Determine the number of solutions to the given system. Remember to use the format (x,y) to type in your points, and do not use spaces. If there is only one, type the point in one space and "none" in the other. If there is none, type none in both the boxes. System: {y=−x+10y=(x−5)2+6

The decimal numbers in this problem are classified as follows:

a) 7.8 is a rational number.

b) 8.25... is an irrational number.

In the context of this problem, we have that:

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The equation of the function in standard form is f(x) = x² + 4x - 12.

Quadratic equation can be represented as follows:

ax² + bx + c

where

Therefore, let's write the equation of the function in standard form.

-12 = a(0)² + b(0) + c

c = -12

Let's use -1 and -15

-15 = a(-1)² + b(-1) + -12

-15 = a - b - 12

a - b = - 3

Let's use -2 and -16.

-16 =  a(-2)² + b(-2) + -12

-16 = 4a - 2b - 12

4a - 2b = -4

2a - b = -2

Therefore,

a - b = - 3

2a - b = -2

subtract the equations

a = 1

b = a + 3

b = 1 + 3

b = 4

Therefore, the equation is as follows:

f(x) = x² + 4x - 12

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Among any group of five integers, there are at least two with the same remainder when divided by 4.

To show that among any group of five integers, there are two with the same remainder when divided by 4, we'll use the Pigeonhole Principle. Here's a step-by-step explanation:

1. Consider the four possible remainders when dividing an integer by 4: 0, 1, 2, and 3.
2. Imagine these remainders as "boxes," where each integer will go into its respective remainder box.
3. We have five integers and four boxes. The Pigeonhole Principle states that if there are more "pigeons" (integers) than "holes" (boxes), at least one hole must contain two or more pigeons.
4. Since we have five integers and only four possible remainders, at least one of these remainder boxes must have two integers.

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The formula that describes the distance Jack covered during the hike  is: S(t) = vt for v = 5 and t is the time

The form of a linear equation in slope intercept form is:'

y = mx + c

where:

m is slope

c is y-intercept

Now, the formula for distance here is:

s(t) = vt

where:

v is speed

t is time

For a speed of 2 mph and a time of 3 hours, we can arriave at:

s(3) = 2 * 3 = 6 m for 2 seconds

Similarly:

s(t) = 5t

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As per the given equation, the center and radius of the circle are (-3, 2) and 12, respectively.

Radius is the distance between the center of a circle and any point on its circumference. It is half the length of the diameter of the circle.

The center-radius form of a circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is the radius.

Comparing the given equation with the standard form, we have:

[tex](x + 3)^2 + (y - 2)^2 = 144[/tex]

This means that the center of the circle is (-3, 2) and the radius is the square root of 144, which is 12.

Therefore, the center and radius of the circle are (-3, 2) and 12, respectively.

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Statistical methods are excellent for capturing quantitative data, which is numerical data that can be measured and analyzed using mathematical calculations.

These methods are commonly used in fields such as economics, psychology, and social sciences to collect, analyze, and interpret data.

In contrast, qualitative data such as opinions, attitudes, and beliefs are better captured using methods such as interviews, focus groups, and case studies.

Which two primary data kinds are there?

Data may be categorized into two main probability : quantitative and qualitative, and both are equally significant.

Why are primary and secondary data different?

Data may be obtained by social and health scientists by speaking with the subjects that interest them directly. These data they gather are referred to as primary data.

The information that has previously been obtained by someone else is another sort of data that might be useful to researchers. Secondary data is what this is.

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Answer:

[tex] \sqrt{ {28}^{2} + {45}^{2} } = \sqrt{784 + 2025} = \sqrt{2809} = 53[/tex]

The value of the expression is 9 1/4.

We have,

We can simplify the expression step by step using the order of operations (PEMDAS).

2 x (1/4 + 11/8 + 3)

First, let's add the fractions inside the parentheses:

1/4 + 11/8 = 2/8 + 11/8 = 13/8

Now we can substitute this result back into the original expression:

2 x (13/8 + 3)

Next, we add the two terms inside the parentheses:

13/8 + 3 = 13/8 + 24/8 = 37/8

Now we can substitute this result back into the expression:

2 x 37/8

Finally, we multiply the coefficient 2 by the fraction 37/8:

2 x 37/8 = 74/8 = 9 1/4

Therefore,

The value of the expression is 9 1/4.

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The radius of the quarter circle is 1 mile.

The formula for calculating the area of a circle is given by A = πr², where A is the area of the circle, r is the radius of the circle, and π (pi) is a mathematical constant equal to approximately 3.14.

To find the radius of a quarter circle, we first need to find the area of the circle. Since the area of a quarter circle is given as 0.785 square miles, we can calculate the area of the circle as follows:

Area of circle = 4 × Area of quarter circle

Area of circle = 4 × 0.785 square miles

Area of circle = 3.14 square miles

Now that we know the area of the circle, we can use the formula for the area of a circle to find the radius. We rearrange the formula as follows:

r² = A/π

r² = 3.14/π

r² = 1

r = √1

r = 1 mile

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The value of the product of the "complex-numbers" (2i)(5+3i) is "-6+10i", Option(a) is correct.

The Complex numbers are defined as the numbers that can be expressed in the form "a + bi", where a and b are real numbers and "i" is the imaginary unit, which is defined as the square root of -1.

To multiply the two complex numbers (2i)(5+3i), we use the distributive property of multiplication:

⇒ (2i)×(5+3i) = (2i)×(5) + (2i)×(3i),

Simplifying this expression,

We get,

⇒ (2i)×(5+3i) = 10i + 6i²,

Since i² = -1, we substitute this value into the expression:

⇒ (2i)×(5+3i) = 10i + 6(-1) = -6 + 10i,

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

What is the value of the product (2i)×(5+3i)?

(a) -6 + 10i

(b) 10 + 6i

(c) -10 + 6i

(d) 10 - 6i

The measure of CD in triangle is 18.

We are given that;

CE=7, HB=13, HF=3

Now, In triangle GDH

GD=1/2 * BD

=24/2=12

BC= 2* EC

=2* 7= 14

By pythagoras theorem;

EH^2 + EB^2 = BH^2

EH^2 + 49 = 169

EH^2 = 120

EH= rt120

FD= 16

CD= 18

Therefore, by the given triangle answer will be 18.

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the missing angle measurement using the angle addition postulate are:

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. Angles are typically measured in degrees or radians.

According to the given information:

The angle addition postulate is a rule used to find the measure of an angle created by two adjacent angles. If two adjacent angles are known, then their sum will equal the measure of the larger angle formed by the two adjacent angles. To use the angle addition postulate, add the measures of the known adjacent angles to find the measure of the larger angle.

In the given set of angles, we are asked to use the angle addition postulate to find the missing angle measures. We can use this rule to find the missing angles by adding the measures of the known adjacent angles. By doing so, we can find the measure of the larger angle formed by the two adjacent angles. It is essential to note that this rule only applies to adjacent angles. Therefore, we can only use the angle addition postulate to find the missing angle measurements for angles that share a common vertex and side

LABC = 60 degrees (angle addition postulate states that the sum of the measures of two adjacent angles is equal to the measure of the larger angle formed by the two adjacent angles)L

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The infusion rate for the given volume to be infused in the given time duration is given by 266.67 ml per hour (rounded to two decimal places).

Volume to be infused = 0.8liters

Time duration = 9 hours

Drop factor = 60 gtt/ml

Use the following formula to calculate the infusion rate,

Infusion rate = (Volume to be infused × Drop factor) / Time in minutes

Convert the units to liters and minutes, respectively,

1 liter = 1000 milliliters

⇒ 0.8 liters = 800 milliliters

1 hour = 60 minutes

⇒ 9 hours = 9 × 60

                 = 540 minutes

Substituting the given values, we get,

⇒ Infusion rate = (800 ml × 60 gtt/ml) / 540 min

⇒Infusion rate = 88.89 gtt/min (rounded to two decimal places)

The infusion rate is 88.89 drops per minute.

To convert this to milliliters per hour,

Use the following conversion,

since the drop factor is 60 gtt/ml

⇒ 1 ml = 20 drops

The infusion rate in ml/hour is,

= (88.89 gtt/min × 1 ml/20 gtt) × 60 min/hour

= 266.67 ml/hour

Therefore, the infusion rate is 266.67 ml per hour (rounded to two decimal places).

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The solution for the inequalities 5x – 10 > 20 or 5x – 10 ≤ –15 is:

x > 6 or x ≤ -1.

We have two inequalities to solve:

5x - 10 > 20

Adding 10 to both sides, we get:

5x > 30

Dividing both sides by 5, we get:

x > 6

And the second inequality is:

5x - 10 ≤ -15

Adding 10 to both sides, we get:

5x ≤ -5

Dividing both sides by 5 (and remembering to flip the inequality since we are dividing by a negative number), we get:

x ≤ -1.

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Answer:

If the dimensions of the scaled painting are 8 times smaller than the actual painting, then the actual dimensions can be found by multiplying the scaled dimensions by 8.

So, the actual dimensions of the painting are:

12 inches x 8 = 96 inches (width)

16 inches x 8 = 128 inches (height)

Answer:

T=15 S=5

Step-by-step explanation:

If you sold 3x more shirts(T) the other number must also apply. So the only one it can be is D. Also, 15x8+5x12=180

Answer:

Step-by-step explanation:

The relation is not a function. A function is a relation in which each input value leads to exactly one output value. In this case, the input value of 1 leads to two different output values, -2 and 3. Therefore, the relation is not a function.

The correct answer is No, because for each input there is not exactly one output.

Answer:  

Because of all the random factors beyond our control that enter the flipping process (force with which the coin is flipped, motion of the air in the room, position of our hand when we catch the coin...) we therefore expect a probability of 1/2 for heads, and 1/2 for tails. Each possible outcome is equally likely.

A coin has 2 possible outcomes because it only has two sides (heads or tails). This means that the probability of landing on heads is 1/2. So, the probability of landing on heads is (1/2) x 100, which is 50%.

What he and his fellow researchers discovered (here's a PDF of their paper) is that most games of chance involving coins aren't as even as you'd think. For example, even the 50/50 coin toss really isn't 50/50 — it's closer to 51/49, biased toward whatever side was up when the coin was thrown into the air.

Answer:

4

Step-by-step explanation:

Let's start by assuming that the initial mass of the hydrate CoCl2 x XH2O is 100 grams. This means that the mass of the anhydrous compound CoCl2 after decomposition is 53.9 grams (since it is 53.9% of the hydrate mass).

The mass of water lost during the decomposition is therefore:

Mass of water lost = Initial mass of hydrate - Mass of anhydrous compound

Mass of water lost = 100 g - 53.9 g

Mass of water lost = 46.1 g

The molar mass of CoCl2 is 129.8 g/mol, and the molar mass of H2O is 18.0 g/mol. Therefore, the molar mass of the hydrate CoCl2 x XH2O is:

Molar mass of hydrate = Molar mass of CoCl2 + Molar mass of H2O × X

Molar mass of hydrate = 129.8 g/mol + 18.0 g/mol × X

We can set up a proportion to solve for X:

Mass of water lost / Molar mass of water = X / Molar mass of hydrate

Plugging in the values we found:

46.1 g / 18.0 g/mol = X / (129.8 g/mol + 18.0 g/mol × X)

Solving for X:

46.1 g / 18.0 g/mol = X / (129.8 g/mol + 18.0 g/mol × X)

2.56 mol = X / (129.8 g/mol + 18.0 g/mol × X)

2.56 mol × (129.8 g/mol + 18.0 g/mol × X) = X

331.968 g/mol × X + 46.368 g/mol × X = X

378.336 g/mol × X = X

X = 4

Therefore, the value of X in the hydrate formula CoCl2 x XH2O is 4, and the formula of the hydrate is CoCl2 x 4H2O.

The approximate probability of drawing one orange marble and one green marble from a bag containing five red marbles, four orange marbles, one yellow marble, and three green marbles is approximately 0.154.

To find the approximate probability of drawing marbles, we can use the following formula

probability = (number of favorable outcomes) / (total number of outcomes)

We need to find the number of favorable outcomes where one marble is orange and the other is green. We can choose one orange marble from four orange marbles in the bag in 4 ways, and one green marble from three green marbles in 3 ways. So, the number of favorable outcomes is 4 x 3 = 12.

The total number of ways of choosing two marbles from the bag is 13C2, which is the number of combinations of 2 marbles that can be drawn from the 13 marbles in the bag. Therefore, the total number of outcomes is

13C2 = (13 x 12) / (2 x 1) = 78

Thus, the approximate probability of drawing one orange marble and one green marble is

probability = number of favorable outcomes / total number of outcomes = 12/78 ≈ 0.154

Therefore, the approximate probability of drawing one orange marble and one green marble from the bag is approximately 0.154.

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Answer:

The total amount of money in the savings account can be represented by the sum of the initial amount of money and the amount of money added each week multiplied by the number of weeks:

S = 450 + 70W

To find the total amount of money in the savings account after 17 weeks, we can substitute W = 17 into the equation:

S = 450 + 70(17)

S = 450 + 1190

S = 1640

Therefore, after 17 weeks of adding $70 to the savings account each week, the total amount of money in the account will be $1640.:)

The value of the variable x is -6

Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, variables, constants and factors.

These expressions also consist of arithmetic operations, such as;

From the information given, we have the equation;

x + 12/2 = 3(x + 7)

expand the bracket

x +12/2 = 3x + 21

cross multiply the values

x + 12 = 6x + 42

collect like terms

-5x = 30

x = -6

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Thus, the value of f6 using a 3-day weighted moving average with w1 is 60.

To calculate the 3-day weighted moving average with w1 for the value of f6, we need to first calculate the weighted average for the past three days.

The formula for weighted moving average is:

WMAt = [(P1 * w1) + (P2 * w2) + (P3 * w3)] / (w1 + w2 + w3)

where:
- WMAt is the weighted moving average for time t
- P1, P2, P3 are the values of the variable for the three time periods being averaged
- w1, w2, w3 are the weights assigned to each period (in this case, w1 = 1 and w2 = w3 = 0)

For the past three days, we have:

- Day 4: 60 rolls sold
- Day 5: 53 rolls sold
- Day 6: 60 rolls sold

Using the formula above with w1 = 1 and w2 = w3 = 0, we get:

WMA6 = [(60 * 1) + (53 * 0) + (60 * 0)] / (1 + 0 + 0) = 60

Therefore, the value of f6 using a 3-day weighted moving average with w1 is 60.

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The length of Rocky Mountain Juniper tree will be 1.5 feet.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that:

A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 6.8 inches.

Now,

Let the height of Rocky Mountain Juniper tree = x feet

And, A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 6.8 inches.

So, The height of a Rocky Mountain Juniper tree be if at the same time of day it casts a shadow of 20.3 feet will be find as:

[tex]\rightarrow \dfrac{5.1}{6.8} =\dfrac{\text{x}}{20.3}[/tex]

Solve for x as:

[tex]\rightarrow \dfrac{51\times20.3}{6.8} = \text{x}[/tex]

[tex]\rightarrow \dfrac{103.53}{6.8} = \text{x}[/tex]

[tex]\rightarrow \text{x} = 1.5 \ \text{feet}[/tex]

Thus, The length of Rocky Mountain Juniper tree will be 1.5 feet.

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The required sample size to construct a 95% confidence interval to estimate the proportion is 602 students.

a. To estimate the sample size needed to construct a 95% confidence interval with a maximum error of 2.5% when the past few years' graduation rate is 70%, we can use the following formula:

n = [Z² × p × (1-p)] / E²

where:

Z = the Z-value for the desired confidence level (95% in this case), which is 1.96

p = the estimated proportion of students who graduate in 4 years (70%)

E = the maximum error, which is 0.025 (2.5%)

Plugging in the values, we get:

n = [(1.96)² × 0.7 × (1-0.7)] / 0.025²

n = 381.16

Always round up to the next integer, so the sample size needed is 382.

b. To estimate the sample size needed when there is no knowledge of the typical graduation rate, we can use a conservative estimate of 50% for p. Plugging in the values, we get:

n = [1.96² × 0.5 × (1-0.5)] / 0.025²

n = 601.64

Always round up to the next integer, so the sample size needed is 602.

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The value of n in the given equation is determined as 5.

option C.

The value of n in the given equation is calculated by applying the following method of simplification.

2n / (n - 5) + (4n - 30) / (n - 5) = n

Since the common denominator is n - 5, multiply through by n - 5;

2n + (4n - 30) = n(n - 5)

6n - 30 = n² - 5n

n² - 11n + 30 = 0

Factorize the expression as follows;

n² - 5n - 6n + 30 = 0

n(n - 5) - 6(n - 5) = 0

(n - 6)(n - 5) = 0

n = 5 or 6

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Answer:

The odds against it snowing the next day can be found by subtracting the probability of it snowing (40%) from 100% (the total possible outcomes) and then expressing it as a ratio of non-snowing outcomes to snowing outcomes.

100% - 40% = 60%

The odds against it snowing the next day are 60:40 or 3:2 (simplifying the ratio).

The step the student first made an error was step B

The given expression in simplest form is 8

From the question we are to determine the step the student first make an error and we are to simplify the given expression correctly.

The given expression is

5 - (-3)

The student steps are as follows:

Step A: 5+ (3)

Step B: 5+8

Step C: 13

The step the student first made an error was step B because

5 + (3) should evaluate to

5 + 3

and eventually 8

The correct simplification process is as follows:

5 - (-3)

Step A: 5+ (3)

Step B: 5 + 3

Step C: 8

Hence, the expression in simplest form is 8

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The probability of picking a T and an N is 1/81.

The correct option is (B).

From the geometric shape we can see that the total number of different letter is = 9

that are M, A, T, H, I, S, F, U, N

Now T is one of the letter from that 9 letters.

Now if we pick T then the probability of that = 1/9

Therefore, P(T) = 1/9

now we again replace T in previous position before picking the next letter.

Again the total number of letters = 9

Again, N is one of the letter from that 9 letters.

So the probability of picking N = 1/9

Therefore, P(N) = 1/9

The required probability of picking T and N

= probability of picking T followed by picking N

= P(T)*P(N)

= (1/9)*(1/9)

= 1/(9*9)

= 1/81

Hence the correct option is (B).

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Answer: 101

Step-by-step explanation:

180 - 76 - 48 = 56

180 - 56 - 23 = 101