if the hole is 5.7 m from a 1.8- m tall person, how tall will the image of the person on the film be?

The value of the expression x²-2(x-y)-z³ is 24.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given;

Expression x²-2(x-y)-z³

To find the value of the expression:

If x = -3, y=4 and z = -1.

Substituting the values to the expression,

x²-2(x-y)-z³

= (-3)²-2(-3-4)-(-1)³

= 9 + 14 - (-1)

= 9+14+1

= 24

Therefore, 24 is the value of the expression.

To learn more about the expression;

brainly.com/question/24242989  

#SPJ1

if G is a finite group, the index of Z(G) cannot be prime.

Let's consider a finite group G with the center Z(G). We want to prove that the index of Z(G) in G cannot be a prime number.

Assume, for the sake of contradiction, that the index of Z(G) in G is a prime number, say p. By definition, the index [G:Z(G)] is equal to the number of distinct cosets of Z(G) in G, which would be p. Since G is a finite group, we can apply the Lagrange's theorem which states that the order of any subgroup (in this case, Z(G)) divides the order of the group (|G|). So, |Z(G)| divides |G| and |G| = p * |Z(G)|.

Now, let's consider the action of G on the set of left cosets of Z(G) by left multiplication. This action gives rise to a homomorphism from G to the symmetric group on p elements, S_p. By the First Isomorphism Theorem, we know that the image of this homomorphism, denoted as Im(φ), is isomorphic to G/Ker(φ), where Ker(φ) is the kernel of the homomorphism.

Observe that Z(G) is a subgroup of the kernel, as any element from Z(G) will fix each coset. This means |Ker(φ)| ≥ |Z(G)|. Furthermore, Ker(φ) is a normal subgroup of G, so the index [G:Ker(φ)] must divide |G| = p * |Z(G)|.

Since |G/Ker(φ)| = |Im(φ)| divides |S_p| = p!, and |Im(φ)| = [G:Ker(φ)], we must have either |Im(φ)| = p or |Im(φ)| = 1. If |Im(φ)| = p, then [G:Ker(φ)] = p, and Ker(φ) = Z(G). However, this would imply that the action is trivial, which is a contradiction. Thus, |Im(φ)| = 1, meaning that the action is trivial, and G = Z(G), which contradicts our initial assumption that the index of Z(G) in G is prime.

Hence, if G is a finite group, the index of Z(G) cannot be prime.

To learn more about Lagrange's theorem click here

brainly.com/question/31637769

#SPJ11

Angle refers to the point at which a vertical line meets with a horizontal line.

The term angle refers to the point at which a vertical line meets with a horizontal line. Given that angles could be related to each other, we have been asked to obtain the kind of relationship that exists among the angles shown.

The relationships are as follows;

Learn more about angles:https://brainly.com/question/13954458

#SPJ1

True. The multiplicity of a root r of the characteristic equation of matrix A is indeed called the algebraic multiplicity of r as an eigenvalue of A.

The characteristic equation of a square matrix A is obtained by subtracting λI (where λ is an eigenvalue and I is the identity matrix) from A and taking its determinant. The roots of this equation are the eigenvalues of matrix A.

The algebraic multiplicity of an eigenvalue r refers to the number of times r appears as a root of the characteristic equation. In other words, it represents the multiplicity of r as a solution of the equation.

The algebraic multiplicity provides information about the behavior of the eigenvalue r within the matrix A. If the algebraic multiplicity of r is greater than 1, it means that r is a repeated eigenvalue and there exist multiple linearly independent eigenvectors associated with it. On the other hand, if the algebraic multiplicity is 1, r is a simple eigenvalue, indicating that there is only one linearly independent eigenvector corresponding to r.

Learn more about square matrix here:

https://brainly.com/question/27927569

#SPJ11

Answer:

152 feet^2

Step-by-step explanation:

1: Set up the formula of the surface area of a rectangular prism:

2: (Solving)

Therefore, the answer is 152 feet^2.

a) Proportion of the population of Douglas Fir trees have a diameter between 55 and 65 cm = 0.219

b) Probability that exactly 2 of them had diameters between 55 and 65 cm = 0.034

c)  The diameters that are symmetric about the mean that include 80% of all Douglas Fir trees are between 36.8 cm and 61.2 cm.

a.) Proportion of the population of Douglas Fir trees have a diameter between 55 and 65 cm

To find the proportion of the population of Douglas Fir trees that have a diameter between 55 and 65 cm, we need to standardize the values of 55 and 65 using the formula:

z = (x - μ)/σwhere, x = 55 and μ = 49, σ = 10z = (55 - 49) / 10= 0.6

Using the z-score table, the area to the left of the z-score is 0.7257.

z = (x - μ)/σz = (65 - 49) / 10= 1.6

Using the z-score table, the area to the left of the z-score is 0.9452.

Proportion of the population of Douglas Fir trees have a diameter between 55 and 65 cm = P(0.6 ≤ z ≤ 1.6)

P(0.6 ≤ z ≤ 1.6) = 0.9452 - 0.7257= 0.2193

Rounding it to three decimal points, we get, Proportion of the population of Douglas Fir trees have a diameter between 55 and 65 cm = 0.219

b.) Probability that exactly 2 of them had diameters between 55 and 65 cm

For calculating the probability that exactly 2 of the 3 trees had diameters between 55 and 65 cm, we will use the Binomial probability formula, which is:

P(X = k) = nCk . p^k . q^(n-k)where, n = 3, k = 2, p = 0.219 and q = 1 - p = 0.781

Now,P(X = 2) = 3C2 . 0.219^2 . 0.781^(3-2)P(X = 2) = 3 . 0.219^2 . 0.781P(X = 2) = 0.0340

Rounding it to three decimal points, we get, Probability that exactly 2 of them had diameters between 55 and 65 cm = 0.034

c.) Determine the diameters that are symmetric about the mean that include 80% of all Douglas Fir trees.

To determine the diameters that are symmetric about the mean that include 80% of all Douglas Fir trees, we need to find the z-scores associated with the 10th and 90th percentiles of the normal distribution.

Since the distribution is symmetric, the z-score at the 10th percentile is -1.28 and the z-score at the 90th percentile is 1.28.

The corresponding values of x can be found using the formula for z-score.

z = (x - μ)/σ-1.28 = (x - 49)/10

Solving for x, we get:

x = 36.8 (rounded to one decimal point)

1.28 = (x - 49)/10

Solving for x, we get:

x = 61.2 (rounded to one decimal point)

Therefore, the diameters that are symmetric about the mean that include 80% of all Douglas Fir trees are between 36.8 cm and 61.2 cm.

To learn more about probability

https://brainly.com/question/13604758

#SPJ11

The Solution:

Given:

Required:

Simplify the given expression using the difference of two squares.

The difference of two squares formula:

Well this is ez Answer:

A. IS THE CORRECT ANSWER I HAD TO FIND IT OUT FOR  A WHILE

Step-by-step explanation:

So first you see r = 4 that is correct the answer we will get from that is 8 so next you multiply every number that r = for A. B. C. And D. so after that you multiply the correct one which is 2 x 4 so that will be 8 next you add 14 + 8 which you get the answer 22 so A. is the correct answer (SMart variable)

Answer:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

An integer exists a whole number that can be positive, negative, or zero and is not a fraction.

Unlike fractional numbers, integers can only be positive, negative, or zero. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. An integer is a whole number that can be positive, negative, or zero and is not a fraction.

Any number that exists a part of a collection of all the aforementioned number categories is considered an integer. Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

To learn more about integers refer to:

https://brainly.com/question/17695139

#SPJ9

Answer:

(3,6)

Step-by-step explanation:

-2x+3y=12

Let x = 3

-2(3) +3y = 12

-6+3y = 12

Add 6 to each side

-6+6 +3y = 12+6

3y = 18

Divide each side by 3

3y/3 = 18/3

y = 6

The ordered pair (x, y) = (3/5, 1/2) satisfies both equations in the given system, making it the solution.

The solution to the given system of linear equations is the ordered pair (x, y) = (3/5, 1/2). This means that when x is equal to 3/5 and y is equal to 1/2, both equations are satisfied simultaneously.

In the first equation, One-half x minus three-fourths y equals 11/60.

By substituting x = 3/5 and y = 1/2 into this equation, we have (1/2)(3/5) - (3/4)(1/2) = 11/60, which simplifies to 3/10 - 3/8 = 11/60. By further simplifying, we get 24/80 - 30/80 = 11/60, which is true since both sides are equal to 11/60.

Similarly, in the second equation, Two-fifths x plus one-sixth y equals 3/10.

Substituting x = 3/5 and y = 1/2, we have (2/5)(3/5) + (1/6)(1/2) = 3/10, which simplifies to 6/25 + 1/12 = 3/10.

By finding a common denominator and simplifying, we get 144/600 + 50/600 = 180/600, which is also equal to 3/10.

Thus, the ordered pair (x, y) = (3/5, 1/2) satisfies both equations in the given system, making it the solution.

For more such answers on linear equations
https://brainly.com/question/2030026

#SPJ8

Answer:

Domain is all values of X or (-∞,∞)

Range is all the possible values of Y. Since it goes up to 3, and then it goes down, it's all values less than or equal to y, or (-∞,3] or y ≤ 3 (depending on how you need to enter the response.

Step-by-step explanation:

The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.

In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ

where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.

To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.

We have , a = 5 , b = 12 , c= 13

cos α =( 12² + 13² - 5² )/2×12×13= 288/312

=> α = cos⁻¹(0.923 ) = 22.63°

cos β = (5² + 13² - 12² )/2×13×5 = 50/130

=> β = cos⁻¹(5/13) = 67.38°

cos γ = (12² + 5² - 13² )/2×12×5= 0

=> γ = cos⁻¹(0) = 90°

Hence, the required angles are 90°, 22.63°, 67.38°.

To learn more about law of cosines formula, refer:

https://brainly.com/question/4372174

#SPJ4

Answer:

u liar>>>>>>

Step-by-step explanation:

The value of x is 7/3, which can be rounded to two decimal places as approximately 2.33.

To solve the equation 2x + 8 + 4x = 22, we need to combine like terms and isolate the variable x.

Combining like terms, we have:

6x + 8 = 22

Next, we want to isolate the term with x by subtracting 8 from both sides of the equation:

6x + 8 - 8 = 22 - 8

6x = 14

To solve for x, we divide both sides of the equation by 6:

(6x) / 6 = 14 / 6

x = 14/6

Simplifying the fraction 14/6, we get:

x = 7/3

Therefore, the value of x is 7/3, which can be rounded to two decimal places as approximately 2.33.

for such more question on decimal places

https://brainly.com/question/24015908

#SPJ8

Answer:

The 2nd equation is false.

Step-by-step explanation:

You don't even have to solve. DE is not 58, it's 40.

The 2nd equation is false.

Answer: Y= -9 + 3x/2

Step-by-step explanation: Down below Have a brilliant day-Lily ^_^

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

The expression \(\lim_{x\rightarrow 3} \frac{2x^2-x+15}{x^3-5x-12}\) is used to denote the function's behavior as \(x\) approaches 3.

From the graph we see that the closer we get to \(x=3\), the closer we get to \(0.5\). Therefore, as \(x\) approaches 3, \(f(x)\) approaches 0.5, hence \(\implies \boxed{\frac{1}{2}}\)

\(\sf 2. \: \frac{7}{8} - \frac{4}{16}\)

\(\sf = \frac{7}{8} + \frac{- 4}{16}

\(\sf = \frac{7}{8} + \frac{- 1}{4}\)

\(\sf = \frac{7}{8} + \frac{- 2}{8} \)

\(\sf = \frac{7 + - 2}{8} \)

\(\sf = \frac{5}{8 }\)

\(\sf3.\)

\( \sf= \frac {1}{2} \)

\(\sf4.\)

\(\sf \frac{8}{15}\)

\(\sf5.\)

\(\sf= \frac{11}{8}\)

Answer:

111

Step-by-step explanation:

72+39+1=111

Answer: -3, 9√, pi, 49√

Step-by-step explanation:

Having the check beside a number, ex: 49√, shows that something squared, in other words multiplied by itself, equals this. In this example it would be 7. For, 7*7=49. For 9√ it would be 3. Pi is 3.14. Listing these out we have:

-3, 3.14, 3, 7. Let's order this...

-3 is the least, then 3, then 3.14 (slightly bigger than 3), lastly, 7.

A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

To know more about System of equation, visit here:

https://brainly.com/question/21620502

#SPJ4

Answer: Perimeter = 40

               Area = 204

Step-by-step explanation:

Perimeter is the sum of all the sides:

    11 + 12 + 17 = 40

The area of a triangle is 1/2 base x height

   1/2( 17 x 24)

   1/2( 408) = 204

Answer:

A. Quadratic, degree 2

Step-by-step explanation:

The degree is found by simply finding the term with the power of, that is the highest. Which would be 2x^2. It is raised to the 2nd power, so the degree is 2.

The probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

The symbol "∩" represents the intersection of two events.

For example, "a ∩ d" means the event where both "a" and "d" occur together.

The symbol "~" means "not" or "complement." So, "~ (a ∩ d)" means the event where "a ∩ d" does NOT occur, or in other words, where "a" OR "d" does not occur.

Now, onto the question.

We are given that p(a ∩ d) = 2/5, which means that the probability of both events "a" and "d" occurring together is 2/5.

We want to find the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur.

To find this probability, we need to use some basic probability rules.

One of these rules is that the probability of an event happening (let's call it "E") is equal to 1 minus the probability of the complement of that event not happening (~E).

In other words, p(E) = 1 - p(~E).

So, if we apply this rule to the event "~ (a ∩ d)", we get:
p(~ (a ∩ d)) = 1 - p(a ∩ d)

Now we can substitute in the value we were given for p(a ∩ d):
p(~ (a ∩ d)) = 1 - 2/5

Simplifying this gives:
p(~ (a ∩ d)) = 3/5

Therefore, the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

Know more about probability here:

https://brainly.com/question/251701

#SPJ11

Answer:

Step-by-step explanation:

Ok: So A is similar to B put different ratios

1. Look at sides

A has one side 12cm while B has the same side 9 cm

9:12 is the ratio or 9/12= 3/4

Sides B is 3/4 of A

2. Caculate

W= 3/4*7=

w=21/4cm

or

w= 5 1/4 cm