Ms. Martinez has a class of 16 students. She can spend $17 on each student to buy math supplies for the year. She first buys all of her students calculators,
which costs a total of $89.76. After buying the calculators, how much does she have left to spend on each student?
su

(a) There is no extreme value of A subject to the given constraint,

(b) For x = 0, y + z² ≤ 16.

y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.

For x = ±y, z = 4 - y².

y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.

When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.

Therefore, one should exclude the value of zero from the domain of the function or expression.

In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.

Let's find the partial derivatives of A with respect to x, y, and z.

∂A/∂x = 3

∂A/∂y = 2y - 2 = 2(y - 1)

∂A/∂z = 0

Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.

\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)

Substituting the values of the partial derivatives, we get:

\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)

The second and third equations are contradictory. So, under the given constraint, A has no extreme value.

In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.

Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.

We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.

2x = λ(2x),

2y = λ(1),

2z = λ(2z).

Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.

Substituting the values of x and λ from the first and second equations into the third equation, we get:

z = 4 - y² or z = 0.

Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:

Case 1: x = 0, y + z² ≤ 16.

So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.

Case 2: x = ±y, z = 4 - y².

So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.

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The orthonormal basis for (2, 1), (2, 5) is therefore u1, u2 = (2/5, 1/5), (2/5, -1/5) because u2 = v2_orth/||v2_orth|| = (2/5, -1/5).

In R2, the internal result of the two vectors u and v is as follows: The Gram-Schmidt procedure can be used to request the transformation of (2, 1), (2, 5) into an orthonormal premise. u, v = 2u1v1 + u2v2. An orthonormal premise is made by changing over a bunch of directly free vectors utilizing the Gram-Schmidt process. Our set's principal vector, v1 = (2, 1), should serve as our starting point.

We standardize v1 to obtain our first orthonormal premise vector: We must locate the second vector in our set, v2 = (-2, -5), and we can orthogonalize v2 by deducting its projection from u1: u1 = v1/||v1|| = (2/5, 1/5) proj_u1(v2) = (v2 u1)u1 = (- 8/5, - 4/5)v2_orth = v2 - proj_u1(v2) = (6, - 21/5)Our second orthonormal premise vector is acquired by normalizing v2_orth: The orthonormal reason for (2, 1), (2, 5) is subsequently u1, u2 = (2/5, 1/5), (2/5, - 1/5) in light of the fact that u2 = v2_orth/||v2_orth|| = (2/5, - 1/5).

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Answer:

7/8

Step-by-step explanation:

add your decimal your fraction inside parentheses then divide it by the rest of the equation

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

The solution for the questions is mathematically given as

a)

t-distribution.

b)

the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952, 7.3048 )

c) the value of the \(\mu_0\) is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_0; otherwise, reject H _0.

d)

you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

Generally, the equation for is mathematically given as

a.

In this case, the standard deviation of the population is unknown.

As a result, we make use of the t-distribution.

b)

We wish to generate a confidence interval with a 98 percent likelihood for the mean.

Because of this,

\((\bar{X}-t_{n-1,\alpha/2}\frac{s}{\sqrt{n}},\bar{X}+t_{n-1,\alpha/2}\frac{s}{\sqrt{n}})\)

\((6.85-t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}},6.85+t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}})\)

\((6.85-t_{147,0.01}\frac{2.12}{12.1655},6.85+t_{147,0.01}\frac{2.12}{12.1655})\)

(6.3952,7.3048)

Therefore, the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952 , 7.3048 )

c )

If the value of the mu _0 is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_o; otherwise, reject H_0.

d . Here, we want to determine the sample size

Therefore,

\(n=t_{n-1,\alpha/2}^2\frac{s^2}{E^2}\)

\(n=t_{148-1,0.05/2}^2\frac{2.12^2}{0.5^2}\)

\(n=t_{147,0.025}^2\frac{2.12^2}{0.5^2}\)

\(n=2.6097^2\frac{2.12^2}{0.5^2}\)

n=122.4364

In conclusion, you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

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Answer:

c

Step-by-step explanation:

hope it helps u have a good day

Answer:

correct answer is A ..because it passed 5 and about to reach 6 ..only 1/8 left to be 6

The F-distribution is used to test the significance of the population coefficient of determination (option D).

The coefficient of determination, denoted as R², measures the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect relationship.

To determine the significance of R², the F-distribution is used. The F-test compares the variation explained by the regression model (numerator) to the unexplained or residual variation (denominator). It calculates the F-statistic, which is the ratio of the two variances.

The F-distribution provides critical values that allow us to determine whether the observed F-statistic is statistically significant or not. By comparing the calculated F-value with the critical value from the F-distribution, we can assess whether the coefficient of determination is significantly different from zero, indicating the presence of a meaningful relationship between the variables. The correct option is d.

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Answer: The numbers of flowers she could have picked are 21, 24, 27, 30, 33, and 36.

Why?: These are all multiples of 3 between 20-40.

From the steps shown in the table given, we can conclude that: D. in solving the equation, the subtraction property of equality was not applied.

If a + b = c, to apply the subtraction property of equality so that b is moved to the other side of the equation, we would have:

a + b - b = c - b

a = c - b

Thus, from the table given, the none of the steps showed that the subtraction property of equality was applied in solving the equation, so, the answer is: D.

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Answer:

\(12-20x^{2}\)

Step-by-step explanation:

\(4(3-5x^{2}) = (4*3)-(4*5x^{2} )\)

\(4*3 = 12\)

\(4*5x^{2} =20x^{2}\) since you only multiply the numbers

\(12-20x^{2}\)

Answer:

The answer is -2 points per question

:)

For those in need of an explanation, she missed 11 problems and got 22 points taken off. Divide 22 by 11 and you get two.

I hope you all found this helpful and if you need a better explanation or have a question, feel free to comment down below and ill get back to you as soon as possible. :)

The team scored 2 field goals, 2 safeties, and 4 touchdowns.

A statement proving the equality of two mathematical expressions is known as an equation. The goal is frequently to ascertain the values of the variables that make the equation true, and it may have one or more variables.

The football team scored 8 times and a total of 38 points.

Let T be the number of touchdowns, F be the number of field goals, and S be the number of safeties.

We know, T = F + S and F + S = 4

Substituting, T = F + S into the equation for total points,

we get, 7T + 3F + 2S = 38

Solving for F and S, we get F = 2 and S = 2.

Therefore, the team scored 2 field goals, 2 safeties, and 4 touchdowns.

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Solve for F and S then get F = 2 and S = 2.

The team scored 4 touchdowns, 2 field goals, and 2 safeties.

The football group scored 8 times, totaling 38 points.

Let,

T is the no.of touchdowns,

F is the no.of field goals, and

S is the no.of safeties.

Touchdown: The ball is in possession of a runner who has moved from the field of play into the end zone and is on, above, or behind the plane of the opposing goal line (extended).

Field Goal: a three-point goal in football obtained by kicking the ball over the crossbar during normal play.

Safeties: NFL defences can score a safety, worth two points, by tackling the offensive player with the ball behind his own goal line or forcing him to run or throw the ball out of bounds behind his own goal line.

We know that,

T = F + S and

F + S = 4

For total points, put T = F + S into the equation.

We get,

7T + 3F + 2S = 38

Solve for F and S,

we get,

F = 2 and S = 2.

As a result, the team tallied 2 field goals, 2 safeties, and 4 touchdowns.

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The value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

The ratio of the neighboring side's length to the longest side, or hypotenuse, in a right triangle is known as the cosine. Let's say that the hypotenuse of a triangle ABC is written as AB, and the angle between the hypotenuse and base is written as.

It's interesting to see that cos's value varies depending on the quadrant. As observed in the above table, cos 0°, 30°, etc. have positive values while cos 120°, 150°, and 180° have negative values. Cos will have a good value in the first and fourth quadrants.

Given that, sin x equals negative 15 over 17.

Using the Pythagoras theorem we have:

(17)² = (- 15)² + y²

y = 8

The value of cos x = 8/17

Then the value of cos2(x) is calculated using the formula:

cos2x = cos²x - sin²x

cos2x = (8/17)² - (15/17)²

cos2x = -161/289

Hence, the value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

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Unit rate at which water evaporates in terms of inches per hour from given condition is equal to 5/36 inches per hour.

As given in the question,

Amount of water evaporating from the pool is equal to 5 /8 inches

Time taken to evaporate 5 /8 inch of water from the pool is 4 1/2 hours

Total time taken = 4 1/2 hours

                         = 9 /2 hours

Unit rate at which water evaporates in terms of inches per hour from given condition is given by:

( 9 /2 ) hours = ( 5/ 8 ) inches of water evaporates

⇒ 1 hour = ( 5/8 ) × (2/9) inches per hour

⇒ 1 hour = (5 /36) inches per hour

Therefore, unit rate at which water evaporates in terms of inches per hour from given condition is equal to 5/36 inches per hour.

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Answer:

2/5

Step-by-step explanation:

If she has 3 chews and 2 mints left, the probability that she picks a mint is 2/5 as they are only 2 mints and 3 chews and 2+3 = 5. So the awnser is 2/5.

0.765

answer is 0.764758824 and because there is a 7 after the 4 we round up

Answer: 135/20=6.75

Step-by-step explanation:

Long division (picture attached below)

Answer:

x=3/2 x=1

Step-by-step explanation:

2x^2-5x+3=0

2x^2 -2x-3x+3=0

2x(x-1) -3(x-1)=0

2x-3=0

2x=3

x=3/2

x-1=0

x=1

Answer:

2x²−2x−3x+3=0

2x(x−1)−3(x−1)=0

(x−1)(2x−3)=0

Step-by-step explanation:

The difference between the shortest and longest species of frog is \(3^{3\\}\).

A line plot is a graph that shows data as checkmarks or points over a number line, indicating the frequency of each value.

When displaying information that changes over time, a line graph, also referred to as a line chart or a line plot, is frequently used. It can be visualized using a series of points connected by straight lines. The "x-axis" and the "y-axis" are two of its axes.

is a graph where the lines connecting the various data points are used. A line graph shows numerical values over a predetermined period of time. The shortest and longest frog species differ in terms of \(3^{3}\).

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The correct answer is c. 6 ft³.To calculate the volume of the sculpture, we need to find the volume of one pyramid and then multiply it by four.

The volume of a pyramid can be calculated using the formula V = (1/3) * base area * height. In this case, the base area of the pyramid is a square with side length 2 feet, so the area is 2 * 2 = 4 square feet. The height of the pyramid is 6 feet. Plugging these values into the formula, we get V = (1/3) * 4 ft² * 6 ft = 8 ft³ for one pyramid. Since there are four identical pyramids, the total volume of the sculpture is 8 ft³ * 4 = 32 ft³.

However, the question asks for the volume of sculpting material needed, so we need to subtract the volume of the hollow space inside the sculpture if there is any. Without additional information, we assume the sculpture is solid, so the volume of material needed is equal to the volume of the sculpture, which is 32 ft³. Therefore, the correct answer is c. 6 ft³.

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The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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A regression equation is a mathematical formula that represents the relationship between a dependent variable and one or more independent variables in a regression analysis. It is used to estimate or predict the values of the dependent variable based on the independent variables.

The answer to the provided question is that C. It is because of the heteroskedasticity of the variance. Heteroscedasticity of variance refers to a situation where the dispersion of the error terms differs throughout the values of the independent variable in a regression equation.

Explanation: The assumptions of classical linear regression model (CLRM) are as follows: Assumption

1: The relationship between dependent and independent variables is linear, and the change in the dependent variable is proportional to the change in independent variables. Assumption

2: The residuals or errors of the regression model are normally distributed, with a mean of zero and a constant variance. Assumption

3: The observations are not reliant on one another. That is, there is no correlation between two residuals or errors from a particular regression model. Assumption

4: There are no extreme outliers in the residuals or errors, and the residuals are homoscedastic. Assumption 5: There is no multicollinearity between any independent variables. In other words, the model does not include any two independent variables that are highly related or correlated. The given regression model

\(\[ y_{i}=\beta_{1}+\beta_{2} x_{i 2}+\cdots+\beta_{K} x_{i K}+e_{i} \]where \[ E\left[e_{i} \mid x_{i}\right]=0 \]and \[ \operatornam{Var}\left(e_{i} \mid x_{i}\right)=\sigma_{i}^{2} \]\)

To check the assumptions of a simple regression model, the best way is to look at the residual plots. If the residual plots show any deviation from the assumption, the particular assumption is violated. In this case, if the residual plot shows a funnel shape, then it is the indication that the residuals have heteroscedasticity of variance.

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Let's assume that the original length of the piece of board is L.

Now you cut two pieces that are 3.4 ft long, so the remaining piece of board is:

L - 3.4ft - 3.4ft = L - 6.8ft long.

Now we know that the remaining must be 2.35 times longer than the pieces of 3.4 ft, then we have the equation:

( L - 6.8ft) = 2.35×3.4ft

solving that for L we get:

L  = 14.79ft

Rounding to the nearest tenth, we get:

L = 14.8ft

You should buy a piece of board that is 14.8 feet long.

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Answer:

44 inches

Step-by-step explanation:

Given that :

Scale of drawing = 1 inch : 8 inches

Height of building in drawing = 5 1/2 inches

Using the scale provide for the drawing, the actual height of the building is :

Height of building in drawing * 8 inches

5 1/2 * 8

5.5 * 8 inches

= 44 inches

Answer:

A is the right awnser

Step-by-step explanation:

hope this helps

Answer:

angle 135° is an obtuse angle

The table represents values of a linear function. The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m = slope

c = y intercept

We would find the slope and y intercept. The formula for determining slope is expressed as

m = (y2 - y1)/(x2 - x1)

From the table,

if x1 = - 1, y1 = 1

if x2 = 0, y2 = 2

m = (2 - 1)/(0 - - 1) = 1/(0 + 1) = 1/1 = 1

To find the y intercept, we would substitute m = 1, x = - 1 and y = 1 into the slope intercept equation. We have

1 = 1 * - 1 + c

1 = - 1 + c

c = 1 + 1 = 2

This means that the y coordinate of the y intercept of g(x) is 2

The y coordinate of the y intercept of f(x) is 1

Thus,

A) The y coordinate of the y intercept of f(x) is less than the y coordinate of the y intercept of g(x)

Lookng at the graph of f(x) and table representing g(x), the maximum of f(x) is y = 3 and g(1) = 3

Thus,

B) The maximum of f(x) is equal to g(1)

f(x) has 2 zeros at the points where the lines cut across the x axis. The linear graph of g(x) has only one zero. Thus,

C) The number of zeros of f(x) is greater than the number of zeros of g(x)

Answer:

Up 5, 2 to the right (5/2)

Step-by-step explanation:

I just counted the units of the Cartesian Plane