15. Hassan is solving x2 + 8x = 6 by
completing the square. His first steps are
shown below.
x? + 8x + C = 6+C
(x + Vc)* = 6+C
a. What is the value of c?

Answer: Split it into 8 pieces.

Step-by-step explanation: If there is 4 halves for your friend, and 3 halves for your other friend, that will be 7. If you add another one, it will be 8. Therefore, you should split the cupcake into 8 pieces.

Answer:

choice 3) acute and equilateral

Step-by-step explanation:

Answer:

=35

Step-by-step explanation:

5d - 25/5

5(8) -25/5

40 - 5

=35

Answer:

the answer is 35

Step-by-step explanation:

d=8, therefore plug 8 into the equation

5d - \(\frac{25}{5}\)

5(8)-  \(\frac{25}{5}\)

40-5

35

Answer:

1/500 is answer.............

Answer:

Step-by-step explanation:

Answer:

√{365×4×365}=√(365²×2²)=±(365×2)=±730

Answer:

\(\sqrt{365\cdot \:4\cdot \:365}=\sqrt{532900}\)

\(=\sqrt{730^2}=730\)

Answer:

number of chairs painted

Step-by-step explanation:

a. Mean = 18.5

b. Median = 16

c. The measure of center would reduce if we eliminate the greatest value, 42.

The mean and the median are both measures of center.

The mean of a data = average of all the data points in the data set.

The median, on the other hand, is the center value of the data distribution or the average of the two center values.

Given the data, 12, 14, 22, 14, 18, 23, 42, 13, 9, 19, 22, 14

a. Mean = (12 + 14 + 22 + 14 + 18 + 23 + 42 + 13 + 9 + 19 + 22 + 14)/12

Mean = 222/12

Mean = 18.5

b. Median = (14 + 18)/2 = 16

c. Eliminating 42, we would have:

Mean = (12 + 14 + 22 + 14 + 18 + 23 + 13 + 9 + 19 + 22 + 14)/11 = 180/11 = 16.3636

Median = 14

This means, the measure of center would reduce if we eliminate the greatest value, 42.

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Answer:

3408cm²

Step-by-step explanation:

The intersection of the sphere with the yz-plane is a circle centered at (2, 6) with a radius of 5.

The equation of a sphere with center (h, k, l) and radius r is given by (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2. In this case, the center is (-3, 2, 6) and the radius is 5, so the equation of the sphere is (x + 3)^2 + (y - 2)^2 + (z - 6)^2 = 25.

To find the intersection of the sphere with the yz-plane (x = 0), we substitute x = 0 into the equation of the sphere. This gives (0 + 3)^2 + (y - 2)^2 + (z - 6)^2 = 25, which simplifies to 6^2 + (y - 2)^2 + (z - 6)^2 = 25. This equation represents a circle in the yz-plane centered at (2, 6) with a radius of 5.

Therefore, the intersection of the sphere with the yz-plane is a circle centered at (2, 6) with a radius of 5.

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Answer:

A) Bald Eagle

Step-by-step explanation:

4,500 meters above sea level

3,000 metres below sea level

4,500m is more farther therefore Bald Eagle

Answer:

A) Curvier Beaked Whale

Step-by-step explanation:

Curvier Beaked Whale travel over 10,440 m or Costa Rica to Antartica.It is the longest mammal migration on Earth.

Answer:

x=1

y=-2

z=-1 ( substitute into equations)

It all depends on how you want your hamburger. If you're serving it as a main dish, 300 hamburger patties (each around 4 ounces) should be plenty to feed 300 people. If you utilize hamburger meat as a topping or filler in a meal, you'll need a different amount.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. The four basic arithmetic operations are addition, subtraction, multiplication, and division. Arithmetic mean is a number calculated by dividing the sum of a set's elements by the number of values in the set.

Here,

It all depends on how you want to eat the hamburger. If you're serving it as a main course, 300 hamburger patties, each weighing around 4 ounces, should plenty to satisfy 300 people. It will need a different quantity of hamburger meat if you use it as a topping or filler in a dish.

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Complete question:

How much hamburger will it take to make 300 three oz patties with a 20% shrinkage?

Probability for the number of correct answers  is fewer than 4 is 0.3993.

The probability that the number x of correct answers is fewer than 4 can be found using the binomial probability formula:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)

Where n is the number of trials, x is the number of successes, and p is the probability of success.

For this problem, n = 8, p = 0.45, and we want to find P(X < 4).

To find P(X < 4), we need to find the probability of 0, 1, 2, and 3 correct answers and add them together:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

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

P(X = 0) = (8 choose 0) * 0.45^0 * (1-0.45)^(8-0) = 0.0059
P(X = 1) = (8 choose 1) * 0.45^1 * (1-0.45)^(8-1) = 0.0416
P(X = 2) = (8 choose 2) * 0.45^2 * (1-0.45)^(8-2) = 0.1275
P(X = 3) = (8 choose 3) * 0.45^3 * (1-0.45)^(8-3) = 0.2243

Adding these probabilities together, we get:

P(X < 4) = 0.0059 + 0.0416 + 0.1275 + 0.2243 = 0.3993

Therefore, the probability that the number x of correct answers is fewer than 4 is 0.3993.

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Answer:

Factor by Grouping

2\(x^{3}\) + 5\(x^{2}\)  - 8x - 20

2\(x^{3}\) + 5\(x^{2}\)

\(x^{2}\) (2x + 5)

-8x - 20

-4 (2x + 5)

(2x + 5) (\(x^{2}\) - 4)

(2x + 5) (x - 2) (x + 2)

Solution:

Putting the terms, which have something in common, in brackets:

Factor them by taking the common terms outside the bracket.

Factor by taking the common expression out of the brackets:

The multiplier (x² - 4) is in squared form.

Square root the multiplier of (2x + 5)(x² - 4), aka (x² - 4):

The factorized form is (2x + 5)(x - 2)(x + 2).

14.4% is the correct answer may be

The instructional context can greatly impact learning with educational technology. In a study with a digital learning game, it was found that the instructional context influences student engagement and motivation. This, in turn, affects their learning outcomes.

The study examined the design of the game, the teacher's role, and the classroom environment. By optimizing these factors, the researchers found that students were more likely to be actively engaged and achieved better learning outcomes.

Therefore, the instructional context plays a crucial role in leveraging the potential of educational technology for effective learning.

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Answer:

Probably A

Step-by-step explanation:

The simplified form of the expression 2x^2 - 3x - 2 remains as 2x^2 - 3x - 2.

To simplify the expression 8x - 2x - x^2, we can combine like terms by adding or subtracting coefficients.

8x - 2x - x^2

First, let's combine the x terms:

(8x - 2x) - x^2

This simplifies to:

6x - x^2

Therefore, the simplified form of the expression 8x - 2x - x^2 is 6x - x^2.

Now, let's simplify the expression 2x^2 - 3x - 2:

The expression is already in simplified form, and no further simplification is possible.

Therefore, the simplified form of the expression 2x^2 - 3x - 2 remains as 2x^2 - 3x - 2.

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The probability that the salesperson will make exactly two sales in a day is 0.1489, the probability that the salesperson will make at least two sales in a day is 0.1451, and the expected number of sales per day is 0.8.

Let X be the number of sales made per day by the salesperson.

Then X follows a binomial distribution with parameters n = 8 and p = 0.10.a. To find the probability that the salesperson will make exactly two sales in a day, we need to find P(X = 2).

P(X = 2) = nCx * p^x * q^(n-x) = 8C2 * (0.10)^2 * (0.90)^6 = 28 * 0.01 * 0.5314 = 0.1489

Therefore, the probability that the salesperson will make exactly two sales in a day is 0.1489.

b. To find the probability that the salesperson will make at least two sales in a day, we need to find P(X ≥ 2).

P(X ≥ 2) = 1 - P(X < 2) = 1 - [P(X = 0) + P(X = 1)] = 1 - [(8C0 * (0.10)^0 * (0.90)^8) + (8C1 * (0.10)^1 * (0.90)^7)] = 1 - [1 * 0.90^8 + 8 * 0.10 * 0.90^7] = 0.1451

Therefore, the probability that the salesperson will make at least two sales in a day is 0.1451.

c. Expected number of sales per day = E(X) = n * p = 8 * 0.10 = 0.8

Therefore, the expected number of sales per day is 0.8.

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a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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The value of the function f(x) = 2x/(2x + 3).

A function is defined as a relationship between a set of inputs that each have one output.

Now, as per the question, the functions are give as;

h(x) = (2x + 3)/x

g(x) = 2/x

And, g(f (x) ) = h(x) =  (2x + 3)/x  ......(equation 1)

To estimate the value of f (x); Substitute x for f(x)

g(f (x) ) = 2/f (x)     ......(equation 2)

Equation (equation 1 and 2).

2/f (x) =  (2x + 3)/x

f (x) = 2x/ (2x + 3)

Thus, the value of the function f (x) = 2x/ (2x + 3).

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The correct question is-

The function h (x) = StartFraction 2 (x + 3) Over x EndFraction is a result of the composition (g compose f) (x). If g (x) = StartFraction 2 over x EndFraction, what is f(x)?

Answer:

There is not a way that I can show you how to graph it, so I will try and explain it.

Step-by-step explanation:

(1,1)

^  ^     y-axis

x-axis

You are just going right however many, and then up however many it says.

So if it's (1,1) you will go right one space, and then up one space.

Once you have all of your points on the graph, you put a line through them.

Hope this helps! :)

In the question, we are told that Graham borrowed $10 from his mum to buy a toy. He pays back his mum $2 per week from his allowance. We can find how long will it take for him to pay her below.

Explanation

Since Graham is paying back every week, this means that the payback time would be measured in weeks.

We can use the formula below;

Thus;

Answer: 5 weeks

An absolute function is represented as: \(y = a|x - h| + k\) where the vertex is (h,k).

The function that describes the path of the sunlight is: \(y= 2|x - 4|\)

We have:

\((h,k) = (4,0)\) --- the vertex i.e. the point where the sun hits the water

\((x,y) =(5.5,3)\)

Recall that:

\(y = a|x - h| + k\)

Substitute \((h,k) = (4,0)\)

\(y = a|x - 4| + 0\)

\(y = a|x - 4|\)

Substitute \((x,y) =(5.5,3)\) to solve for a

\(3 = a|5.5 - 4|\)

\(3 = a|1.5|\)

Take absolute value of 1.5

\(3 = 1.5a\)

Solve for a

\(a = \frac 3{1.5}\)

\(a = 2\)

Recall that:

\(y = a|x - 4|\)

Substitute \(a = 2\)

\(y= 2|x - 4|\)

Hence, the function that describes the path of the sunlight is: \(y= 2|x - 4|\)

See attachment for the graph of \(y= 2|x - 4|\)

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Answer: Y = -3x

Step-by-step explanation:not needed

Answer:

$1,585.70

Step-by-step explanation:

15% of $2,200 = $330

7.65% of $2,200 = $168.3

3% of $2,200 = $66

$330 + $168.3 + $66 = $564.3

$564.3 + $50 (healthcare cost) = $6.14.3

$2,200 $614.3 = $1585.70

The mean is found by adding all the observations and dividing by the number of observations, so in this case, (15+7+8+95+19+12+8+22+14)/9 = 22. The middle observation is 14, so that is the median. The mode is the most frequently occurring observation, so in this case, the mode is 8, since it occurs twice.

It's difficult to say which measure of center is the best without more information about the distribution of the data and the purpose for which the information is being used. If the data is relatively symmetric and not skewed by extreme values, the mean may be a good measure of center. However, if the data is skewed or has extreme values, the median may be a better measure of center. The mode is useful when we want to know the most common observation. Ultimately, the best measure of center depends on the specific situation and what information is most important to the decision-making process.

To find the mean, median, and mode for this sample, follow these steps:

1. First, arrange the data in ascending order: 7, 8, 8, 12, 14, 15, 19, 22, 95.

2. To find the mean (average), sum the values and divide by the number of observations:
(7+8+8+12+14+15+19+22+95)/9 = 200/9 ≈ 22.22.

3. To find the median (middle value), locate the value that is in the middle of the ordered list:
There are 9 values, so the median is the 5th value, which is 14.

4. To find the mode (most frequent value), identify the value that occurs the most:
The value 8 appears twice, so the mode is 8.

Mean: 22.22
Median: 14
Mode: 8

In this case, the median (14) seems to be the best measure of the center of these data because it is less affected by the outlier (95) than the mean. The mode (8) represents only the most frequent value and does not account for other values in the dataset.

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Answer:

6

Step-by-step explanation:

Answer: 31 years

Explanation- Since 5 people have a mean age of 30, the sum of their ages is 5⋅30=150. Adding one more person of age 36 to the group gives 6 people with sum of ages 150+36=186. Now divide this by 6 to get the new mean for the group of 6 people: 1866=31 years.

⭐ Answered by TurttlePrincess

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