Students were asked to write 6x^5 + 8x - 3x^3 + 7x^7 in standard form. Shown below are four
student responses.
Anna: 7x^7+ 6x^5 - 3x^3 + 8x
Mario: -3x^3 + 6x^5 + 7x^7 + 8x
William: 8x + 7x^7+ 6x^5 - 3x^3
Olivia: 8x - 3x^3 + 6x^5 + 7x^7
Which student is correct?

Answer:

\(187.74\:\mathrm{cm}\)

Step-by-step explanation:

The area of a rectangle is given by \(l\cdot w\). Therefore, we can set up the following inequality:

\(l\cdot 16 \leq 3,003.84\).

Solving this inequality, we have:

\(l \leq 187.74\).

Therefore, the largest length Carmen's painting can be is \(\fbox{$187.74\:\mathrm{cm}$}\).

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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The probability of exactly 14 members out of a sample of 20 adults aged 65 and over receiving a pneumococcal vaccination can be determined using the binomial probability formula.

In this scenario, we are dealing with a binomial setting, where we have a fixed number of trials (20 adults in the sample) and two possible outcomes for each trial (either receiving or not receiving a pneumococcal vaccination). The probability of success, denoted as "p," is the proportion of U.S. adults aged 65 and over who have received the vaccination, which is 70% or 0.7 in this case.

To find the probability of exactly 14 successes, we can use the binomial probability formula:

P(X = 14) = C(n, x) * \(p^x\) * \((1 - p)^{(n - x)}\)

Here, C(n, x) represents the binomial coefficient, which calculates the number of ways to choose x successes out of n trials. In this case, n = 20 and x = 14.

Calculating the probability:

P(X = 14) = C(20, 14) * \(0.7^{14}\)* \((1 - 0.7)^{(20 - 14)}\)

Using the binomial coefficient formula C(n, x) = n! / (x!(n - x)!), we can find the value of C(20, 14) to be 38760.

Substituting the values, we get:

P(X = 14) = 38760 * \(0.7^{14}\) * \(0.3^6\)

Evaluating this expression will give us the probability that exactly 14 members of the sample received a pneumococcal vaccination.

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The height of the highest point of the flyover will be 12 feet.

What is Maxima?

The curve of a function has maxima and minima, which are its peaks and valleys. A function's maximum and minimum values are infinitely variable. Without even looking at the function's graph, we may use calculus to determine any function's maximum and minimum value. Within the specified range, the maxima and minima of the curve, respectively, will represent its highest and lowest points.

Given function :  h(x) = −3x2 + 36x − 96

we have to find the height of highest point which can only be found by maximizing the function.

So, h'(x) = -6x + 36 = 0

we get,   x = 6

Now, h''(x) = -6  (maxima)

So, the given function will be maxima at x=6

So, the height at x=6 will be :

   h(6) = −3× 6² + 36 (6)− 96

          = -3×36 + 216 - 96

          = -108 + 120

          = 12 feet

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Answer:

The answer is 12 feet

Answer:

3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Angle-Side-Angle. The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Answer:

hodiwkwoleñelflelflgkkg

The bearing is the angle measured clockwise from the north direction to a specified direction. To find the bearing of Town Y from Town B, we use the given information that Town B is located south 38 degrees east from Town Y. By subtracting this angle from 180 degrees, we find that the bearing is 142 degrees.

To determine the bearing, we need to find the angle between the north direction and the direction from Town B to Town Y.

Since Town B is located south of Town Y, the bearing will be a southern direction. The bearing angle can be calculated as 180 degrees minus the given angle, which is 38 degrees.

Therefore, the bearing of Town Y from Town B is 180 - 38 = 142 degrees.

In conclusion, the main answer is that the bearing of Town Y from Town B is 142 degrees.

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Answer:

40%

Step-by-step explanation:

15% + 25% = 40%

Answer:

4050/9 = $450.00 each

1573/3 = $524.33 each

The y-intercept of g(x) is -23.

Even function f(x), g(x)=2f(x-6)-7, y-intercept of g(x)?

Since f(x) is an even function, f(-x) = f(x) for all x. Therefore, we have f(6) = f(-6).

We know that f(6) = -8, so f(-6) = -8.

Now, let's find g(0), the y-intercept of g(x):

g(0) = 2f(0-6) - 7

= 2f(-6) - 7

= 2(-8) - 7

= -23

Therefore, the y-intercept of g(x) is -23, which is option (1).

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After doing some mathematical operations, we can conclude that the reading rate in words per minute is 260.71 words per minute.

So, the reading rate per minute:

Then reading rate per minute will be:

Therefore, after doing some mathematical operations, we can conclude that the reading rate in words per minute is 260.71 words per minute.

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Answer:

"what are angles"

Step-by-step explanation:

En la geometría euclidiana, un ángulo es la figura formada por dos rayos, llamados lados del ángulo, que comparten un punto final común, llamado vértice del ángulo. Los ángulos formados por dos rayos se encuentran en el plano que contiene los rayos. Los ángulos también se forman por la intersección de dos planos. Estos se llaman ángulos diedros

Answer:

2:3

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Adelaide's monthly payment for financing the refrigerator over 36 months at an APR of 12.5% is approximately $55.33

This calculation is based on the formula for calculating the monthly payment on a loan, taking into account the principal amount, the monthly interest rate, and the number of months.

In the first paragraph, we determine the principal amount as $1750, which represents the cost of the refrigerator. The annual percentage rate (APR) of 12.5% is converted to a monthly interest rate (r) by dividing it by 12 and then by 100. The number of months (n) is given as 36.

In the second paragraph, we substitute the values into the monthly payment formula and perform the necessary calculations. The formula incorporates the principal, the monthly interest rate, and the number of months to determine the monthly payment amount. After evaluating the expression, we find that Adelaide's monthly payment is approximately $55.33.

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Managers, goods, services, and technology are all needed in developing countries, and therefore, they provide new markets for companies that can supply these essentials.

Developing countries often have growing economies and increasing consumer demands. As these countries strive for development and improvement, they require effective management to drive their businesses and organizations. Managers play a crucial role in overseeing operations, implementing strategies, and maximizing efficiency.

Additionally, developing countries require goods and services to meet the needs of their populations. This includes basic necessities such as food, clothing, and shelter, as well as other essential products and services like healthcare, education, infrastructure development, and transportation. Companies that can provide these goods and services have an opportunity to enter new markets and cater to the demands of the growing population.

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The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.

1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".

2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".

Therefore, the value of the expression "true && !false" is "true".

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Answer:

\( \frac{ {m}^3{} }{25} \)

Step-by-step explanation:

that is the answer

Answer:

72π (I think)

Step-by-step explanation:

Think of it in terms of the entire circle. A semi-circle is just half a circle, so the area of a semicircle will be half of the area of the entire circle. The radius of the semicircle is 6, so the radius of the whole circle is 12. Then, we can do \(\frac{pi*r^{2} }{2}\) to get the area of the semicircle is 72π. I'm pretty sure that's right. Let me know if I made a mistake somewhere.

Answer:

1) y= 3x + 7

2) y= 3/4x + 10

3) y= -5x - 2

4) y= 12x - 6

5) y= 1/2 + 9

Step-by-step explanation:

After the 7th iteration of the selection sort algorithm, the array becomes [-5, 1, 8, 12, 21, 22, 32, 56, 77, 34].

To apply the selection sort algorithm to the given data set, starting with the array [56, 32, 1, 12, -5, 34, 22, 21, 77, 8], we perform the following steps:

On the first iteration, we find the minimum value (-5) and swap it with the first element. The array becomes [-5, 32, 1, 12, 56, 34, 22, 21, 77, 8].

On the second iteration, we find the minimum value (1) starting from the second element and swap it with the second element. The array becomes [-5, 1, 32, 12, 56, 34, 22, 21, 77, 8].

On the third iteration, we find the minimum value (8) starting from the third element and swap it with the third element. The array becomes [-5, 1, 8, 12, 56, 34, 22, 21, 77, 32].

On the fourth iteration, we find the minimum value (12) starting from the fourth element and swap it with the fourth element. The array remains unchanged: [-5, 1, 8, 12, 56, 34, 22, 21, 77, 32].

On the fifth iteration, we find the minimum value (21) starting from the fifth element and swap it with the fifth element. The array remains unchanged: [-5, 1, 8, 12, 21, 34, 22, 56, 77, 32].

On the sixth iteration, we find the minimum value (22) starting from the sixth element and swap it with the sixth element. The array remains unchanged: [-5, 1, 8, 12, 21, 22, 34, 56, 77, 32].

On the seventh iteration, we find the minimum value (32) starting from the seventh element and swap it with the seventh element. The array remains unchanged: [-5, 1, 8, 12, 21, 22, 32, 56, 77, 34].

Thus, after the 7th iteration of the selection sort algorithm, the array becomes [-5, 1, 8, 12, 21, 22, 32, 56, 77, 34].

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So, the answer to the question is that the fourth-degree polynomial with integer coefficients that has zeros at 3i is:
x^4 - 2x^3 - 7x^2 + 54x - 72.

To find a fourth-degree polynomial with integer coefficients that has zeros at 3i, we know that the conjugate of 3i, which is -3i, must also be a zero. So, we can start by setting up our polynomial with the factors (x-3i)(x+3i).
Expanding this, we get:
(x-3i)(x+3i) = x^2 - (3i)^2
= x^2 + 9
Now, we need to find two more roots that will make this a fourth-degree polynomial. We can choose any two integers for these roots, but let's say we choose -2 and 4. Then, our polynomial would be:
(x-3i)(x+3i)(x+2)(x-4) = (x^2+9)(x+2)(x-4)
Expanding this out gives us our fourth-degree polynomial with integer coefficients:
x^4 - 2x^3 - 7x^2 + 54x - 72
So, the answer to the question is that the fourth-degree polynomial with integer coefficients that has zeros at 3i is:
x^4 - 2x^3 - 7x^2 + 54x - 72.

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A differential equation with some initial conditions is used to solve an initial value problem.

The required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.

Let the given equation be \($y^{1/2} dy\ dx y^{3/2} = 1\), y(0) = 9

\($(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1\) …..(1)

Divide the given equation (1)  by \($\sqrt{ y} $\)  giving

\($y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$\), which is in Bernoulli's form.

Put \($u=y^{(1+1 / 2)}=y^{(3 / 2)}$\)

Then \($(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$\).

Multiply (2) by \($\sqrt{ } y$\) and we get

\(y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1\)

(2/3) \(u^{\prime}+u=1$\) or \($u^{\prime}+(3 / 2) y=3 / 2$\),

which is a first order linear equation with an integrating factor

exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is

\(u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$\)  or

\(\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}\)

To obtain the particular solution satisfying y(0) = 4,

put x = 0, y = 4, then

8 = (9/4) + c

c = (23/4)

Hence, the required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

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The given polynomial is negative for negative values of x with very large absolute value because the dominant term x⁷ is negative and its absolute value is much larger than the absolute value of the other terms.

When x is negative and has a very large absolute value, the dominant term in the given polynomial is x⁷.

Since x⁷ is being raised to an odd power, it will also be negative.

The other terms in the polynomial are added to this dominant term. Notice that all the other terms have positive coefficients except for -6x³. This term is negative, but its absolute value is much smaller than the absolute value of the dominant term.

Therefore, when negative values of x with very large absolute value are substituted into the polynomial, the dominant term will be a large negative number, which will overpower the other smaller positive terms and the negative term -6x³.

This results in a negative value for the entire polynomial.

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The manager wants to control the maximum probability of Type I error at 1% (i.e. the manager wants the significance level to be 1%). To calculate the critical value, we need to find the Z-score associated with a 1% significance level.
To find the critical value, we can use a Z-table or a Z-score calculator. Since the significance level is 1% (0.01), we need to find the Z-score corresponding to the area of 0.99 (1 - 0.01) in the upper tail of the standard normal distribution.
By looking up the Z-table or using a Z-score calculator, we find that the Z-score corresponding to a 0.99 cumulative probability is approximately 2.33. The critical value the manager should use to conduct the hypothesis test is 2.33.

To calculate the probability of Type II error, we need to specify an alternative hypothesis and determine the corresponding population mean value. In this case, the alternative hypothesis is that the mean daily output is greater than 200, and the specified population mean value is 205.

To calculate the probability of Type II error, we need to find the area under the null hypothesis distribution that falls to the right of the critical value. In other words, we need to find the probability that the test statistic, assuming the null hypothesis is true, falls in the rejection region. Since we are assuming the population mean is 205, we can calculate the Z-score using the formula:

Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
Substituting the values, we get:
Z = (205 - 200) / (18 / sqrt(81)) = 5 / (18 / 9) = 5 / 2 = 2.5

Now, we can calculate the probability of Type II error by finding the area under the null hypothesis distribution to the right of the critical value, which is 2.33. Using the Z-table or a Z-score calculator, we find that the probability of Type II error is approximately 0.0062, or 0.62%.
If the sample mean turns out to be 205, we compare it to the critical value. If the sample mean is greater than the critical value (2.33), we reject the null hypothesis. In this case, since the sample mean is 205, which is greater than the critical value of 2.33, we would reject the null hypothesis. The conclusion of the test would be that there is sufficient evidence to suggest that the mean daily output is greater than 200.

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Answer:

$4,379

Step-by-step explanation:

Doris only earns commission on the amount above $80,000 so you have to figure out how much of the total sales is subject to commission.  

Subtract      $382000-$80000= $302000

Multiply       $302000 x 1.45% = $4,379

Answer:

360°

Step-by-step explanation:

degrees are needed

The correct option is

This relation is a function because each input has exactly one output.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

From the figure the input are distinct and no input get coincide with output.

So, A function is a relation that states that there should only be one output for each input.

Alternatively, we could say that a function is a special sort of relation (a collection of ordered pairs) that adheres to the rule that every X-value should only be connected with one y-value.

Hence, This relation is a function because each input has exactly one output.

This relation is a function because each input has exactly one output.

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Answer:

14x and 3 x

Step-by-step explanation:

14x and 3 x are like terms.

This is because they both have 'x'. (They can even be simplified)

Whereas unlike terms are terms which do not contain the same variable or numerical value. (They cannot be simplified with other terms than its like term)