What is the product?

The critical point of f at z = 1 is a local minimum.

To find the critical points of the function f(z, 3) = 4z^2 - 8z + 1, we need to find the values of z where the first partial derivatives with respect to z are equal to zero. Let's solve it step by step.

Take the partial derivative of f with respect to z:

∂f/∂z = 8z - 8

Set the derivative equal to zero and solve for z:

8z - 8 = 0

8z = 8

z = 1

The critical point of f occurs when z = 1.

To determine whether the critical point is a local minimum, local maximum, or a saddle point, we can use the second partial derivative test. We need to calculate the second partial derivative ∂²f/∂z² and evaluate it at the critical point (z = 1).

Taking the second partial derivative of f with respect to z:

∂²f/∂z² = 8

Evaluate the second derivative at the critical point:

∂²f/∂z² at z = 1 is 8.

Analyzing the second derivative:

Since the second derivative ∂²f/∂z² = 8 is positive, the critical point (z = 1) corresponds to a local minimum.

Therefore, the critical point of f at z = 1 is a local minimum.

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SOLUTION

We want to use the information in the diagram to prove that

Now, we have been given for number 1

2.

3.

4.

5.

6.

7.

8.

9. and 10. is good (correct)

11.

12.

13.

14.

A 90% confidence interval for the mean of the population is (499.39, 532.99).

To find a 90% confidence interval for the mean of the population, we can use the formula:

CI = x ± zα/2 * σ/√n

where x is the sample mean, σ is the population standard deviation, n is the sample size, and zα/2 is the critical value for a level of significance α/2.

First, we need to calculate the sample mean and standard deviation:

x = (516 + 536 + ... + 509 + 587) / 87 = 516.19

s = 28

Next, we need to find the critical value for a 90% confidence interval. Using a standard normal distribution table or calculator, we find that zα/2 = 1.645.

Substituting these values into the formula, we get:

CI = 516.19 ± 1.645 * 28 / √87

= (499.39, 532.99)

Therefore, we can be 90% confident that the true population mean lies within the interval (499.39, 532.99).

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Answer:

solution set for x = { 4,5,6}

Answer:

2<x<12

Step-by-step explanation:

Firstly, look at this formula-

a-b<x<a+b

If we make 7, A, and 5, B, then the formula would be 7-5<x<7+5

So after you do the math it would be 2<x<12

Hence, the answer is 2<x<12

BTW if the answer is correct then can you please mark me brainlyest?

I'm only 9 years old

Thanks!

A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips without replacement and the different samples possible are 416,965,528.

A  batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips without replacement.

Assume 10 of the chips do not conform to customer requirements

The different number of samples can be calculated by combinations and permutations.

Given n = 140 semiconductor chips

r = 5 chips without replacement

The number of different samples can be calculated using combinations formulae. The  batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips without replacement.

n = 140

r = 5

10 of the chips do not conform to customer requirements.

order is not important,  whether chip selected last or at the first, by using the combinations formulae , we get

n! / (r!)(n! - r!)

140! / (5!) (140! - 5!)

140! / (5!) (135!)

So, the number of different samples possible are 416,965,528.

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Answer:

Step-by-step explanation:

This is a parallelogram. In parallelogram, opposite sides are equal.

x + 3 = 6

     x = 6 - 3

    x = 3

Answer:

3

Step-by-step explanation:

parallelogram - top side = bottom side (parallel sides)

; x + 3 = 6

; x = 6 - 3

; x = 3

Answer:

180 = 3x + 90°

Step-by-step explanation:

180 = x + 2x + 90

Answer:

B

Step-by-step explanation:

Got it right on edgy

Answer:

1 2 3

Step-by-step explanation:

The area of the six-pointed star is equal to twice the area of the hexagon. Once "show step 2" is checked, you can move the slider below the box to map the triangles into the internal part of the hexagon.

hope it helped

Answer:

kkjv77

Step-by-step explanation:

j66

Answer:

Multiply the first equation by 5 and the second equation by 2. Then add.

Multiply the first equation by 2 and the second equation by 5, then subtract.

Step-by-step explanation:

Given

\(- 2x + 5y = -15\)

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

Required

Steps to solve using elimination method

From the list of given options, option 2 and 3 are correct

This is shown below

Option 2

Multiply the first equation by 5

\(5(- 2x + 5y = -15)\)

\(-10x + 25y = -75\)

Multiply the second equation by 2.

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

\(10x + 4y = -12\)

Add

\((-10x + 25y = -75) + (10x + 4y = -12)\)

\(-10x + 10x + 25y +4y = -75 - 12\)

\(29y = -87\)

Notice that x has been eliminated

Option 3

Multiply the first equation by 2

\(2(- 2x + 5y = -15)\)

\(-4x + 10y = -30\)

Multiply the second equation by 5

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

\(25x + 10y = -30\)

Subtract.

\((-4x + 10y = -30) - (25x + 10y = -30)\)

\(-4x + 25x + 10y - 10y= -30 +30\)

\(21x = 0\)

Notice that y has been eliminated

Answer:

How many solutions does the system have?

✔ exactly one

The solution to the system is

(

⇒ 0,

⇒ -3).

Step-by-step explanation:

the next two parts

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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They must sample 385 subscribers to obtained this interval.

What do you mean by sample?

An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values.

According to the given question,

We have:

95% confidence interval for z-score is  1.96

Using this formula to find the number of  subscribers  they must sample to obtain this interval

n≥ (zσ/2 ÷ 2ME)²

Where:

n= Sample

zσ = Z-score

ME = margin of error

Let put in the formula,

n≥ [1.96 / 2(0.05)]²

n≥ [1.96 / 0.1]²

= (19.6)²

= 384.16

=385 (Rounded)

Therefore, they must sample 385 subscribers to obtained this interval.

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Answer:

n = 23

Step-by-step explanation:

n - 13 x -6 = -60

distribute:

(n x -6) - (13 x -6) = -60

-6n - (-78) = -60

two negatives in front of a number makes it a positive number

so rewrite -6n + 78 = -60

-6n = -60 - 78

-6n = -138

n = \(\frac{-138}{-6}\)

n = 23

Answer:

34

Step-by-step explanation:

Its true trust me.

The value of angle x in the triangle shown is 78°

An equation is an expression that shows the relationship between two or more numbers.

A triangle is a polygon that has three sides and three angles. The sum of angles in a triangle is 180 degrees. Types of triangles are isosceles, scalene, equilateral

In the large triangle let the missing angle by y, hence:

y + 87 + 36 = 180  (sum of angle in a triangle)

y = 57°

In the triangle containing the angle 45, let the missing angle be z, hence:

z + y + 45 = 180 (angle in a triangle)

z + 57 + 45 = 180

z = 78°

x = z (corresponding angles are equal)

x = 78°

The value of x is 78°

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The expression has 3 terms and 3 factors

The terms are the constant, the r term and the t term

The factors that are in the equation are 1500, 1 and 12

An exponential equation is an equation that involves an exponential function, which has the form f(x) = a^x, where "a" is a constant base and "x" is the exponent. Exponential equations are used to model phenomena that grow or decay at a constant relative rate. The solutions to exponential equations can be found by manipulating the equation algebraically to isolate the variable in the exponent, taking logarithms of both sides, or by using exponential rules such as the power rule or the product rule.

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Answer:

18

Step-by-step explanation:

cause I took the test and I its right

The number of participants changed at -60 contestants from the second to the fourth round

The rate at which one value in a function changes in proportion to another is known as the average rate of change. The slope of a graphed function is typically calculated using the average rate of change.

When x=2, f(x) = 128

when x = 4, f(x) = 8

Rate of change:

8-128/4-2 = -60

As the tournament draws closer to the final, the number of competitors is decreasing at this fluctuating rate.

The average rate at which the number of participants changed from the second round to the fourth round was -60 contestants per round.

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The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Answer:

Exact Form:

4√ 3

Decimal Form:

6.92820323  

Explanation: bc ik brainliest pls

Both AB and BA exists and AB = [30] and BA= \(\left[\begin{array}{cccc}1&2&3&4\\2&4&6&8\\3&6&9&12\\4&8&12&16\end{array}\right]\)

To multiply two matrices we need to check if the number of columns of first matrix is equal to number of rows in second matrix. Then the multiplication exists.

Hence the order of the resulting matrix formed will be equal to number of rows of first matrix and number of columns of second matrix.

Thus AB exists since, Number of columns in matrix A = Number of rows in matrix B.

Therefore, AB = [ 1 2 3 4 ] \(\left[\begin{array}{ccc}1\\2\\3\\4\end{array}\right]\)

⇒AB = [ (1)(1) +(2)(2) +(3)(3) + (4)(4)]

⇒ AB = [ 1+ 4+ 9+ 16]

⇒AB = [30]

Thus BA exists since, Number of columns in matrix B = Number of rows in matrix A.

Therefore, BA =\(\left[\begin{array}{ccc}1\\2\\3\\4\end{array}\right]\) [ 1 2 3 4 ]

⇒BA = \(\left[\begin{array}{cccc}(1)(1)&(1)(2)&(1)(3)&(1)(4)\\(2)(1)&(2)(2)&(2)(3)&(2)(4)\\(3)(1)&(3)(2)&(3)(3)&(3)(4)\\(4)(1)&(4)(2)&(4)(3)&(4)(4)\end{array}\right]\)\({4*4}\)

⇒BA= \(\left[\begin{array}{cccc}1&2&3&4\\2&4&6&8\\3&6&9&12\\4&8&12&16\end{array}\right]\)

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Answer:

6

Step-by-step explanation:

Games played on Friday = 2 1/2

Games played on Saturday = 3 1/2

Total Games played = Games on Friday + Games on Saturday

= \(2\frac{1}{2}+3\frac{1}{2}\)

These are mixed fractions. To covert them into 'normal fractions' there are two steps:

1. Multiple denominator by the whole number

2. add numerator to the product

\(2\frac{1}{2} = \frac{5}{2} \\3\frac{1}{2} = \frac{7}{2} \\\frac{5}{2} + \frac{7}{2}\)

now because denominator is the same, simply add the numerators so the answer is \(\frac{12}{2} \\=6\)

The demand equation is  b. D = -25x + 225.

Since the demand equation is linear and involves "x" as the price, and "D" as the number of units, we can use the two points given to determine the equation.

At a price of $1, 200 units are demanded: (1, 200)
At a price of $9, 0 units are demanded: (9, 0)

Now, we can find the slope (m) using the formula:

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

In this case:

m = (0 - 200) / (9 - 1)
m = -200 / 8
m = -25

Now, we can use one of the points (either point will give the same result) to find the y-intercept (b) by plugging the values into the linear equation:

D = m * x + b

Using the point (1, 200):

200 = -25 * 1 + b
b = 200 + 25
b = 225

Now, we have the demand equation:

D = -25x + 225

So the correct answer is: b. D = -25x + 225.

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To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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The percentage of people who filed their taxes during the week of tax day is 10%

I can estimate how many people filed their taxes during the week of April 15th using a percentage of 100 is a/b * 100.

A percentage is a portion of a sum divided into 100 equal parts.

Calculate (Number of persons who submitted their taxes during the week of April 15th / total people who filed their taxes that year) times 100 to get the percentage of people who filed during that week.

Let :

a represents the total number of taxpayers during the week of April 15th.

b represents the total number of taxpayers for that year.

The original equation is reduced to

a/b× 100

As an illustration, 100 individuals submitted their taxes the week of April 15th and

Let's say that year, 1000 persons filed their taxes.

= 100/1000 = 10%

Thus, 10% of Americans submitted their taxes during the week of April 15th, or 100 out of 1,000.

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When a train takes 17 seconds to pass a 206-meter long bridge at normal speed. The length of train is equals to the 227.86 metres.

We have a train with a normal speed. With a normal speed, the length of long bridge covered by train in 17 seconds

= 206 meter

Let the length of train and normal speed of train be 'x meter' and 's m/sec ' respectively. As we know speed of an object ratio of covered distance to the time taken by object to covered the distance

=> s = (206 + x)/ 17 m/sec --(1)

In case second, the speed of same train which covered a length 170 m of bridge in 45 seconds = one-third of the normal speed

=> s/3 = (170 + x) /45 m/sec --(2)

We have to determine the length of train.

Using substitution, substitute value of s in equation(2) from equation (1) ,

=> (206+ x)/17 = (170 + x)/45

Cross multiplication

=> 45( 206 + x) = ( 170 + x) 17

=> 45 x - 17x = 45× 206 - 170 × 17

=> x = 227.86 m

Hence, required value is 227.86 m.

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Answer:

n=2m+2.50

Step-by-step explanation:

I used n cause it didint list the other variable

Answer:

fixed rate - 2.50

varied rate- 2m(m= number of miles he travelled)

expression - 2m + 2.5

Answer:

\( - 2 + 4 = + 2\)

I hope I helped you^_^

Answer:2

Step-by-step explanation:

Answer:

y = 3x - 17

Step-by-step explanation:

Parallel lines have the same slope.

The slope of the given line, y = 3x - 2 is 3.

The equation we are looking for is of the form

y = mx + b

Since we know the slope, m, is 3, we have

y = 3x + b

To find the value of b, we substitute x and y with the values from the given point and solve for b.

-2 = 3(5) + b

b = -17

The equation is

y = 3x - 17

Answer: A

Step-by-step explanation:

Answer:

A is correct

Step-by-step explanation:

9² + 12² = 15²

This would make a right triangle because 81+144=225

That's how the Pythagorean Theorem works for right triangles.