Which of the following is a solution to the equation 4x2+4x−3=0?


-1.5


-0.5


1


3

Yes, a random variable can assume a value equal to its expected value.

In probability theory, the expected value of a random variable represents the average value it is expected to take over many repetitions of the experiment.

While it is not guaranteed that the random variable will always assume its expected value, there is a possibility that it can indeed be equal to its expected value in some instances. The likelihood of this happening depends on the specific probability distribution and the nature of the random variable.

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Answer:

m = d - n + a

Step-by-step explanation:

Subtract n and add a on both sides to isolate m

The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

\(((\bar p_{1} -\bar p_{2})\)±\(Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })\)

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±\(1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })\)

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

The key conceptual difference between escape velocity and orbital velocity is that escape velocity enables an object to break free from the gravitational pull and move away from the celestial body, while orbital velocity allows an object to maintain a stable circular orbit around the celestial body.

To type the equations for Escape and Orbital (circular) Velocities using the equation editor tools on CANVAS, you can follow the instructions below:

1. Escape Velocity Equation:

  - Click on the "Insert Math Equation" button (represented by a square root symbol) in the CANVAS equation editor.

  - In the equation editor, type the following equation:

\(v_{\text{escape}} = \sqrt{\frac{2GM}{r}}\)

  - Here, "\(v_{\text{escape}}\)" represents the escape velocity, "G" is the gravitational constant, "M" is the mass of the celestial body, and "r" is the distance from the center of the celestial body.

2. Orbital (Circular) Velocity Equation:

  - Click on the "Insert Math Equation" button in the CANVAS equation editor.

  - In the equation editor, type the following equation:

  \(v_{\text{orbital}} = \sqrt{\frac{GM}{r}}\)

  - Here, "v_{\text{orbital}}" represents the orbital velocity, "G" is the gravitational constant, "M" is the mass of the celestial body, and "r" is the distance from the center of the celestial body.

Now, let's discuss the conceptual difference between these two equations:

1. Escape Velocity: The escape velocity is the minimum velocity required for an object to escape the gravitational pull of a celestial body, such as a planet or a star. The equation for escape velocity includes an additional factor of 2 compared to the orbital velocity equation. This factor accounts for the additional energy required to overcome the gravitational field completely and move away from the celestial body. The escape velocity equation takes into consideration the mass of the celestial body and the distance from its center.

2. Orbital Velocity: The orbital velocity is the velocity required for an object to maintain a stable circular orbit around a celestial body. It is the speed at which the object would need to travel in order to balance the gravitational force pulling it inward with the centrifugal force pushing it outward. The equation for orbital velocity does not include the additional factor of 2 because it only considers the energy required to maintain a stable circular orbit. The orbital velocity equation also takes into account the mass of the celestial body and the distance from its center.

In summary, the key conceptual difference between escape velocity and orbital velocity is that escape velocity enables an object to break free from the gravitational pull and move away from the celestial body, while orbital velocity allows an object to maintain a stable circular orbit around the celestial body.

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Answer:

63

Step-by-step explanation:

We are taking a dilation of 3, so that means we are multiplying by 3. We multiply 3 to 21 to get 63.

Answer:

6+-3 =-9

Step-by-step explanation:

so if u add a positive number to a negative number the whole answer  is a negative number i

The mark-up, as a percentage = 125%

What is Markup?

The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity.

A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.

Markup percentage=[(selling price - unit cost)/unit cost]*100

Markup percentage= [(900-400)/400]*100=1.25*100

                                = 125%

So, the mark-up, as a percentage = 125%

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Answer:

One solution

Step-by-step explanation:

I added a photo of my solution

Answer:

The system has one solution: (0, 4).

Answer:

1,440

Step-by-step explanation:

if first two digits must be odd, then there are 4x3 or 12 combinations for that

if the next three digits can be even or odd but not repeats then there can be 6 (two odds remaining plus four evens) x 5 x 4 = 120

120 x 12 = 1,440

The multiplication equation to find 5 divided by 1/3 is 5 x 3 = 15.

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.

At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another.

Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend.

Division has two parts dividend and divisor.

Division is not commutative, meaning that a / b is not always equal to b / a.

Division is also not, in general, associative.

Division is traditionally considered as left-associative.

Division is right-distributive over addition and subtraction.

Division is shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a fraction bar, between them. For example, "a divided by b" can written as:

a/b

Now it is given that,

5 divided by 1/3

This can be expressed as,

5 divided by 1/3 = 5 ÷ 1/3

Since to convert the division of fraction into multiplication, we reciprocate the fraction

So, applying division we get,

5 ÷ 1/3 = 5 x 3

So, the multiplication equation is,

5 x 3

Now multiplying 5 and 3 we get,

5 x 3 = 15

this is the required multiplication equation of 5 divided by 1/3.

Thus, the multiplication equation to find 5 divided by 1/3 is 5 x 3 = 15.

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The solution of the system of equations is (x, y) = (1/3, 1/3).

To solve the given system of equations, we can use any of the following three methods; the substitution method, the elimination method (also known as the addition/subtraction method), and the graphical method. Below, we will solve it using each of these methods.

1. Substitution method:

We will use the substitution method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2) From equation (1), we have

Y + 2x = 3y ...(3)Now substitute equation (3) into equation

(2)2y = 3x - 2 ...(2)Y + 2x = 3y ...(3)2(3y - 2x) = 3x - 2

Multiplying both sides by 2:

6y - 4x = 3x - 2 Grouping like terms:

6y - 3x = 2 Adding 3x to both sides:

6y = 3x + 2Dividing both sides by 6:

y = (3/6)x + 2/6y = (1/2)x + 1/3

Therefore, the solution of the system of equations is (x, y) = (1/3, 1/3).

2. Elimination method:

We will use the elimination method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2)Multiplying equation (1) by 2,

we get;2Y = 6y - 4x ...(3)Multiplying equation (2)

by -3, we get;-6y = -9x + 6 ...(4) Adding equations (3) and (4),

we get;-4x = -9x + 8

Simplifying;-4x + 9x = 8x = -8x = -2

Therefore, we found the value of x, which is -2.

Substitute the value of x in either equation (1) or (2);

If we substitute x = -2 in equation (1), we get;

Y = 3y - 2(-2)Y = 3y + 4Y - 3y = 4Y = 4/2Y = 2Substitute the value of y in equation (1)

;Y = 3y - 2xY = 3(2) - 2(-2)Y = 6 + 4Y = 10

Therefore, the solution of the system of equations is (x, y) = (-2, 10/2).3.

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Answer:



Step-by-step explanation:

The correct hypothesis statement would be C. The null hypothesis states that the population mean time to complete the statistics exam is equal to 45 minutes, while the alternative hypothesis states that it is not equal to 45 minutes.

This means that the professor is testing whether there is evidence to support the idea that the true population mean time to complete the exam is different from 45 minutes. The professor would collect a sample of student exam completion times and perform a hypothesis test to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. This test would involve calculating a test statistic and comparing it to a critical value or p-value to make a decision about the null hypothesis.

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Full Question: A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. The correct hypothesis statement would be:

A. Null hypothesis (H0): The population mean time to complete the statistics exam is less than or equal to 45 minutes.

Alternative hypothesis (Ha): The population mean time to complete the statistics exam is greater than 45 minutes.

B. Null hypothesis (H0): The population mean time to complete the statistics exam is greater than or equal to 45 minutes.

Alternative hypothesis (Ha): The population mean time to complete the statistics exam is less than 45 minutes.

C. Null hypothesis (H0): The population mean time to complete the statistics exam is equal to 45 minutes.

Alternative hypothesis (Ha): The population mean time to complete the statistics exam is not equal to 45 minutes.

D. Null hypothesis (H0): The sample mean time to complete the statistics exam is equal to 45 minutes.

Alternative hypothesis (Ha): The sample mean time to complete the statistics exam is not equal to 45 minutes.

Answer:

Term to add is (3/8)^2 = 9/64

Step-by-step explanation:

Here, we want to know the value that must be added to make the equation a perfect square.

x^2 - 3/4x = 5

x^2 -3/4x -(3/8)^2+ (3/8)^2 = 5

x^2 -3/4x + (3/8)^2 = 5 + (3/8)^2

= (x-3/8)^2 = 5 + (3/8)^2

So the term to add is (3/8)^2 = 9/64

Answer:

\(\dfrac{9}{64}\)

Step-by-step explanation:

Given the equation: \(x^2-\frac{3}{4}x=5\)

To make the left hand side of the equation a perfect trinomial, we follow these steps.

Step 1: Divide the coefficient of x by 2.

Coefficient of x \(=-\frac{3}{4}\)

\(-\frac{3}{4} \div 2 =-\frac{3}{8}\)

Step 2: Square your result from step 1

\(\implies (-\frac{3}{8})^2 \\=\dfrac{9}{64}\)

Therefore, to make the Left-Hand side a  perfect-square trinomial, we add 9/64.

Answer:

\(x=\sqrt{10}\)

Step-by-step explanation:

For first right angled tringle,

Hypotenuse = 10

Height = 9

We can find the base of first triangle using Pythagoras therorem,

\(b=\sqrt{10^2-9^2}\\\\=\sqrt{100-81}\\\\=\sqrt{19}\)

Now, for other triangle,

Height = 3

Hypotenuse = \(\sqrt{19}\)

So,

\(x=\sqrt{(\sqrt{19})^2-3^2}\\\\=\sqrt{19-9}\\\\=\sqrt{10}\)

So, the value of x is equal to \(\sqrt{10}\).

Answer:

0.80*c = 20

Step-by-step explanation:

"80% of c is 20" can be written as:

  0.80*c = 20

80% of c is 0.80*c

"is" can be written as "="

Put these two together to obtain:

  0.80*c = 20

The probability will be b) 4/(52 13)

In a standard deck, there are four suits (hearts, diamonds, clubs, and spades), each containing 13 cards. To find the probability of obtaining a bridge hand with all 13 cards of the same suit, we need to determine the number of favorable outcomes (hands with all 13 cards of the same suit) and divide it by the total number of possible outcomes (all possible bridge hands).

Calculate the number of favorable outcomes

There are four suits, so for each suit, we can choose 13 cards out of 13 in that suit. Therefore, there is only one favorable outcome for each suit.

Calculate the total number of possible outcomes

To determine the total number of possible bridge hands, we need to calculate the number of ways to choose 13 cards out of 52. This can be represented as "52 choose 13" or (52 13) using the combination formula.

Calculate the probability

The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Since there is one favorable outcome for each suit and a total of 4 suits, the probability is 4 divided by the total number of possible outcomes.

Therefore, the probability that a bridge hand will contain all 13 cards of the same suit is 4/(52 13).

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Answer:

1899.7 in^3.

Step-by-step explanation:

Radius = 1/2 diameter

= 22 * 1/2 = 11.

Volume = 1/3 pi r^2 h,  so

= 1/3 * 3.14 *1 1^2 *1 5

= 1899.7 in^3.

The new function after applying the sequence of transformation include: B. 1/2f(x + 5) - 11

In Mathematics and Geometry, the translation of a graph to the left means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x + N)

Conversely, the translation of a graph downward means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

Since the parent function f(x) was translated 11 units downward, 5 units to the left, and vertically compressed (making it wider) by a factor of 1/2, the equation of the image g(x), we have:

g(x) = 1/2f(x + 5) - 11

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Complete Question:

If f(x) is transformed by compressing the function vertically (making it wider) by a factor of 1/2, shifting 5 units to the left, and shifting 11 units downward, what will be the new function?

Answer:

1000 grams= 1 kilograms

4700 grams = 4.7 kilograms

Answer:

A b or c

Step-by-step explanation:

Easy shahhshhshs free points hehe

The maximum distance that the plane can travel due west and just be able to return home is approximately ______ kilometers. (The actual value will be calculated in the explanation.)

To determine the maximum distance the plane can travel due west and return home, we need to consider the effect of the wind on the plane's ground speed. The ground speed is the speed of the plane relative to the ground.

Let's first convert the given speed of the plane to kilometers per hour:

Speed of the plane = 3.38 × 10^2 m/s

Speed of the plane in km/h = (3.38 × 10^2 m/s) × (3600 s/1 h) × (1 km/1000 m) = 1.2168 × 10^3 km/h

Next, we'll calculate the effective ground speed of the plane by considering the wind:

Effective ground speed = Speed of the plane - Speed of the wind

Effective ground speed = 1.2168 × 10^3 km/h - 67.3 km/h = 1.1495 × 10^3 km/h

Now, let's determine the maximum flight time based on the given fuel capacity:

Flight time = 7.3 hours

Finally, we can calculate the maximum distance the plane can travel due west:

Maximum distance = Effective ground speed × Flight time

Maximum distance = (1.1495 × 10^3 km/h) × (7.3 hours) = 8.38335 × 10^3 km

Therefore, the maximum distance that the plane can travel due west and just be able to return home is approximately 8.383 × 10^3 kilometers. (rounded to three significant figures)

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Answer:

68°

Step-by-step explanation:

22°+68°=90° ......

Answer:

125.6cm

Step-by-step explanation:

circumference of a circle is 2pir

pi=3.14

r=d/2=40cm/2=20cm

So, 2pir=2X20cmX3.14=40cmX3.14=31.4cmX4=125.6cm

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Answer:

\(87.5\ miles\)

Step-by-step explanation:

Step 1:  Determine how far

Rate of speed * total hours

\(\frac{25\ miles}{hour}*3.5\ hours\)

\(87.5\ miles\)

Answer:  \(87.5\ miles\)

The motion of  curve in the xy-plane is up and to the right: (-∞, 0), up and to the left: (√(4/3), ∞), down and to the right: (0, ∞), and down and to the left: (0, √(4/3)).

The intervals of t values indicate the direction of motion of the curve in the xy-plane:

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By using basic meaning of percentage we got that the originally puppy's weight  was 50 pounds

Percentage is a number or ratio expressed as a fraction of 100.

Here given that Juan's puppy currently weighs 80 pounds and his is a 60% increase in weight from when he got her.

Let's suppose original weight of puppy was x pounds

We can calculate x as

\(x+ \frac{60}{100} \times x=80\\\\x+ \frac{6}{10} \times x=80\\\\x+ 0.6\times x=80\\\\\\1.6x=80\\\\x=\frac{80}{1.6} \\\\x=\frac{800}{16} \\\\\\x=50\)

By using basic meaning of percentage we got that the originally puppy's weight  was 50 pounds .

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