If angle, a and angle B are supplementary angles, in angle a is three times, as large, as angle be find the measures of angle a and angle B

Therefore, the statement is not necessarily true, and the value of ½f(a, b) depends on the specific function f and the nature of the local minimum at (a, b).

If f has a local minimum at (a, b) and f is differentiable at (a, b), then it is true that the partial derivatives of f at (a, b) must be zero (i.e., fx(a, b) = 0 and fy(a, b) = 0). This is because at a local minimum, the function is not increasing in any direction, so the directional derivatives in all directions must be zero, which implies that the partial derivatives are also zero.

However, this does not necessarily mean that ½f(a, b) = 0. For example, consider the function f(x, y) = (x - 1)² + (y - 1)². This function has a local minimum at (1, 1), and the partial derivatives are zero at that point. However, ½f(1, 1) = ½(0) = 0, so the statement is true in this case, but this is not necessarily true in general.

On the other hand, consider the function g(x, y) = x² + y². This function also has a local minimum at (0, 0), and the partial derivatives are zero at that point. However, ½g(0, 0) = ½(0) = 0, so the statement would suggest that g(0, 0) is a local minimum, which is not true (in fact, it is a global minimum).

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Answer:

Step-by-step explanation:

1807

There are 21 unique ways the first and second place ribbons can be awarded.

The given information can be solved using permutations. The total number of ways the first and second place ribbons can be awarded is: `7P2`The formula for permutation is given by:nPr = n!/(n-r)!Where, n is the total number of objects and r is the number of objects to be arranged in a permutation.

As per the given question, n = 7 (number of contestants) and r = 2 (number of ribbons).Therefore, the total number of ways the first and second place ribbons can be awarded is:7P2 = 7!/(7-2)! = 7!/5! = 7 x 6/2 x 1 = 21Thus, there are 21 unique ways the first and second place ribbons can be awarded.

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The rate of change of the annual u.s. factory sales in 2000 is 7.7 billion dollars per year

From the question, we have the following parameters that can be used in our computation:

s(t) = 0.12t² − t + 5.7

In 2000, we have the value of t to be

t = 2000 - 1990

Evaluate

t = 10

So, we have

s(10) = 0.12 * 10² − 10 + 5.7

Evaluate

s(10) = 7.7

Hence, the rate in 2000 is 7.7 billion dollars per year

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Question

the rate of change of annual u.s. factory sales (in billions of dollars per year) of consumer electronic goods to dealers from 1990 through 2001 can be modeled as s(t) = 0.12t2 − t + 5.7 billion dollars per year

Calculate the rate of change in 2000

6.6,your answer is correct.

As the theorem is a^2+b^2=c^2 you first must assign the proper components to each variable. Since 12 is the longest since it is the hypotenuse that means it is c so in this case 144. And since 10 is the leg it is a.

To solve you must take

10^2+b^2=12^2

100+b=144

144-100=44

Since b^2 is 44 you must find the square root \(\sqrt{44}\)=6.6

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

The if statement evaluates the test expression inside the parenthesis ().

If the test expression is evaluated to true, statements inside the body of if are executed.

If the test expression is evaluated to false, statements inside the body of if are not executed.

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

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In conditional statements, the part of the statement following 'if' is called the antecedent.

The antecedent is the condition that needs to be true for the consequent to occur.

The consequent is the part of the statement that follows 'then.'

An antecedent is a noun or pronoun that denotes a specific being, place, object, or clause.

It's also referred to as a referent. Without an antecedent, a sentence may be insufficient or nonsensical since it is

required to establish what or to whom a pronoun in a sentence is referring.

In summary, a conditional statement is structured as "if (antecedent) then (consequent)."

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Answer: D= csc theta

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

There are 46 children attending the field trip.

Each van needs to transport 8 children.

To find the number of vans they need, we will divide the number of children by the number of children per van:

46 / 8 = 5.75 ≅ 6 vans

They need 6 vans.

Answer:

No solution

Step-by-step explanation:

45x + 27 + 2x - 8 = 47x + 28

47x + 19 = 47x + 28

19 = 28

19 can never equal 28

Answer:

divide 460/60

Step-by-step explanation:  

60 rep one hour and you will find your answer

Form the composition f(x) = 3x2 + 1, g(x) = 4x - 2 - 2, the , (g º f)(x) = 12x^2 + 2 and (8 º f)(x) = 770.

To find the composition (g º f)(x) where f(x) = 3x^2 + 1 and g(x) = 4x - 2, we substitute the expression for f(x) into g(x).

First, let's find the composition (g º f)(x):

(g º f)(x) = g(f(x))

Substituting f(x) into g(x):

(g º f)(x) = g(3x^2 + 1)

Now, let's substitute the expression for g(x) into g(3x^2 + 1):

(g º f)(x) = 4(3x^2 + 1) - 2

Simplifying:

(g º f)(x) = 12x^2 + 4 - 2

(g º f)(x) = 12x^2 + 2

Therefore, (g º f)(x) = 12x^2 + 2.

Now, let's find (8 º f)(x) by substituting x = 8 into the expression for f(x):

(8 º f)(x) = 12(8)^2 + 2

(8 º f)(x) = 12(64) + 2

(8 º f)(x) = 768 + 2

(8 º f)(x) = 770.

Therefore, (8 º f)(x) = 770.

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The residual standard error is a useful measure of the precision and accuracy of a regression model's predictions, and it helps to assess the goodness of fit of the model.

The measure that indicates how precise a prediction of y is based on x or how inaccurate the prediction might be is called the residual standard error (RSE).

RSE is a measure of the variation or dispersion of the errors (or residuals) in a regression model. It is calculated by taking the square root of the sum of the squared residuals divided by the degrees of freedom.

The RSE provides an estimate of the standard deviation of the errors, and it is expressed in the same units as the response variable y.

In other words, the RSE measures the average distance that the observed values deviate from the predicted values in the regression model.

A smaller RSE indicates that the model is better at predicting the response variable, while a larger RSE indicates that the model has higher prediction error and may not be as accurate.

In summary, the residual standard error is a useful measure of the precision and accuracy of a regression model's predictions, and it helps to assess the goodness of fit of the model.

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The measure that indicates how precise a prediction of y is based on x, or conversely, how inaccurate the prediction might be, is called the residual standard error (RSE). The RSE is a measure of the average distance that the observed values fall from the predicted values, and it is typically expressed in the same units as the response variable (y). A smaller RSE indicates a better fit of the model to the data, and a larger RSE indicates a poorer fit.

Answer: y = -19/8 + 9x/8

Step-by-step explanation: Move all terms that don't contain y to the right side and solve.

The ordered pairs that are solutions to y + 2 = -3(x - 4) include :

To find the ordered pairs, insert the x value in an ordered pair, into the equation. If the y value that you are given is the same as the one in the ordered pair, then the ordered pair is a solution to the equation.

Ordered pair ( 5, - 5 ) :

y + 2 = - 3 ( 5 - 4 )

y + 2 = - 3

y = - 3 - 2

y = - 5

Ordered Pair ( 2, 4 )

y + 2 = - 3 ( 2 - 4 )

y + 2 = 6

y = 6 - 2

y = 4

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Options for this question are:

In set theory, two sets are considered equal if they have the same elements. In this case, A is a set containing the elements 1, 2, and 3, while B is an empty set (also known as the null set),

A contains three distinct elements, and B contains none, we can conclude that A and B are not equal, i.e., A is not equal to B.

A ≠ B

Set theory is a branch of mathematics that studies collections of objects, called sets, and the relationships between them. A set is defined as a well-defined collection of distinct objects, which can be anything from numbers and letters to more abstract concepts like functions and geometrical shapes. The set theory provides a foundation for other areas of mathematics, including algebra, topology, and logic.

One of the fundamental concepts of set theory is the notion of membership, which states that an object either belongs to a set or does not. Sets can also be combined through operations such as union, intersection, and complementation, and the relationships between sets can be represented using Venn diagrams.

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Answer:

x² + (y + 3)² = 25

Step-by-step explanation:

the centre (C) of the circle is at the midpoint of the diameter.

using the midpoint formula

midpoint = ( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

with (x₁, y₁ ) = P (3, 1 ) and (x₂, y₂ ) = Q (- 3, - 7 )

C = ( \(\frac{3-3}{2}\) , \(\frac{1-7}{2}\) ) = ( \(\frac{0}{2}\) , \(\frac{-6}{2}\) ) = (0, - 3 )

the radius r is the distance from the centre to either P or Q

using the distance formula

r = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = C (0, - 3 ) and (x₂, y₂ ) = P (3, 1 )

r = \(\sqrt{(3-0)^2+(1-(-3)^2}\)  

 = \(\sqrt{3^2+(1+3)^2}\)

 = \(\sqrt{3^2+4^2}\)

 = \(\sqrt{9+16}\)

 = \(\sqrt{25}\)

 = 5

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (0, - 3 ) and r = 5 , then

(x - 0 )² + (y - (- 3) )² = 5² , that is

x² + (y + 3)² = 25

AB,BC, CD, AD, AC, BD.

Answer is 6.

Answer:

32

Step-by-step explanation:

Answer:

it will take 10 months

Looking at the back to back stem and leaf plot for the test scores, we can tell that D) The median and mean for Class A are higher than those for Class B. They have equal IQRs of 15.

The mean of Class A can be found to be :
= ( 70 + 70 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 90 + 95 + 95 + 95 + 95 + 95 + 95 + 100 + 100 + 100 ) / 22

= 92

The mean of Class B would be :

= ( 70 + 70 + 70 + 75 + 75 + 75 + 75 + 75 + 80+ 80 + 80 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90+ 90 + 95 + 95 + 100 ) / 23

= 82

The mean of Class A is therefore larger than Class B. The IQR cannot be up to 70 given that the lowest value of 70 and the highest is 100 so the correct option is option D.

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Answer:

a. $14.99k + $24+ $25 = x

b. $14.99(3) + $24+ $25 = x

   $44.97 + $24 + $25 = $93.97

Step-by-step explanation:

Answer:

i) C= $14.99 k + $24

ii) $93.97

Step-by-step explanation:

Let the number of models be represented by -----------k

Let the amount spent on books to be--------$24

The equation that represent amount spent in the mall is given as;

C= $14.99 k + $24   ---------------where ;

C= the equation for the total amount spent in the mall

k = the number of plane models

ii)

Using the equation : C= $14.99 k + $24    and if k = 3 and the amount spent on the store is $25  then ;

C= $14.99 * 3 + $24 = $44.97 + $24 = $68.97

C+ 25 = $68.97 + 25 =$93.97

Answer: x= 5

Step-by-step explanation: Refer to the image, all the explanations included

Answer:

Step-by-step explanation:

To solve this, find the value of n to one side of the equation.

N is a variable.

Variable is a quantity that can assume any of a set of values.

3n-4=11

First, you add by 4 from both sides.

\(\sf{3n-4+4=11+4}\)

Solve.

\(\sf{11+4=15}\)

\(\sf{3n=15}\)

Then, you divide by 3 from both sides.

\(\sf{\dfrac{3n}{3}=\dfrac{15}{3} }\)

Solve.

15/3=5

\(\Rightarrow \boxed{\sf{n=5}}\)

As a result, the solution is n=5, which is our answer.

I hope this helps, let me know if you have any questions.

Answer:

-4

Step-by-step explanation:

so t is greater than -5, and for negatives, you need to get nearer zero.

Answer:

(x + 4)^2 + (y - 1)^2 = 61.

Step-by-step explanation:

We need to find the square of the radius and the coordinates of the center.

Center = (-10 + 2)/2 , (-4 + 6)/2

= (-4, 1).

Length of the diameter

=  √((-10-2)^2 + (-4-6)^2)

= √(144 + 100)

=√244

So the radius = √244/2

and r^2 = 244/4 = 61,

So the equation of this circle is:

(x - (-4)^2 + (y - 1)^2 = 61

(x + 4)^2 + (y - 1)^2 = 61.

(x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given coordinates of the diameter of circle are  (-10,-4) and (2,6)

Diameter=√(x₂-x₁)²+(y₂-y₁)²

x₂=2,x₁=-10, y₁=-4, y₂=6

Diameter=√(2-(-10))²+(6-(-4))²

=√(12)²+(10)²

=√144+100

=√244

We know that Radius=Diameter/2

R=√244/2

Squaring both sides

R²=244/4

R²=61

So the equation of this circle is:

(x - (-4)² + (y - 1)² = 61

(x + 4)²+ (y - 1)² = 61.

Hence (x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

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Calculate the probability of more than 1 student contacting the Advising Office during a randomly selected one-minute interval between 8:00a.m. and 9:00a.m., we can use the Poisson distribution with a mean of 2 students per minute. The probability is approximately 0.7358.

The Poisson distribution is commonly used to model the number of events that occur in a fixed interval of time or space, given a known average rate of occurrence. In this case, the mean number of students contacting the Advising Office per minute is 2.

To find the probability of more than 1 student contacting the office during a one-minute interval, we can use the Poisson probability formula:

P(X > 1) = 1 - P(X <= 1)

Using the Poisson distribution formula, we can calculate the probabilities for X = 0 and X = 1, and then subtract them from 1 to find the probability of more than 1 student.

\(P(X = 0) = (e^(-λ) * λ^0) / 0! = e^(-2) ≈ 0.1353\)

\(P(X = 1) = (e^(-λ) * λ^1) / 1! = 2 * e^(-2) ≈ 0.2707\)

P(X > 1) = 1 - (P(X = 0) + P(X = 1))

= 1 - (0.1353 + 0.2707)

≈ 0.7358

Therefore, the probability of more than 1 student contacting the Advising Office during a randomly selected one-minute interval between 8:00a.m. and 9:00a.m. is approximately 0.7358, or 73.58% rounded to four decimal places.

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a is called the real part of the complex number and bi is called the imaginary part of the complex number. In the complex number 6 - 4i, for example, the real part is 6 and the imaginary part is -4i.

The area of the trapezoid is 94.5x cm².

In this case, we have a right trapezoid with bases of 12x cm and 15x cm and a height of 7 cm. To find the area of this trapezoid, we use the formula:

Area = (b1 + b2) * h / 2

where b1 and b2 are the lengths of the two bases, h is the height, and the whole expression is divided by 2.

Substituting in the values given, we get:

Area = (12x + 15x) * 7 / 2

Area = 27x * 7 / 2

Area = 189x / 2

Area = 94.5x

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The coordinates of the image of triangle ABC after a dilation with center (0,0) and a scale factor of 1/2 are (1,2), (3,0.5), and (1.5,2.5).

A dilation is a transformation that changes the size of a figure, but not its shape. It can either enlarge or reduce a figure, depending on the scale factor.

In this problem, we are asked to find the coordinates of the image of triangle ABC after a dilation with center (0,0) and a scale factor of 1/2. To do this, we need to apply the rule for dilations, which states that the coordinates of the image of a point after a dilation with center (h,k) and scale factor s are given by:

(x', y') = (s(x-h) + h, s(y-k) + k)

where (x,y) are the coordinates of the original point, and (x', y') are the coordinates of its image.

In our case, the center of dilation is (0,0), which means that h = k = 0. The scale factor is 1/2, so we substitute s = 1/2 into the formula. Now we can apply this formula to each vertex of triangle ABC to find its image.

Let's start with point A, which has coordinates (2,4). Applying the formula, we get:

(x', y') = (1/2(2-0) + 0, 1/2(4-0) + 0)

Simplifying, we get:

(x', y') = (1, 2)

Therefore, the image of point A is (1,2).

We can repeat this process for points B and C, which have coordinates (6,1) and (3,5), respectively. After applying the formula, we get:

The image of point B is (3, 0.5)

The image of point C is (1.5, 2.5)

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