giving brainlest to whoever can solve ^^

Answer:

2

Step-by-step explanation:

if f(4), than -4^2=-16

5(4)=20

-16+20-2=2

Answer:

D

Step-by-step explanation:

Given a quadratic function in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

• If a > 0 then minimum value

• If a < 0 then minimum value

For

f(x) = x² + 16x + 3

a = 1 > 0 then f(x) has a minimum value

The minimum is the value of the y- coordinate of the vertex.

The x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

Here a = 1 and b = 16 , then

\(x_{vertex}\) = - \(\frac{16}{2}\) = - 8

To find the y- coordinate of the vertex, substitute x = - 8 into f(x)

f(- 8) = (- 8)² + 16(- 8) + 3 = 64 - 128 + 3 = - 61

Thus the function has a minimum value of - 61 → D

The correct option is (D). Approximately 77.3% of new machine set ups are completed in less than 25 minutes.

Given a local manufacturing plant, employees must complete new machine set ups within 30 minutes.

The new machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. The typical worker needs five minutes to adjust to their surroundings before beginning their duties.

To find the percentage of new machine set ups completed in less than 25 minutes, we need to calculate the z-score. For this, we will use the formula:

z = (X - μ) / σ

where X = 25 minutes, μ = 22 minutes, and σ = 4 minutes

z = (25 - 22) / 4z = 0.75

We can now look up the percentage of the area under the normal distribution curve that corresponds to z = 0.75. Using a standard normal distribution table, we find that the area to the left of z = 0.75 is approximately 0.7734.

So, the percentage of new machine set ups completed in less than 25 minutes is approximately 77.34%.

Therefore, the correct option is (D).Approximately 77.3% of new machine set ups are completed in less than 25 minutes.

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Answer: Bonato

Step-by-step explanation:

a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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The maximum value of f(x, y, z) = 4x + 2y + z subject to the constraint x^2 + y + z^2 = 1 is 4, and it occurs at the point (1, 0, 0).

To solve the given optimization problem using Lagrange multipliers:

Let's define the function g(x, y, z) = x^2 + y + z^2 - 1.

We need to find the critical points of the function f(x, y, z) = 4x + 2y + z subject to the constraint g(x, y, z) = 0.

Using Lagrange multipliers, we set up the following system of equations:

∇f = λ∇g,

g(x, y, z) = 0.

Taking the partial derivatives of f and g:

∂f/∂x = 4, ∂f/∂y = 2, ∂f/∂z = 1,

∂g/∂x = 2x, ∂g/∂y = 1, ∂g/∂z = 2z.

Setting up the equations:

4 = λ(2x),

2 = λ(1),

1 = λ(2z),

x^2 + y + z^2 = 1.

From the second equation, λ = 2. Substituting this value into the first equation, we get:

2 = 2x,

x = 1.

Substituting these values into the fourth equation, we have:

1 + y + z^2 = 1,

y + z^2 = 0.

Since we want to maximize f(x, y, z), we consider the test point (1, 0, 0) which satisfies the constraint.

Evaluating f(1, 0, 0):

f(1, 0, 0) = 4(1) + 2(0) + 0 = 4.

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Answer:B

Step-by-step explanation:

B

the standard matrix of the linear transformation T: ℝ² → ℝ², which first reflects points through the line x₂ = -x₁ and then reflects points through the origin, is:

[ -1  0 ]

[  0  1 ]

To find the standard matrix of the linear transformation T: ℝ² → ℝ², we can determine how the basis vectors of ℝ² transform under the given transformation.

The standard basis vectors of ℝ² are:

e₁ = (1, 0) (corresponding to the x-axis)

e₂ = (0, 1) (corresponding to the y-axis)

First, let's apply the reflection through the line x₂ = -x₁:

For e₁ = (1, 0), the reflection through the line x₂ = -x₁ maps it to (-1, 0).

For e₂ = (0, 1), the reflection through the line x₂ = -x₁ maps it to (0, 1).

Next, let's apply the reflection through the origin:

For (-1, 0), the reflection through the origin keeps it the same (-1, 0).

For (0, 1), the reflection through the origin keeps it the same (0, 1).

Now, we have the transformed basis vectors:

T(e₁) = (-1, 0)

T(e₂) = (0, 1)

The standard matrix of the linear transformation T is constructed by placing the transformed basis vectors as columns:

[ -1  0 ]

[  0  1 ]

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The reciprocal (inverse or indirect quote) for the given exchange rates is as follows:

USO/DKK: The reciprocal exchange rate is 0.1557 DKK/USO.

GBP/NZD: The reciprocal exchange rate is 0.4898 NZD/GBP.

USO/INR: The reciprocal exchange rate is 0.0226 INR/USO.

To calculate the reciprocal quote, we take the reciprocal of the given exchange rate. For example, for USO/DKK with an exchange rate of 6.4270 DKK per USO, the reciprocal is 1 divided by 6.4270, which equals 0.1557 DKK per USO.

Similarly, for GBP/NZD with an exchange rate of 2.0397 NZD per GBP, the reciprocal is 1 divided by 2.0397, which equals 0.4898 NZD per GBP.

Finally, for USO/INR with an exchange rate of 44.333 INR per USO, the reciprocal is 1 divided by 44.333, which equals 0.0226 INR per USO.

These reciprocal quotes represent the inverse of the original exchange rates.

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Complete question: Calculate the reciprocal (inverse or indirect quote) for the following currency pairs:
1. USO/DKK: 1/6.4270 or DKK/USO: 1/350
2. GBP/NZD: 1/2.0397 or NZD/GBP: 1/0.7000
3. USO/INR: 1/44.333 or INR/USO: 1/44.333

Answer:

Step-by-step explanation:

P(both) = 4/7 * 3/7 = 12 / 49

Answer:

The mean is the best measure. The mean waiting time for doctor #2 is 2.5 minutes longer than for doctor #1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Compare ratios and rates by finding equivalent ratios and rates with a common second term . Make predictions by finding a common factor and multiplying by it.

To compare ratios and rates favorably we need to find a common second term also to make predictions as well we need to find a common factor

Answer:

error made in step 2, should be 3x² + 15x - 18 = 0

3(x+6)(x-1) = 0

x = -6 and x = 1

Step-by-step explanation:

Answer:X squared =4/9 is c

              X to the third power is a

               X squared =81/46 is b or d

               X to the third power is d or b

Based on the calculations, the volume of this pyramid is equal to 1440 cm³.

Given the following data:

Length of right triangular base = 9 centimeters and 15 centimeters.

Height of right triangular base = 32 centimeters.

Mathematically, the volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × b × h

Where:

h is the height of a pyramid.

b is the base area of a pyramid.

Substituting the parameters into the formula, we have:

Volume = 1/3 × 9 × 15 × 32

Volume = 3 × 15 × 32

Volume of pyramid = 1440 cm³.

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Answer:

y = -1.5x -1

Step-by-step explanation:

moves right 8

and down 12

so m = -12/8x or -1.5x

(4,-7) moves up 6, (0, -1)

Answer:

353340 + x + 33

Step-by-step explanation:

real life sum situation

(a) To calculate the probability of exactly half of the spins landing on black, we need to consider the number of ways we can choose exactly five out of the ten spins to land on black. The probability of a single spin landing on black is 18/38, and the probability of a single spin landing on red (since there are only two possibilities) is 20/38.

We can use the binomial probability formula to calculate the probability:

P(X = k) = C(n, k) * p^k * q^(n-k)

where:

P(X = k) is the probability of exactly k successes,

C(n, k) is the number of combinations of n items taken k at a time,

p is the probability of success on a single trial, and

q is the probability of failure on a single trial.

For exactly half of the spins (k = 5), the probability can be calculated as:

P(X = 5) = C(10, 5) * (18/38)^5 * (20/38)^5

Calculating this expression will give us the probability that exactly half of the spins land on black.

(b) To calculate the probability of at least eight spins landing on black, we need to consider the probabilities of eight, nine, or ten spins landing on black and add them up.

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

Using the same binomial probability formula, we can calculate each of these probabilities:

P(X = 8) = C(10, 8) * (18/38)^8 * (20/38)^2

P(X = 9) = C(10, 9) * (18/38)^9 * (20/38)^1

P(X = 10) = C(10, 10) * (18/38)^10 * (20/38)^0

By calculating these expressions and summing them up, we can determine the probability of at least eight spins landing on black.

Please note that the calculations provided are based on the assumption of a fair roulette wheel with 18 black spaces out of 38 total spaces.

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Answer:

c

Step-by-step explanation:

Answer: Yes, 59 is a prime number

Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.

Yes, 59 is a prime number.

What is a prime number?

Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.

In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.

The number in question, which is 59,  has only two factors: 1 and 59.

Therefore 59 is a prime number.

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The value of the angle 7 is 80 degrees. Option B

A transversal line can be defined as a line that intersects two or more lines at distinct points.

It is important to note that corresponding angles are equal.

Also, the sum of angles on straight line is equal to 180 degrees.

From the information given, we have that;

Angle 3 and angle 7 are corresponding angles

Also, we have that

Angle 3 and angle 4 are on a straight line

equate the angles

<3 + 100 = 180

collect the like terms

<3 = 180 - 100

<3 = 80 degrees

Then, the value of <7 is 80 degrees

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f (x) = (x-1) (x+3)..........................................less the periods

We can obtain 6 different numbers by multiplying 2 distinct integer divisors of 10.

The divisors of 10 are 1, 2, 5, and 10.

To determine how many different numbers can be obtained from multiplying 2 distinct integer divisors.

We need to select 2 distinct divisors and find their product.

The possible pairs are:

Therefoore, we can obtain 6 different numbers.

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Answer:

B and C

Step-by-step explanation:

area of square= 81

L^2= 81

L=√81

L=9ft

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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Final Answer: All Real Numbers

Steps/Reasons/Explanation:

Question: Solve for a. \(4(a + 3)=12 + 4a\).

Step 1: Expand.

\(4a + 12 = 12 + 4a\)

Step 2: Cancel \(4a\) on both sides.

\(12 = 12\)

Step 3: Since both sides equal, we would have infinitely many solutions.

~I hope I helped you :)~

Answer:1

Step-by-step explanation:1

Two complex numbers that have a product of 14 + 2i are z₁ = (2 + i) and z₂ = (7 - i).

Let's assume z₁ = a + bi and z₂ = c + di, where a, b, c, and d are non-zero and non-one real numbers.

To find two complex numbers whose product is 14 + 2i, we can set up the equation:

z₁ * z₂ = (a + bi) * (c + di) = 14 + 2i

Expanding the product, we have:

(ac - bd) + (ad + bc)i = 14 + 2i

Comparing the real and imaginary parts, we get two equations:

ac - bd = 14 -- (1)

ad + bc = 2 -- (2)

We need to solve these equations to find suitable values for a, b, c, and .One possible solution that satisfies these equations is a = 2, b = 1, c = 7, and d = -1.Substituting these values into z₁ and z₂, we have z₁ = 2 + i and z₂ = 7 - i.

Therefore, the two complex numbers that have a product of 14 + 2i are z₁ = (2 + i) and z₂ = (7 - i).

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Answer:

Step-by-step explanation:

You want the sums of various geometric series.

The sum of n terms of a geometric sequence with first term a1 and common ratio r is ...

 Sn = a1·(r^n -1)/(r -1)

When the series is infinite, the sum will converge if and only if |r| < 1.

The ratio can be found as the ratio of the first two terms:

  r = a2/a1

The ratio is ...

  r = 16/2 = 2

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 25/5 = 5

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 4/1 = 4

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 12/24 = 1/2

The sum of the first 8 terms is ...

  S8 = 24·((1/2)^8 -1)/(1/2 -1) = 24·(-255/256)/(-1/2) = 24(255/128)

  S8 = 47 13/16

The ratio is ...

  r = -6/3 = -2

The sum of the first 10 terms is ...

  S10 = 3·((-2)^10 -1)/(-2 -1) = 3(1023)/(-3)

  S10 = -1023

__

Additional comment

If you have a number of these, a spreadsheet or graphing calculator can do the math for you.