipment may be defective.

The answer  is that the probable percentage of defective articles in the original shipment can be estimated using the formula:

Probable percentage of defective articles = (Number of defective articles in sample / Sample size) x 100

In this case, the number of defective articles in the sample is 4, and the sample size is 50. Plugging these values into the formula, we get:

Probable percentage of defective articles = (4/50) x 100 = 8%

Therefore, based on the inspection of the sample, it can be estimated that 8% of the articles in the original shipment may be defective.


Sampling is a technique used to estimate the characteristics of a large population by examining a smaller subset of it. In this case, a sample of 50 articles was inspected to estimate the probable percentage of defective articles in the original shipment of 500 articles. The number of defective articles in the sample was found to be 4, which represents 8% of the sample size. This percentage can then be used to estimate the probable percentage of defective articles in the entire shipment. However, it is important to note that the estimate may not be completely accurate, as the sample may not be fully representative of the entire population.

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The properties that can be used to show that the expression 5^(3/2) = is equivalent to √5³ is; Option 4

We want to show that the expression 5^(3/2) = √5³

Now, to break it down, we can express the fraction 3/2 as 3(1/2) and so we now have;

5³^(1/2)

Now, any number raised to the power of 1/2 is simply referring to square root and so we now have;

5³^(1/2) = √5³

Thus, option 4 is correct.

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Answer: the answer is choice b

Step-by-step explanation:

First we need to find the inverse function.  To do this, I'd put f(x) into vertex form:

    \(\begin{aligned}f(x) &= (x^2-4x)-6\\[0.5em] &= (x^2-4x+4)-6-4\\[0.5em] &= (x-2)^2-10\\[0.5em]\end{aligned}\)

Now, we can try to invert the function, keeping in mind this is only used when x≥2.

     \(\begin{aligned}y&= (x-2)^2-10\\[0.5em]y+10&= (x-2)^2\\[0.5em]\sqrt{y+10}&= x-2\\[0.5em]\sqrt{y+10}+2&= x\\[0.5em]\end{aligned}\)

(The fact that x ≥ 2 allowed us only keep the positive square root on the third line.)

So our inverse function is \(f^{-1}(y)=\sqrt{y+10}+2\).

Now, let's find the derivative of this function:

    \(\begin{aligned}\dfrac{df^{-1}}{dy}&= \dfrac{1}{2\sqrt{y+10}}\cdot\dfrac{d}{dy}[y+10]\\[0.5em] &= \dfrac{1}{2\sqrt{y+10}}\end{aligned}\\\)

(The chain rule was used, but the derivative of the inside function equals 1.)

So \((f^{-1})'(-6) = \dfrac{1}{2\sqrt{-6+10}} = \dfrac{1}{4}\)

Now having done all of that, it did cross my mind that since \(f\) and \(f^{-1}\) are simply reflections over the line y=x, if we had actually just found f'(4) and then used the reciprocal slope, we'd also get the same answer more quickly.

f'(x) = 2x - 4

when y = -6, then x = 4 (by solving f(x) = -6).

f'(4) = 4, so reflecting that slope of 4/1 over the line y=x, we'd get a slope of 1/4.

Step-by-step explanation:

A

a vertical line is parallel the y-axis (up and down). if this line now intersects the grain at 2 points, it means that the x value of that line has 2 different result values as y.

but as function it can have only one result value per x value.

Answer:

pyramid

Step-by-step explanation:

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The smallest sample mean out of 1000 sample means is 133.273 ( minimum in table ) & largest sample mean is 166.887 (minimum in table ).

What does the word "sample" mean?

X ≈ U ( 100 , 200 )                a = 100 , b = 200

E(X)  = a + b/2 = 150

Var(X) = (b - a )²/12 = 100²/2

sal(x) = √100²/2 = 50/√3  = 28.8675

E(X) = 150

Sd (x) ≈  sd(x)/√n  = 50/√3 . 1/√30 = 5.27046

The mean of the population is 150 [ E(x) ] , the mean of ( exact ) sampling distribution of x is also 150  [ E(x) ] , and the mean of the approximation of the sampling distribution of x is 150.123 .

The smallest sample mean out of 1000 sample means is 133.273 ( minimum in table ) & largest sample mean is 166.887 (minimum in table ).

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