Given
a = -4, b = -4 and c = -5
work out
b² - 2ac

Answer: 0.10175

Step-by-step explanation:

First, bring the decimal points to the right for both numbers, to be a total of 5 decimal points to the right. Then, with the numbers 25 and 407, multiply them, and we get 10175. Then, we must bring the 5 decimal points back, and we end up with 0.10175.

Answer: 0.10

Step-by-step explanation:

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A cone is a three-dimensional geometric shape that has a circular base and tapers to a point, or vertex, at the top.

1. First, let's examine the inequalities:
  a. 0 ≤ r ≤ 1: This represents the radial distance from the origin. It means the solid is within a radius of 1 unit from the origin.
  b. −2 ≤ θ ≤ 2: This represents the angle around the z-axis, measured in radians. It means the solid spans from -2 to 2 radians around the z-axis.
  c. 0 ≤ z ≤ 3: This represents the vertical distance along the z-axis. It means the solid extends from the base at z=0 to the top at z=3.

2. Now let's sketch the solid:
  a. Start by drawing a circle with a radius of 1 centered at the origin. This represents the base of the solid at z=0.
  b. Next, draw a line representing the angle of -2 radians and another line representing the angle of 2 radians from the positive x-axis on the base. These lines divide the circle into two parts.
  c. Shade the area of the circle between the two angle lines. This is the cross-section of the solid at z=0.
  d. To represent the height, draw a vertical line from the center of the circle, extending up to z=3. This is the top of the solid.
  e. Connect the edges of the base to the top, forming a solid shape. This is the final sketch of the solid described by the given inequalities.

The solid is a section of a right circular cone with a radius of 1 and a height of 3, and it spans an angle of 4 radians around the z-axis.

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Answer:

4

Step-by-step explanation:

Hope this helps!! Have a good day!

 300 people subscribe to the Sunday edition only.

Out of the 3000 subscribers surveyed, 2700 people subscribe to the daily morning edition. Among these 2700, 1500 people also subscribe to both the daily and Sunday editions. To determine the number of people who subscribe to the Sunday edition, we need to subtract the number of people who subscribe to both editions from the total number of daily subscribers.

Number of people who subscribe to the Sunday edition = Total number of daily subscribers - Number of people who subscribe to both editions

= 2700 - 1500

= 1200 people

Therefore, 1200 people subscribe to the Sunday edition.

To find the number of people who subscribe to the Sunday edition only, we subtract the number of people who subscribe to both editions from the total number of Sunday subscribers.

Number of people who subscribe to the Sunday edition only = Total number of Sunday subscribers - Number of people who subscribe to both editions

= 1500 - 1200

= 300 people

Therefore, 300 people subscribe to the Sunday edition only.

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Step-by-step explanation:

In a parallelogram, opposite sides are equal and parallel. Therefore,

QT = PS = 3y ...(1)

PT + TR = PS

y + 2x + 1 = 3x + 9

2x - y = 4 .....(2)

PR = QT = 3y

PR = SQ = 3x + 9 ....(3)

From equations (1) and (3), we can see that:

3y = 3x + 9

y = x + 3

Substitute this value of y in equation (2):

2x - (x + 3) = 4

x = 7

To find the value of y, we can substitute x = 7 in equation (2):

2(7) - y = 4

y = 10

Therefore, x = 7 and y = 10.

Answer:

4x <= 20

x <= 5

A single cupcake can cost at most $5.

Step-by-step explanation:

Let the price of a single cupcake be x.

We know that there are 4 cupcakes in a box, so 4x is equal to the price of 4 cupcakes and hence the price of a box.

The question tells us that a box costs at most $20, so we can write this as an inequality:

4x <= 20

Divide both sides by 4 to isolate and solve for x:

x <= 5

x is less than or equal to 5, which can be interpreted as a cupcake costing at most $5.

The x-intercepts of a quadratic function are the points where the function graph intersects the x-axis. To find the x-intercepts of the given quadratic function, we need to determine the values of x when the y-value (or the function value) is equal to 0.

From the given information, we can see that the quadratic function passes through the points (-2, 0) and (1, 0), which indicates that the function intersects the x-axis at x = -2 and x = 1. Therefore, the quadratic function x-intercepts are (-2, 0) and (1, 0).

The correct answers are (d) (-2, 0) and (1, 0).

Answer:

I think it might be 4072 I forget how to do this kind of math sorry.

Step-by-step explanation:

From the given values, we can see that the lowest values is -32 and the highest value ie -4. Since the range is the difference betwwwn the highest and the lowest value, the range is

On the other hand, the sample variance formula is

where x^bar is the mean and n is the total number of sample elements. In our case, n=7 and the mean is

Then, the sample variance is given by

Since the standard deviation is the square root of the sample variance, we have

By rounding the solutions to the nearest tenth, the answers are:

Each box has a mass of 90 grams, which is found by setting up a proportion using the ratio of cans to boxes and the known mass of each can.

To solve this problem, we need to use proportions. We know that 3 cans have the same mass as 9 identical boxes, which means that the ratio of cans to boxes is 3:9 or simplified to 1:3.

We also know that each can has a mass of 30 grams. Therefore, we can set up the proportion:

1 can / 30 grams = 1 box / x grams

where x is the mass, in grams, of each box.

To solve for x, we can cross-multiply:

1 can * x grams = 30 grams * 1 box

x grams = 30 grams / 1 can * 1 box

Since the ratio of cans to boxes is 1:3, we can substitute 3 for the number of boxes:

x grams = 30 grams / 1 can * 3 boxes

x grams = 90 grams

Therefore, the mass of each box is 90 grams.

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Answer:

1:2

Step-by-step explanation:

because there are 9 stars and 18 squares giving you 9:18 but when you simplyfi you get 1:2

Answer: 9:18

Step-by-step explanation:

Count the amount of stars which is 9, then count the amount of circles which is 18. So therefore the answer would be 9:18

The population growth of a small town is projected to be approximately 1829 at the beginning of 2028, assuming an average annual growth rate of 2.3%.

We can use the formula for exponential growth to solve this problem:

P(t) = P₀ * (1 + r)^t

Where

P₀ = initial population (1500)

r = annual growth rate (2.3% or 0.023)

t = number of years

Plugging in the values, we get

P(8) = 1500 * (1 + 0.023)^8

P(8) = 1500 * 1.2003^8

P(8) = 1500 * 1.2197

P(8) ≈ 1829

Therefore, the population of the small town at the beginning of 2028 will be approximately 1829.

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Answer:

Bouquets of roses = 20

Bouquets of carnations = 08

Step-by-step explanation:

Let,

x be the bouquets of roses sold

y be the bouquets of carnations sold

According to given statement;

x + y = 28       Eqn 1

16x + 10y = 400     Eqn 2

Multiplying Eqn 1 by 16

16(x+y=28)

16x + 16y = 448    Eqn 3

Subtracting Eqn 2 from Eqn 3

(16x+16y)-(16x+10y) = 448 - 400

16x + 16y - 16x - 10y = 48

6y = 48

Dividing both sides by 6

\(\frac{6y}{6}=\frac{48}{6}\\y=8\)

Putting y=8 in Eqn 1

x + 8 = 28

x = 28 - 8

x= 20

Hence,

Bouquets of roses = 20

Bouquets of carnations = 08

Answer:

B and D

Step-by-step explanation:

3/4 = a/36

4a = 36*3 = 108

a = 108/4 (which is answer choice D) = 27 (which is answer choice B)

Step-by-step explanation:

y-15=x^2+10x

y-15+25=x^2+10x+25

y+10=(x+5)^2

Based on the options provided, the most appropriate answer would be option C: No, P(bald | over 45) ≠ P(bald). This suggests that baldness and being over 45 are not independent events.

To determine whether baldness and being over 45 are independent events, we need to compare the conditional probability of being bald given that a person is over 45 (P(bald | over 45)) with the probability of being bald (P(bald)) and the probability of being over 45 (P(over 45)).If baldness and being over 45 are independent events, then the occurrence of one event should not affect the probability of the other event.

The options provided are:

A) Yes, P(bald | over 45) = P(bald)

B) Yes, P(bald | over 45) = P(over 45)

C) No, P(bald | over 45) ≠ P(bald)

D) No, P(bald | over 45) ≠ P(over 45)

Option A states that P(bald | over 45) is equal to P(bald), which implies that the probability of being bald does not depend on whether a person is over 45 or not. This suggests that baldness and being over 45 are independent events.

Option B states that P(bald | over 45) is equal to P(over 45), which implies that the probability of being bald is the same as the probability of being over 45. This does not provide information about their independence.

Option C states that P(bald | over 45) is not equal to P(bald), indicating that the probability of being bald depends on whether a person is over 45 or not. This suggests that baldness and being over 45 are not independent events.

Option D states that P(bald | over 45) is not equal to P(over 45), implying that the probability of being bald is not the same as the probability of being over 45. This does not provide information about their independence.Based on the options provided, the most appropriate answer would be option C: No, P(bald | over 45) ≠ P(bald). This suggests that baldness and being over 45 are not independent events.

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The ladder touches the wall at a height of approximately 9.2 feet above the ground.

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side, which is the ladder in this case) is equal to the sum of the squares of the lengths of the other two sides (the distance from the wall and the height of the ladder on the wall).

Let's call the distance from the wall "x" and the height of the ladder on the wall "h". Then we have:

\(x^2 + h^2 = 14^2\)

We also know that the bottom of the ladder is placed 3 feet from the wall, so we have:

x + 3 = 14

Solving for x, we get:

x = 11

Substituting this value into the first equation, we get:

\(11^2 + h^2 = 14^2\)

Simplifying and solving for h, we get:

\(h = \sqrt{(14^2 - 11^2)}\)

h ≈ 9.2

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The median is the best choice to predict how many miles Gina will drive in the sixth year because it is not skewed by the high outlier of 16,211 miles in the second year.

The data for Gina's car mileage is:

12,200 miles in the first year

16,211 miles in the second year

12,050 miles in the third year

To find the mode, we need to identify the value that occurs most frequently in the data set. In this case, there is no mode because no value appears more than once.

To find the median, we need to arrange the data set in order from smallest to largest and identify the middle value. If there is an even number of values, we take the average of the two middle values.

12,050, 12,200, 16,211

The median is 12,200 because it is the middle value when the data set is arranged in order.

To find the mean, we add up all of the values and divide by the number of values.

(12,200 + 16,211 + 12,050) / 3 = 13,027

Therefore, the mean is 13,027.

Based on the given data, the median is the best choice to predict how many miles Gina will drive in the sixth year because it is not skewed by the high outlier of 16,211 miles in the second year. The mean is also a reasonable choice, but it may be influenced by the high value. However, since we do not have any information about any changes in Gina's driving patterns or other relevant factors, it's difficult to accurately predict how many miles she will drive in the sixth year based solely on the given data.

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Algorithm Il always works correctly, but Algorithm I only works correctly when the maximum value is greater than or equal to - 1

=====================================================

Explanation:

Let's say we have the data set {-4,-3,-2}. The value -2 is the largest.

If we follow algorithm 1, then the max will erroneously be -1 after all is said and done. This is because the max is set to -1 at the start even if -1 isn't in the data set. Then we see if each data value is larger than -1.

Each statement being false means we do not update the max to its proper value -2. It stays at -1.

This is why we shouldn't set the max to some random value at the start.

It's better to use the some value in the data set to initialize the max. Algorithm 2 is the better algorithm. Algorithm 1 only works if the max is -1 or larger.

Answer:

X + 6

Step-by-step explanation:

Think of it as (3x + 5) + (-1 x 2x) + (-1 x -1)

3x + 5 - 2x + 1

Combine like terms

3x - 2x = x + 5 + 1 = x + 6

Answer:

Yes

Step-by-step explanation:

Every input has only one output.

Answer:

Step-by-step explanation:

In my opinion yes I think so

Answer:no

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is YES.

equation 1 is equal to equation 2 in a system. by this we have :

3x+3=4x+1 ⇒ x=2

let's put the value of 2 for x in one of the equations :

equation 1: (3×2)+3=6+3=9 ⇒ y=9 ⇒ correct

equation 2: (4×2)+1=8+1=9 ⇒ y=9 ⇒ correct

so (x,y)=(2,9) is the answer of the system.

The perturbation formulae in quantum mechanics, Eₙ₍₃₎ and Cₙₘ₍₃₎, calculate energy correction and transition probability for a perturbed quantum system.

In quantum mechanics, perturbation theory is used to calculate corrections to the energy and transition probabilities of a quantum system when it is subjected to a perturbing potential. The perturbation formulae for the third-order corrections, Eₙ₍₃₎ and Cₙₘ₍₃₎, can be derived through mathematical methods.

The third-order correction to the energy, Eₙ₍₃₎, represents the correction to the energy level of the quantum system in the nth state. It can be calculated using the perturbation formula:

Eₙ₍₃₎ = ∑[m≠n] (|⟨m|H'|n⟩|² / (Eₙ - Eₘ)),

where H' is the perturbing potential and Eₙ and Eₘ are the unperturbed energies of the nth and mth states, respectively. This formula sums over all other states (m≠n) and takes into account the matrix elements and energy differences.

Similarly, the third-order correction to the transition probability between two states, Cₙₘ₍₃₎, can be calculated using the perturbation formula:

Cₙₘ₍₃₎ = ⟨n|H'|m⟩ / (Eₙ - Eₘ),

where ⟨n|H'|m⟩ represents the matrix element between the initial state |n⟩ and the final state |m⟩, and Eₙ and Eₘ are the unperturbed energies of the initial and final states, respectively. This formula accounts for the matrix element and energy difference between the states.

These perturbation formulae provide a way to calculate the third-order corrections to the energy and transition probabilities in a quantum system, allowing for more accurate predictions and descriptions of quantum phenomena in the presence of perturbations.

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Substituting the value of x and solving the function we get the value of y as y = 1

To evaluate the co-ordinate point (x, y) for the function

y = f(x) = -1.25x -0.25,

you need to substitute the value of x into the function and solve for y.

If x = -1,

then y = f(-1) = -1.25×(-1) - 0.25 = 1.25 - 0.25 = 1.

Therefore, the coordinate point (x, y) for the function:

y = f(x) = -1.25x - 0.25 when x = -1 is (-1, 1).

A function in mathematics is a collection of values connected by a predetermined rule or formula. The output value (also known as the dependent variable) is represented by a letter or a symbol that depends on the input value, whereas the input value (also known as the independent variable) is represented by a letter (such as x or y). Functions are frequently used to represent relationships between several numbers or to simulate real-world occurrences.

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The required sum of the coordinate of T is given as 9.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate the y is called ordinate.

Here,
The coordinates of the endpoints of RS are R(4, -8) and S(25, -1).
Ratio ST / RT = 4 / 3 = n/m

Coordinates of the point are given by section formula,
x = mx₁ + nx₂ / m  + n ; y =  my₁ + ny₂ / m  + n

Substitute the values,
x = 3 × 4  + 25 × 4 / 4 + 3 ; y = 3 × -8  + 25 × -1 / 4 + 3
x = 16                               ; -7

Coordinates of T = (x ,y) = (16, -7)

Sum of the coordinate of T = 16 + {-7} = 9

Thus, the required sum of the coordinate of T is given as 9.

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Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

The given equation is equivalent to y = -5x/7 - 2

Given that an equation, 5x+7y = -14, we need to find an equivalent equation for thus,

So,

5x+7y = -14

Minus 5x from both the sides

7y = -14 - 5x

Divide the equation by 7,

y = -5x/7 - 2

Hence the given equation is equivalent to y = -5x/7 - 2

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Answer:

The second option is correct.

Step-by-step explanation:

This is because when multiplied, they all equal the same number.

3*6 = 18

6*3 = 18

9*2 = 18

18*1 = 18