lim┬(x→+[infinity])⁡〖sin3x/x=〗
O 1
O Does not exist
O +[infinity]
O 0
O 3

Answer:

A. Students 1 and 3

Step-by-step explanation:

Student 3's equation is -5r + 3s - 1

Student 1's equation is -(5r - 3s + 1)

We distribute the negative like this: -5r + 3s - 1, which is the same as student 1.

In the future, you should post all possible answer choices to have a complete post. However, there's enough information to get the answer.

The original set has points in the form (x,y)

The first point is (x,y) = (-49,7) making x = -49 and y = 7. When we find the inverse, we simply swap the x and y values. The inverse undoes the original function and vice versa. So if (-49, 7) is in the original function, then (7, -49) is in the inverse. The rest of the points follow the same pattern.

We end up with this answer

{ (7, -49), (8, -56), (9, -63), (10, -70) }

The proportion of all novels that are between 50,000 and 60,000 words is approximately 0.

A. The random variable X, representing the number of words in a randomly selected romance novel, follows a normal distribution with a mean (μ) of 64,182 and a standard deviation (σ) of 17,154.

B. To find the proportion of all novels that are between 50,000 and 60,000 words, we need to calculate the area under the normal curve between those two values.

First, we need to standardize the values using the z-score formula:

z₁ = (50,000 - μ) / σ

z₂ = (60,000 - μ) / σ

Substituting the given values:

z₁ = (50,000 - 64,182) / 17,154

z₂ = (60,000 - 64,182) / 17,154

Calculating these z-scores will give us the standardized values.

Next, we need to find the corresponding cumulative probabilities for each z-score using a standard normal distribution table or a statistical calculator.

Let's assume we find P(Z < z1) = P(Z < z2) = p.

The proportion of all novels between 50,000 and 60,000 words is given by:

Proportion = P(z1 < Z < z2)

= P(Z < z2) - P(Z < z1)

= p - p

= 0

Since the probabilities are the same, the proportion of novels between 50,000 and 60,000 words is approximately 0.

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a) the calculated t-value (2.344) is greater than the critical t-value (1.984), we reject the null hypothesis. b) The p-value associated with a t-value of 2.344 is approximately 0.010 (two-tailed test).

(a) To determine if the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, we can conduct a two-sample t-test.

Let's define our null hypothesis (H0) as "there is no significant difference in average yearly reading growth between Program A and Program B" and the alternative hypothesis (H1) as "Program A leads to higher average yearly reading growth than Program B."

We have the following information:

For Program A:

Sample size (na) = 64

Sample mean (xA) = 1.2

Sample standard deviation (sA) = 0.26

For Program B:

Sample size (nb) = 100

Sample mean (xB) = 1.0

Sample standard deviation (sB) = 0.28

To calculate the test statistic, we use the formula:

t = (xA - xB) / sqrt((sA^2 / na) + (sB^2 / nb))

Substituting the values, we have:

t = (1.2 - 1.0) / sqrt((0.26^2 / 64) + (0.28^2 / 100))

t ≈ 2.344

Next, we determine the critical t-value corresponding to a 5% significance level and degrees of freedom (df) equal to the smaller sample size minus 1 (df = min(na-1, nb-1)). Using a t-table or statistical software, we find the critical t-value for a two-tailed test to be approximately ±1.984.

(b) To calculate the p-value, we compare the calculated t-value to the t-distribution. The p-value is the probability of observing a t-value as extreme as the one calculated, assuming the null hypothesis is true.

From the t-distribution with df = min(na-1, nb-1), we find the probability corresponding to a t-value of 2.344. This probability corresponds to the p-value.

(c) Based on the results of the hypothesis test, where we rejected the null hypothesis, we can conclude that there is evidence to suggest that Program A leads to higher average yearly reading growth compared to Program B.

(d) To calculate the probability of a Type II error (β), we need additional information such as the significance level (α) and the effect size. The effect size is defined as the difference in means divided by the standard deviation. In this case, the effect size is (xA - xB) / sqrt((sA^2 + sB^2) / 2).

Let's assume α = 0.05 and the effect size (xA - xB) / sqrt((sA^2 + sB^2) / 2) = 0.1. Using statistical software or a power calculator, we can calculate the probability of a Type II error (β) given these values.

Without the specific values of α and the effect size, we cannot provide an exact calculation for the probability of a Type II error. However, by increasing the sample size, we can generally reduce the probability of a Type II error.

In summary, the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, suggesting that Program A leads to higher average yearly reading growth. The p-value of the test results is approximately 0.010. Based on these findings, it may be recommended to adopt Program A over Program B. The probability of a Type II error (β) cannot be calculated without specific values of α and the effect size.

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Summary:

(i) To find the value of α such that the vectors v1, v2, and v3 are linearly dependent, we can set up a system of equations and solve for α.(ii) The Basis Theorem states that any set of linearly independent

(i) To check if v1, v2, and v3 are linearly dependent, we can set up the following equation:

c1v1 + c2v2 + c3v3 = 0,

where c1, c2, and c3 are constants. Substituting the given values of v1, v2, and v3, we have:

c1(3,7,7) + c2(1,4,4) + c3(α,1,1) = 0.

Simplifying this equation, we get the following system of equations:

3c1 + c2 + αc3 = 0,

7c1 + 4c2 + c3 = 0,

7c1 + 4c2 + c3 = 0.

We can solve this system of equations to find the value of α that satisfies the condition.

(ii) The Basis Theorem states that any set of linearly independent vectors that span a vector space can be used as a basis for that vector space. By applying the Basis Theorem to the vectors v1, v2, and v3, we can check if they form a basis for ℝ3. If they do, we can find the coordinates of a given vector, such as (2,3,5), in terms of the basis using Gaussian Elimination.

To apply Gaussian Elimination, we set up the augmented matrix [v1 | v2 | v3 | b], where b is the given vector (2,3,5). Then we perform row operations to obtain the row-echelon form of the augmented matrix. The resulting matrix will allow us to determine the coordinates of b in terms of the basis vectors.

By performing the Gaussian Elimination process, we can find the coordinates of (2,3,5) in terms of the basis vectors.

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There is no value of α that makes the vectors linearly dependent, and the basis for ℝ³ using the vectors [377, 148, 11α] is {v₁, v₂, v₃}, with the coordinates of [2, 3, 5] in terms of the basis found through Gaussian Elimination.

(i) To find the value of α such that vectors v₁, v₂, and v₃ are linearly dependent, we need to determine if there exist scalars a, b, and c, not all zero, such that a(v₁) + b(v₂) + c(v₃) = 0. Substituting the given values, we have a(377) + b(148) + c(11α) = 0. By solving this equation, we can find the value of α that satisfies the condition for linear dependence.

(ii) The Basis Theorem states that any set of linearly independent vectors that spans a vector space forms a basis for that vector space. Using a different value of α than the one found in (i), we can apply the Basis Theorem to determine a basis for ℝ³ using the vectors v₁, v₂, and v₃.

By performing Gaussian Elimination or row reduction on the augmented matrix [v₁ v₂ v₃], we can determine the basis vectors. The coordinates of vector [2 3 5] in terms of the basis can be found by solving the system of equations formed by equating the linear combination of the basis vectors to [2 3 5].

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2. a. A belongs to either the first or second quadrant, while B belongs to the second quadrant.

b. Displacement is \(\sqrt{(B*cos(60.0\°))^2 + (A + B*sin(60.0\°))^2}\).

c. The graphical representation is drawn.

3. a. Choose an origin (0, 0) on the ground with x-axis towards the basket and y-axis upwards.

b. Horizontal distance from you to the basket is Vx * (B/50).

c. The height of the basket is H = (D/50) * sin(60.0°).

d. It is a realistic basketball problem if the calculated height is within a reasonable range for a basketball hoop.

2. a. In quadrant notation, the first quadrant is top right, the second quadrant is top left, the third quadrant is bottom left, and the fourth quadrant is bottom right.

For vector A, the rural mail carrier walks in a northerly direction, so it lies in the positive y-axis direction. Therefore, vector A belongs to either the first or second quadrant.

For vector B, the carrier walks in a direction 60.0 degrees north of west. Since west is in the negative x-axis direction, a direction 60.0 degrees north of west will be in the second quadrant.

b. To find the displacement from the post office, we need to find the resultant vector by adding vectors A and B.

Let's assume A = A magnitude and B = B magnitude.

The horizontal component of vector B can be found using cosine: Bx = B * cos(60.0°).

The vertical component of vector B can be found using sine: By = B * sin(60.0°).

The displacement in the x-direction is the sum of the horizontal components of A and B: Dx = 0 + Bx.

The displacement in the y-direction is the sum of the vertical components of A and B: Dy = A + By.

The displacement from the post office can be calculated using the Pythagorean theorem: Displacement = sqrt(Dx^2 + Dy^2).

c. To sketch the graphical representation of vector addition, you can draw a coordinate system with the x-axis and y-axis. Start at the origin (representing the post office), and draw vector A in the northerly direction. Then draw vector B starting from the end point of vector A at an angle of 60.0 degrees north of west. The displacement vector will be the straight line connecting the initial point (post office) to the end point of vector B.

3. a. It's difficult to draw a cartoon in this text-based format, but you can imagine a basketball court. Choose an origin (0, 0) on the ground, with the x-axis extending horizontally from the origin towards the basket and the y-axis extending vertically upwards.

b. The horizontal distance from you to the basket can be calculated using the horizontal component of the ball's velocity. Let's assume the horizontal component is Vx. Then the horizontal distance traveled can be found using the equation: Distance = Vx * (B/50).

c. The height of the basket can be determined by calculating the vertical displacement of the ball. Let's assume the height is H. The vertical displacement can be found using the equation: H = (D/50) * sin(60.0°), where D is the initial speed of the ball.

d. It's unclear what you mean by "real basketball problem." However, based on the given information, if the height calculated in part c is a positive value and within a reasonable range for a basketball hoop, then it would be a realistic scenario. If the calculated height is negative or unreasonably large, it would indicate an unrealistic situation.

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The radius of convergence,R, of the series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\) is (1, ∞)

We know that for a power series ∑an (x - p)^n

if |x - p| < R then the series converges,

and if |x - p| > R then the series diverges.

Here, the number R is called the radius of convergence.

We have been given a series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\)

We need find the radius of convergence.

We use ratio test.

We know for \($\lim_{x\to\infty}~ | \frac{a_{n+1}}{a_n}|=L\)

if L < 1, then the series converges

and If \($\lim_{x\to\infty}~a_n \neq 0\) then \(\sum a_n\) diverges.

Using ratio test for given series,

\($\lim_{x\to\infty}~ | \frac{9(-1)^{n+1}~ (n+1)x^{n+1}}{9(-1)^n~ nx^n}|\\\\\\\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x^{n+1}}{nx^n}|\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x}{n}|\)

\(=|x| $\lim_{x\to\infty}~ | \frac{n+1}{n}|\)

= |x|

This means, the series is convergent for |x| < 1.

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Answer:

Equation that can be used = \(\frac{4(88)+2x}{6} = 90\)

Step-by-step explanation:

Given that:

Amir's average on four tests = 88

Let,

x be the score on one test

For two tests = 2x

Sum of all scores = Average of four tests + Score of two tests

Sum of all scores = 4(88) + 2x

Total number of tests = 6

Overall average needed = 90

Now,

\(Average = \frac{Sum\ of\ quantities}{Number\ of\ quantities}\\90 = \frac{4(88)+2x}{6}\\\\\frac{4(88)+2x}{6} = 90\)

Hence,

Equation that can be used = \(\frac{4(88)+2x}{6} = 90\)

Answer: 150 boys

Step-by-step explanation:

Let the number of boys be x

Since there were 200 more girls than boys, the number of girls will be: = x + 200

Since the ratio of boys to girls was 3:7, this can be solved further below:

3/7 = x/x+200

Cross multiply

(7 × x) = 3(x + 200)

7x = 3x + 600

7x - 3x = 600

4x = 600

x = 600/4

x = 150

The number of boys enrolled is 150

Number of Girls will be:

= X + 200

= 150 + 200

= 350

Check: Number of boys / Number of girls

= 150/350

= 3/7

= 3:7

Horizontal velocity of the bullet which was at a distance of 0.600m just before it strikes the disk from the axle is  648 m/s.

As given in the question,

Radius of the given disk 'r' = 0.600m

Mass of the given disk 'M' = 1.60 kg.

Mass of the used bullet 'm' = 0.0200 kg.

Distance of the rime from the axle 'L' = 0.600 m.

Angular speed of given disk 'ω' = 4.00 rad/s

Let us consider 'v' as the horizontal velocity of the given bullet

Angular momentum of given bullet = Angular momentum of given disk

m × v × L = (1/2)rω² ( M + m )

Substitute the value

0.0200 × v × 0.600 = ( 1/2) (0.600)(4)²( 1.60 + 0.0200)

⇒0.012v = 4.8( 1.62)

⇒ v= 7.776/ 0.012

⇒ v= 648m/s

Therefore, the horizontal velocity of the bullet which was strikes the disk just before at 0.600 m distance from axle is 648 m/s.

The above question is incomplete, the complete question is :

A uniform solid disk made of wood is horizontal and rotates freely about a vertical axle at its center. The disk has radius 0.600 m and mass 1.60 kg and is initially at rest. A bullet with mass 0.0200 kg is fired horizontally at the disk, strikes the rim of the disk at a point perpendicular to the radius of the disk, and becomes embedded in its rim, a distance of 0.600 m from the axle. After being struck by the bullet, the disk rotates at 4.00 rad/s. What is the horizontal velocity of the bullet just before it strikes the disk?

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The two inequalities that describe the unshaded region in the diagram are:

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of the solid line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3 - 1)/(2 - 1)

Slope (m) = 2/1 = 2

At data point (1, 1) and a slope of 2, a linear equation for this solid line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 2(x - 1)

y = 2x - 2 + 1

y ≥ 2x - 1 (since the solid line is shaded above).

For the dashed line, we have:

y - y₁ = m(x - x₁)

y - 6 = -1(x - 0)

y = -x + 6

y < -x + 6 (since the dashed line is shaded below).

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Let x = the number of 5¢ fare increases

Let y = money the company gets

Equation: y = (360 - 20x) (0.50 + 0.05x)

Solve for x when y = 196

196 = 180 + 18x - 10x - x^2

x^2 - 8x + 16 = 0

Factor to solve for x

(x - 4)^2 = 0

x = 4

Remember what x means

Total fare = 0.50 + 0.05x = 0.50 + 0.20 = 0.70

Total fare = 70¢

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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Distance between the points (-3, 5, -7) and (2, -4, 6) is 5√11 units.

What is cartesian coordinate points?

The Cartesian coordinates of a point in three dimensions are the triple (x, y, z). The three numbers or coordinates give the signed distance from the origin along the x, y, and z axes respectively.

Solution:

Given, x1 = -3     ,  x2 = 2

           y1 = 5      ,  y2 = -4

           z1 = -7     ,  z2 = 6

The formula for finding the distance between two points on 3D graph is given below

Distance =√((x2-x1)²+(y2-y1)²+(z2-z1)²)

⇒Distance =√{(2-(-3))²+(-4-5)²+(6-(-7))²}

⇒Distance =√{(2+3)²+(-9)²+(6+7)²}

⇒Distance =√{5²+81+13²}

⇒Distance =√(25+81+169)

⇒Distance =√275

⇒Distance =5√11

Thus, the distance between (-3, 5, -7) and (2, -4, 6) is 5√11.

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According to the given information the distance between the points 16.58 units.

the algebraic phrase known as the distance formula, which provides the distances between two places in terms of respective dimensions (see coordinate system). The distance formulae for locations in rectangular coordinates in two- and two half Euclidean space are based upon that Pythagorean theorem.

We can determine an object's actual size by learning how far it is from us. The area that an object occupies in the sky may be measured. The distance to an object is then necessary to calculate its real size. An thing appears smaller the farther it is away.

The distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂)

\(\begin{equation}d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}\end\)

x₁, y₁, z₁ = -3, 5, -7

x₂, y₂, z₂ = 2, -4, 6

\(\begin{equation}d=\sqrt{\left(2+3\right)^2+\left(-4-5\right)^2+\left(6+7\right)^2}\\\begin{equation}d=\sqrt{\left(5\right)^2+\left(-9\right)^2+\left(13\right)^2}\\\begin{equation}d=\sqrt{25+81+169}\\\begin{equation}d=\sqrt{275}\\\)

= 16.58 units

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Answer:

C, D

Step-by-step explanation:

1/5 is .20 which is 20%

4/20 is equal to 1/5 which is 20%

Hope this helps

Answer:

Its A, b, c, e

Step-by-step explanation:

Answer:

x=3

y=6

Step-by-step explanation:

2x+5=11

2x=6

x=3

Input x for 2x+4

2×3+4=10

y+4=10

y=6

Hope this helps! :)

Answer:

slope is 4/5

Step-by-step explanation:

Answer:

\(m=\frac{4}{5}\)

Step-by-step explanation:

add y to both sides

\(2x+4y+y=6x\)

add 4y and y

\(2x+5y=6x\)

subtract 2x from both sides

\(5y=6x-2x\)

subtract 2x from 6x

\(5y=4x\)

divide each term by 5

\(\frac{5y}{5} =\frac{4x}{5}\)

cancel common factor

\(y=\frac{4x}{5}\)

reorder the term x

\(y=\frac{4}{5}x\)

using the slope-intercept form, the slope is \(\frac{4}{5}\)

a. To find the 30th percentile for the standard normal distribution, we first need to locate the z-score that corresponds to this percentile. We can use a standard normal distribution table or a calculator to find this value. From the table, we can see that the z-score that corresponds to the 30th percentile is approximately -0.524. Therefore, the 30th percentile for the standard normal distribution is z = -0.524.

b. To find the 30th percentile for a normal distribution with mean 10 and standard deviation 1.5, we can use the formula for transforming a standard normal distribution to a normal distribution with a given mean and standard deviation. This formula is:
z = (x - μ) / σ
where z is the standard normal score, x is the raw score, μ is the mean, and σ is the standard deviation.
To find the 30th percentile for this distribution, we first need to find the corresponding z-score using the formula above:
-0.524 = (x - 10) / 1.5
Multiplying both sides by 1.5, we get:
-0.786 = x - 10
Adding 10 to both sides, we get:
x = 9.214
Therefore, the 30th percentile for a normal distribution with mean 10 and standard deviation 1.5 is x = 9.214. This means that 30% of the observations in this distribution are below 9.214.

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Let's isolate y first

\(\\ \rm\Rrightarrow 12x-6y=-36\)

\(\\ \rm\Rrightarrow 6y=12x+36\)

\(\\ \rm\Rrightarrow y=\dfrac{12}{6}x+\dfrac{36}{6}\)

\(\\ \rm\Rrightarrow y=2x+6\)

Compare to y=mx+b

The linear equation y = -x+45 models the scenario.

Solving the linear equation, it exists found that Hans will paint 16 snapdragons.

Since the rate of change exists always the exact, this question exists modeled by a linear equation.

Linear equation: y = mx + b

Where, m exists the slope and b exists the y-intercept.

To find the slope, we have to get two points (x, y), and the slope exists  given by the change in y divided by the change in x.

Points: (11, 34) and (12, 33).

Change in y: 33 - 34 = -1

Change in x: 12 - 11 = 1.

Slope: m = -1/1 = -1

The equation of the line exists y = -x + b

Replacing one of the points, the y-intercept can be found.

Point (11, 34) means that when x = 1, y = 34.

y = -x + b

34 = -1+b

b = 45

Therefore, the equation y = -x+45 models the scenario.

29 daisies mean that y = 29, we have to estimate the value of x for which y = 29.

y = -x+45

simplifying the equation,

29 = -x+45

x = 45 - 29 = 16

The value of x = 16

Therefore, Hans will plant 16 snapdragons.

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Answer:

The equation ✔ x = 45 – y models the scenario.

Hans will plant✔ 16 snapdragons

Step-by-step explanation:

The value of SSE (sum squared error) is 40 in the given analysis of the variance problem if SST = 120 and SSR = 80. Option b is correct.

Here the words SSE means Sum Squared Error, SST means Sum of Squares Total and SSR means Sum of Square Regression.

In the SSE accuracy measure, errors are squared and then added. It is used when the data points are similar in magnitude.

The formula is SST = SSR + SSE ⇒ SSE = SST - SSR

The given values of the analysis of the variance problem are

SST = 120; SSR = 80

Then, the value of SSE = SST - SSR = 120 - 80 = 40

So, option b is correct.

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The equation of the parabola in factored form is: y = 16(z - 1/2)(z - 8)

What is parabola?

A parabola is a symmetrical plane curve that is shaped like an arch. It is a quadratic function and is defined by the equation y = ax² + bx + c, where a, b, and c are constants.

Ryan's reasoning is justified because the z-intercepts of a parabola are the points where the parabola intersects the z-axis, which are the points where x = 0. Therefore, if the parabola can be expressed in the form y = a(x + 1)(x - 4), then its z-intercepts are at x = -1 and x = 4. This is because when x = -1, (x + 1) = 0 and when x = 4, (x - 4) = 0, which makes y = 0, indicating that the parabola intersects the z-axis at these two points.

To find the value of a, we need to use the given information that the y-intercept of the parabola is at (0, 2). Substituting x = 0 and y = 2 into the equation y = a(x + 1)(x - 4), we get:

2 = a(0 + 1)(0 - 4)

2 = -4a

Therefore, a = -1/2. So the equation of the parabola is y = (-1/2)(x + 1)(x - 4), in factored form.

To find the equation of the parabola in factored form y = a(z-p)(z-g), we can use the given information about its intercepts and symmetry axis. Since the symmetry axis is parallel to the y-axis, the parabola is of the form y = a(z - h)² + k, where (h, k) is the vertex. We know that the a-intercepts are -2 and 3, which means that the points (-2, 0) and (3, 0) lie on the parabola. Substituting these points into the equation, we get:

0 = a(-2 - h)² + k

0 = a(3 - h)² + k

Solving for h and k, we get:

h = 1/2

k = 4

Therefore, the vertex is at (1/2, 4), and the equation of the parabola is:

y = a(z - 1/2)² + 4

We can find the value of a by using the fact that the y-intercept is 4. Substituting z = 0 and y = 4, we get:

4 = a(0 - 1/2)² + 4

4 = a(1/4)

a = 16

Therefore, the equation of the parabola in factored form is:

y = 16(z - 1/2)(z - 8), which is sometimes referred to as intercept form because it explicitly shows the intercepts of the parabola on the z-axis.

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Answer:

hi friends how are you all about you my friend

Answer:

|x-7|+4

Step-by-step explanation:

Right 7, and up 4

To approximate the solution and maximize the given objective function we need to find the steepest ascent direction and iteratively update the values of x₁ and x₂ to approach the maximum value of z.

The method of steepest ascent involves finding the direction that leads to the maximum increase in the objective function and updating the values of the decision variables accordingly. In this case, we aim to maximize the objective function z = -(x₁ - 3)² - (x₂ - 2)².

To find the steepest ascent direction, we can take the gradient of the objective function with respect to x₁ and x₂. The gradient represents the direction of the steepest increase in the objective function. In this case, the gradient is given by (∂z/∂x₁, ∂z/∂x₂) = (-2(x₁ - 3), -2(x₂ - 2)).

Starting with initial values for x₁ and x₂, we can update their values iteratively by adding a fraction of the gradient to each variable. The fraction determines the step size or learning rate and should be chosen carefully to ensure convergence to the maximum value of z.

By repeatedly updating the values of x₁ and x₂ in the direction of steepest ascent, we can approach the solution that maximizes the objective function z. The process continues until convergence is achieved or a predefined stopping criterion is met.

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Answer:

26/16    or 1  7/19

Answer:

12590/80*100 = $15,737.50 4. Is your Answer

Step-by-step explanation:

12590 is 80% so simply divide by 80 and multiply by 100 to get the answer.

Answer:

This function doesn't have zeros because it doesn't touch the x-axis.

EDIT: I didn't see the negative sign before the 3. The function crosses the x-axis at (-5,0) and (5,0). Sorry!

The radius of each of the smaller molds is r = 1/3 ft. Using the volume of the given hemisphere, the required radius is calculated.

The volume of the hemisphere is calculated by using the formula,

= \(\frac{2}{3}\) × π × r³ cubic units

where r is the radius of the hemisphere.

It is given that,

A hemisphere-shaped bowl with a radius r = 1 ft is filled with chocolate.

So, the volume of the bowl is

V =  \(\frac{2}{3}\) × π × (1)³

  =  \(\frac{2}{3}\) × π cubic feets

The volume of each smaller hemisphere-shaped mold =  \(\frac{2}{3}\) × π × r³ cubic units

So, for 27 molds, the volume = 27 × \(\frac{2}{3}\) × π × r³ cubic units

All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds.

Then,

\(\frac{2}{3}\) × π = 27 × \(\frac{2}{3}\) × π × r³

⇒ r³ = 1/27

⇒ r = 1/3 ft

Therefore, the required radius of each of the smaller molds is 1/3 foot.

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