Quadratic equation y=(x-5)²-2

Answer:

my guess is the flagpole is 164 in tall

Step-by-step explanation:

if she 60 in tall then her shadow is 36 in taller

the flagpole's shadow is 200in so subtract 36 from 200

Answer: x=pi/8+npi    and x=5pi/8+npi

Step-by-step explanation:

Among the provided options, the most accurate statement would be:      "It unites many different Arabic cultures against a common enemy, the Jews."

The creation of the nation-state of Israel in 1948 led to increased Pan-Arabism in several ways. Firstly, the establishment of Israel as a Jewish state in the heart of the Arab world was perceived by many Arabs as a direct threat to their own national aspirations. This common enemy, the Jews, served as a rallying point that united various Arabic cultures against a perceived external threat.

Additionally, the existence of Israel became a central issue for Arab nationalism, with the goal of liberating Palestine from Israeli control becoming a unifying cause among Arab nations. The Arab-Israeli conflict and ongoing tensions between Israel and its Arab neighbors further fueled Pan-Arab sentiment.

It is important to note that the other options provided do not accurately reflect the impact of Israel's creation on Pan-Arabism. The creation of Israel did not justify Jewish expansion into the Sinai Peninsula, nor did it lead to Israeli-Palestinian unity after the Yom Kippur Wars.

The statement that it demonstrated the need for an Arabic homeland is also not accurate, as the creation of Israel was not a direct factor in the Arab world's pursuit of national self-determination.

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We are to solve the inequality:

|x + 3| + 2 ≤ 4

First let's subtract 2 from both sides

|x + 3| + 2 - 2 ≤ 4 - 2

|x + 3| ≤ 2

Apply absolute rule: if |u| ≤ a, a > 0 then -a ≤ u ≤ a

-2 ≤ x + 3 ≤ 2

x + 3 ≥ -2 and x + 3 ≤ 2

x ≥ -5 and x ≤ -1

-5 ≤ x ≤ -1

The length and width of the rectangle is 27 inches and 13 inches, respectively.

Let the width be w inches and the length be l inches

According to the question, length of the rectangle is 12 less than 3 times the width of the rectangle

=> l = 3w - 12

=> 3w - l = 12      -   eq 1

The perimeter of the rectangle is also given as 40.

We know, perimeter of a rectangle is equal to twice the sum of the length and width of the rectangle.

=> 2 (l + w) = 40

=> l + w = 20

=> w + l = 20      -   eq 2

Adding eq 1 and eq 2, we get

4w = 32

=> w = 8

Substituting the value of w in any of the two equations, we get

l = 12

Therefore, by using the given information in the question and elimination method, we get the length and width of the rectangle as 27 inches and 13 inches, respectively.

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The head of the psychology department has employed a sampling technique called simple random sampling.

This technique involves selecting a sample from the population in such a way that every member of the population has an equal chance of being included in the sample.
In this case, the population of interest is all the psychology major students in the university.

The department head wants to understand their attitudes toward implementing an internship as a requirement for completing their degree.

To obtain a representative sample, she first compiles a list of all psychology majors.

Then, she randomly selects 100 students from this list to participate in her survey.
Simple random sampling is an effective method to ensure that the sample is unbiased and representative of the entire population.

It minimizes selection bias, as each student has an equal chance of being selected.

This allows the department head to generalize her findings and make valid inferences about the attitudes of all psychology students in the university.
To summarize, the department head employed a simple random sampling technique to gather information about students' attitudes towards implementing an internship as a requirement for completing their psychology degree.

This approach helps ensure the sample is representative and unbiased, allowing for accurate and generalizable conclusions.

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Answer:

\(4m^{2} -10mn+6n^{2}\)

Step-by-step explanation:

Using FOIL,

(2m-2n)(2m-3n)

= 4m^2-4mn-6mn+6n^2

=4m^2-10mn+6n^2

Answer:

4m^2+9n^2-12mn

Step-by-step explanation:

(2m-3n)(2m-3n)

first we will multiply the 2m out

2m*2m= 4m*2

2m*-3n=-6mn

then we will multiple the -3n out

-3n*2m=-6mn

-3n*-3n=9n^2

finally we add it all together

4m^2+9n^2-12mn

Answer:

Step-by-step explanation:

let the plane intersects the join of points in the ratio k:1

let (x,y,z) be the point of intersection.

\(x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}= \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}\)

point of intersection is (8/3,14/3,8/3)

and ratio of division is 2:1

Answer:

I am sorry I don't know how to

Step-by-step explanation:

Answer:

AngleASZ Is-congruent-to AngleZSB

Step-by-step explanation:

The incenter of a triangle is a point inside a triangle that is equidistant from all the sides of a triangle. The incenter is the point formed by the intersection of all the three angles of the triangle bisected. The lines drawn from the incenter to the sides of the triangle forming right angles to the sides are congruent.

If Point Z is equidistant from the sides of ΔRST, point Z is the incenter of triangle RST. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. This lines are therefore congruent to each other, i.e. ZA = ZB = ZC.. Since the angles of the sides of the triangles are bisected to form the incenter, therefore:

AngleASZ Is-congruent-to AngleZSB

Answer:

AngleASZ Is-congruent-to AngleZSB

Step-by-step explanation:

D is the correct answer

the gradients of each of the sides of the triangle are \(m_1=\frac{8}{5}, m_2=\frac{4}{-9} and m_3=-3\)

Given  vertices of triangle ABC are A(2,-3),B(7,5) and C(-2,9).

Let's find out the gradients of each side of the sides of the triangle using given points.

Formula for Gradient  using two points.

Gradient denoted by m.

Gradient can also called as slope.

First gradient using two points are A(2,-3) & B(7,5)

           \(m_1=\frac{y_2-y_1}{x_2-x_1}\)

           \(m_1=\frac{5-(-3)}{7-2}\)

           \(m_1=\frac{8}{5}\)

Second gradient using two points are B(7,5) & C(-2,,9)

            \(m_2=\frac{y_2-y_1}{x_2-x_1}\)

            \(m_2=\frac{9-5}{-2-7}\)

            \(m_2=\frac{4}{-9}\)

Third gradient using two points are   A(2,-3) & C(-2,9)

              \(m_3=\frac{y_2-y_1}{x_2-x_1}\)

              \(m_3=\frac{9-(-3)}{-2-2}\)

              \(m_3=\frac{12}{-4}\)

              \(m_3=-3\)

Therefore, the gradients of each of the sides of the triangle are \(m_1=\frac{8}{5}, m_2=\frac{4}{-9} and m_3=-3\)

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Answer:

Fraction: x= 8/5

Decimal: x= 1.6

Mixed Number: x= 1 3/5

Step-by-step explanation:

Refer to attachment.

Hope it helps.

1a)The values of l range from 0 to (n-1), so for n = 3, l can have the values 0, 1, and 2.

b) The values of m can be -2, -1, 0, +1, and +2

c) There are a total of 9 orbitals

The qualities and traits of quantum systems, like the electrons in atoms, are described by a set of numbers known as quantum numbers. They offer knowledge on the system's energy, angular momentum, orientation, and spin, among other characteristics.

Using the formula, number of electrons = \(n^2\)

Number of electrons =\(3^2 = 9\)

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A whopping 95% of people fall within the IQ ranges of 70 and 130. 99.7% of people in the world have IQs between 55 and 145. Only about 0.3% of people have IQ scores that fall outside of this range (less than 55 or higher than 145).

According to the one-standard-deviation rule, 32 percent of the population has an IQ score that is at least 15 points off from 100: 16 percent have IQs over 115, and 16 percent have IQs below 85.

The equation IQ=mc100, where m is the mental age and c is the chromological age, determines a person's IQ. Find the range of their mental ages if a group of 12-year-old youngsters has an IQ between 80 and 140.

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The cardinality (number of elements) of set A, denoted as n(A), is 21.

The set A is defined as {110, 111, 112, 113, ..., 130}. The ellipsis (...) implies that the pattern continues with consecutive numbers until 130. To get the number of items in set A, remove the smallest from the biggest and multiply by 1. To get the number of elements in set A, subtract the smallest from the largest and multiply by one.

The smallest element in set A is 110, and the largest element is 130. Therefore, the calculation is as follows:

n(A) = 130 - 110 + 1 = 21.

Thus, the cardinality of set A, n(A), is 21. The cardinal number is basically the number of elements in the set and it tell us about the subsets possible.

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Given  set A.=  {110,111,112,113,…130} . Find n(A) of the given set A in whole numbers.

Answer: 43 and 49

Step-by-step explanation:

Answer:

43, 89

Step-by-step explanation:

A prime number is any number above 1 that can evenly divide out.

Hope This Helps :)

Answer:

Step-by-step explanation:

Use pythagorean   the hypotenuse is always across from th right angle and is the longest in a right triangle

34² = 16² + x²

1156 = 256 + x²                bring 256 over to other side by subtracting

900 = x²                take square root of both sides to solve for x

x = 30

Answer:

Step-by-step explanation:

In the given figure,

34 is Hypotenuse i.e the largest side

16 is perpendicular

b = Base

Using Pythagoras theorem,

(Hypotenuse)² = (Perpendicular)² + (Base)²

(34)² = (16)² + (b)²

1156 = 256 + b²

1156 - 256 = b²

900 = b²

b = √900

b = 30

Therefore, Value of b is 30.

The standard normal distribution that represents the variable in the question indicates that we get;

a. The probability is about 0.42858

b. The probability that the average mpg of 3 randomly selected passenger cars is more than 32 mpg is 0.35197

c. The probability that all the three cars get more than 32 mpg is about0.0788

A standard normal distribution, also known as the Gaussian distribution, and the z-distribution, has a mean of 0, and a standard deviation of one.

a. The standard score (z-score) of 32 mpg can be obtained as follows;

z = (32 - 31.2)/4.5 ≈ 0.178

The probability that a standard normal variable has a z-score, larger than 0.178, obtained from the z-score table is therefore;

P(Z > 0.178) ≈ 1 - 0.57142 = 0.42858

b. The of the sample is μ = 31.2

The standard deviation of the sample is, σ = 4.5/√(3)

z = (x - μ)/(σ/√n)

Therefore;

z = (32 - 31.2)/(4.5/√(3)) ≈ 0.308

The probability that a standard normal variable has a z-score larger than 0.308, from the z-score table, therefore is; p(z > 0.308) = 1 - 0.64803 = 0.35197

c. The mpg ratings are independent, therefore, we get;

P(the three cars get more than 32 mpg) = P(car 1 gets more than 32 mpg) × P(car 2 gets more than 32 mpg) × P(car 3 gets more than 32 mpg)

The probability that a car gets more than 32 mpg is about 0.42858

Therefore;

P(the three cars get more than 32 mpg) = 0.42858 × 0.42858 × 0.4288 ≈ 0.0788

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A horizontal line is a line extending from left to right. When you look at the sunrise over the horizon you are seeing the sunrise over a horizontal line. The x-axis is an example of a horizontal line.

Now, According to the question:

What is a Horizontal Line?

Horizontal lines are also known as sleeping lines. In coordinate geometry, horizontal lines are those lines that are parallel to the x-axis. In geometry, we can find horizontal line segments in many shapes, such as quadrilaterals, 3d shapes, etc. In real life, we can find horizontal lines on the steps of the staircase, planks on the railway tracks, etc.

The x-axis is an example of a horizontal line.

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Answer:

The solutions of the system are (5, 1) and (-7, -5)

Step-by-step explanation:

The factorization of a² - b² = (a + b)(a - b)

Let us use this rule to solve the question

∵ x² - y² = 24

→ Factorize the left side

∴ (x + y)(x - y) = 24 ⇒ (1)

∵ x = 3 + 2y → (2)

→ Substitute x in equation (1) by equation (2)

∵ (3 + 2y + y)(3 + 2y - y) = 24

∴ (3 + 3y)(3 + y) = 24

→ Take 3 from the first bracket as a common factor

∵ 3 + 3y = 3(1 + y)

∴ 3(1 + y)(3 + y) = 24

→ Divide both sides by 3

∴ (1 + y)(3 + y) = 8 ⇒ (3)

→ Multiply the two brackets on the left side

∵ (1 + y)(3 + y) = (1)(3) + (1)(y) + (y)(3) + (y)(y)

∴ (1 + y)(3 + y) = 3 + y + 3y + y²

∴ (1 + y)(3 + y) = 3 + 4y + y²

→ Substitute it in the equation (3)

∴ 3 + 4y + y² = 8

→ Subtract 8 from both sides

∵ 3 - 8 + 4y + y² = 8 - 8

∴ -5 + 4y + y² = 0

→ Arrange the left side from greatest power of y

∵ y² + 4y - 5 = 0

→ Factorize it into two factors

∴ (y - 1)(y + 5) = 0

→ Equate each bracket by 0 to find y

∵ y - 1 = 0 ⇒ Add 1 to both sides

∴ y - 1 + 1 = 0 + 1

∴ y = 1

∵ y + 5 = 0 → Subtract 5 from both sides

∴ y + 5 - 5 = 0 - 5

∴ y = -5

→ Substitute the values of y in equation (2) to find x

∵ x = 3 + 2(1) = 3 + 2

∴ x = 5

∵ x = 3 + 2(-5) = 3 + -10

∴ x = -7

∴ The solutions of the system are (5, 1) and (-7, -5)

Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

a) Given preferences are not monotonic.

b) The budget constraint is binding and the consumer cannot afford that bundle.
c) The interpretation of these choices is that the consumer maximizes their utility.

(a) These preferences are not monotonic. Monotonicity means that if one bundle is preferred to another, any bundle with more of both goods should also be preferred. In this case, if x1'+x2' < x1''+x2'', it does not necessarily mean that x1'+x2' < x1''+x2'' for all bundles with more of both goods.

(b) To determine which bundle would be chosen by the consumer, we need to compare the total expenditure on each bundle to the consumer's income. If the total expenditure on a bundle is less than or equal to the consumer's income, then that bundle would be chosen.

If the total expenditure exceeds the consumer's income, then the budget constraint is binding and the consumer cannot afford that bundle.

(c) When prices are strictly negative (p1 = -ω, p2 = -e), the budget set can be represented graphically as a set of bundles that the consumer can afford.

The initial endowment P represents the amount of good 2 that the consumer already possesses without having to spend any money. It is a starting point for the consumer's choices.

(d) To characterize the optimal selection of the consumer, we need to consider whether ω > e or e > ω.

If ω > e, the consumer's optimal choice would lie on the highest attainable indifference curve that is tangent to the budget set.

If e > ω, the optimal choice would lie on the indifference curve that is tangent to the budget set at a point where the consumer exhausts their initial endowment P.

The interpretation of these choices is that the consumer maximizes their utility by selecting the bundle that provides the most satisfaction given their budget constraints and initial endowment.

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The cost of "x" radios is $10x and transportaiton fee of $5. So cost equation for "x" radios is,

(b)

The selling price of one radio is $12. So for "x" radio Profit(selling price) equation is,

(c)

Determine the value of x for which profit equation is equal to cost equation.

The number of radios can never be in fraction. So individual has to buy 3 radios to have equal cost and profit,.

Answer:

One side length is 17. Because you square root 289 to figure out the side length.

Step-by-step explanation:

The area of a square is a side length * a side length

or l^2 = 289

sqrt or 289 = 17

Answer:

The total number of your ancestors for the past 42 generations would be 8,796,093,022,206.

Step-by-step explanation:

To calculate the total number of your ancestors for the past 42 generations, we can use the formula for the sum of a geometric sequence:

Sum = a * (1 - r^n) / (1 - r)

where: - a is the first term in the sequence - r is the common ratio between terms - n is the number of terms in the sequence

For this problem: - a = 2 (since you have 2 parents) - r = 2 (each generation doubles the number of ancestors) - n = 42 (the number of generations)

Now, plug these values into the formula:

Sum = 2 * (1 - 2^42) / (1 - 2) Sum = 2 * (1 - 4398046511104) / (-1) Sum = 2 * (4398046511103) / 1 Sum = 8796093022206

So, the total number of your ancestors for the past 42 generations would be 8,796,093,022,206.

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BEST ANSWER :

CIRCLE

solve for area

A = 113.1 cm^2

d diameter = 12 cm.

Answer:

Area of circle = π r^2

Step-by-step explanation:

Diameter = 12
Radius = 12/2
           = 6
Area =  π  x 6^2
        =  π  x 36
        = 113.04

therefore the area of the circle is 113.04

Inverse error is a logical error, when a rule is true and we assuming that the inverse also has to be true.

What is the inverse? Is to take the if-then statement and re write it negatively, for example the inverse of ''if you are an animal, then you need to eat to survive'' is if you are not an animal, then you do not need to eat to survive''

a. The probability of a randomly selected American having type B blood is 12%.

b. The probability of a randomly selected American having type AB or O blood is 48%.

c. The probability of a randomly selected American not having type O blood is 55%.

Human blood is categorized into four types which are A, B, AB, and O. The percentages of Americans who have each of the four types are given below:

O - 43% A - 40% B - 12% AB - 5%

To calculate probabilities for various scenarios, we can use these percentages as follows.

a. The probability of a randomly selected American having type B blood is 12%.

b. The probability of a randomly selected American having type AB or O blood is 48%. The combined percentage of O and AB blood types is 48%. We can therefore say that the probability of an American having O or AB blood is 48%.

c. The probability of a randomly selected American not having type O blood is 55%. The percentage of Americans who don't have type O blood is the sum of percentages of A, B, and AB blood types, which is  Hence, the probability of not having O blood is lower than 57%. Therefore, the probability of a randomly selected American not having type O blood is 57%.

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