An architect builds a scale model of a building, where 1 cm = 0.5 m. If the scale model is 15 cm tall, how tall will the actual building be, in meters, written as a decimal?

Answer:

200 in²

Step-by-step explanation:

To find the area, you need to split it into two squares. The upper square would be 10 inches times 10 inches which would give you 100 inches squared. Since both are the same size, you can add both square areas together to give you 200 inches squared.

Answer:

the is 1.25

Step-by-step explanation:

multiply 4 time 1.25 to check

Answer:

x=13

Step-by-step explanation:

180 is the total degree of any triangle. Divide by 3 and you get 60 degree angles. Subtract 8 and you gey 4x=52. Divide then to get 13

a) The utility depends on both health (H) and consumption of other goods (X).

b) The coefficient is negative, indicating a negative relationship between two variables.

c) Health (H) is greater than zero, suggesting a positive value for health.

d) Health (H) is a function of a variable denoted as 'm'.

e) The variable 'm' is greater than zero and the coefficient is negative.

f) The product of two variables, 'm' and 'm', is negative.

a) The expression in (a) is reasonable as it acknowledges that utility is influenced by both health and consumption of other goods. It recognizes that happiness or satisfaction is derived not only from health but also from other aspects of life.

b) The expression in (b) suggests a negative coefficient and a negative relationship between the variables. This could imply that an increase in one variable leads to a decrease in the other. The reasonableness of this relationship would depend on the specific variables involved and the context of the theoretical framework.

c) The expression in (c) states that health (H) is greater than zero, which is reasonable as health is generally considered a positive attribute that contributes to well-being.

d) The expression in (d) indicates that health (H) is a function of a variable denoted as 'm'. The specific nature of the function or the relationship between 'm' and health is not provided, making it difficult to assess its reasonableness without further information.

e) The expression in (e) states that the variable 'm' is greater than zero and the coefficient is negative. This implies that an increase in 'm' leads to a decrease in some other variable. The reasonableness of this relationship depends on the specific variables involved and the theoretical context.

f) The expression in (f) suggests that the product of two variables, 'm' and 'm', is negative. This implies that either 'm' or 'm' (or both) are negative. The reasonableness of this expression would depend on the meaning and interpretation of the variables involved in the theoretical framework.

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The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the linear function y = 3x:

When x = -2; y = 3(-2) = -6

When x = -1; y = 3(-1) = -3

When x = 0; y = 3(0) = 0

When x = 1; y = 3(1) = 3

When x = 2; y = 3(2) = 6

The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).

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Answer: ( -6/ 6/ 9

Step-by-step explanation:

if v1= [5 −4] and v2 = [4 −5] are eigenvectors of a matrix corresponding to the eigenvalues λ1=5 and λ2=6, respectively, then a(-3 - v1) = [-64 50].

To find the value of a(v1 + v2), we can use the fact that eigenvectors are vectors that are scaled by a matrix without changing direction. Therefore, we have:

a(v1 + v2) = a(v1) + a(v2) = λ1v1 + λ2v2

Substituting in the given values, we get:

a(v1 + v2) = 5[5 -4] + 6[4 -5] = [35 -26]

To find the value of a(-3 - v1), we can use the same idea:

a(-3 - v1) = -3a - av1 = -3(-3[5 -4]) - a[5 -4]

Substituting in the given values, we get:

a(-3 - v1) = [-39 30] - a[5 -4]

To find the value of 'a', we can use the fact that v1 is an eigenvector of a corresponding to the eigenvalue λ1=5. Therefore, we have:

av1 = λ1v1

Substituting in the given values, we get:

a[5 -4] = 5[5 -4] = [25 -20]

Substituting this value back into the expression for a(-3 - v1), we get:

a(-3 - v1) = [-39 30] - [25 -20] = [-64 50]

Therefore, a(-3 - v1) = [-64 50].

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The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard equation of a circle is:

(x - h)² + (y - k)² = r²

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

The diameter of the circle DE is at D(-3, 3) and E(13, 11). Hence the coordinate of point center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7)

\(Diameter = \sqrt{(3-11)^2+(-3-13)^2} = 8\sqrt{5}\)

Radius = diameter / 2 = 8√5 ÷ 2 = 4√5

The equation of the circle is:

(x - 5)² + (y - 7)² = (4√5)²

(x - 5)² + (y - 7)² = 80

The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80

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Answer:



To find the indirect utility function, we need to solve the utility maximization problem subject to the budget constraint and express the maximum utility achieved as a function of the prices and income.

Given the utility function U = max(X, Y) and the budget constraint P₁X + P₂Y = M, we can solve for X and Y in terms of prices (P₁, P₂) and income (M).

First, let's consider the different cases:

If P₁ ≤ P₂:

In this case, the individual would choose to consume only good X. Therefore, X = M / P₁ and Y = 0.

If P₂ < P₁:

In this case, the individual would choose to consume only good Y. Therefore, X = 0 and Y = M / P₂.

Now, we can express the indirect utility function in terms of the prices (P₁, P₂) and income (M) for each case:

a) If P₁ ≤ P₂:

In this case, the individual maximizes utility by consuming only good X.

Therefore, the indirect utility function is V(P₁, P₂, M) = U(X, Y) = U(M / P₁, 0) = M / P₁.

b) If P₂ < P₁:

In this case, the individual maximizes utility by consuming only good Y.

Therefore, the indirect utility function is V(P₁, P₂, M) = U(X, Y) = U(0, M / P₂) = M / P₂.

c) and d) do not match any of the cases above.

Therefore, among the given options, the correct answer is:

a) M / max(P₁, P₂).

Answer:

64"

Step-by-step explanation:

Pythagoras theorem

√(80²-48²)

√4096

=64

Answer:

Width = 64"

Step-by-step explanation:

It forms a right angled triangle. We can use Pythagorean theorem to find the base of the triangle

Base² + altitude² = Hypotenuse²

base² + 48² = 80²

base² +  2304 = 6400

           base² = 6400 - 2304

            base² = 4096

           base = √4096

base =  64

Width = 64"

Answer:

5.2=x

5=y

4x+y=25.8

Step-by-step explanation:

180-94=86

86=15x+8

78=15x

5.2=x

180-94=86

86=17y+1

85=17y

5=y

4x+y=

4(5.2)+5=25.8

The area of the circle with radius 'r' is πr² units² because the formula for the area of a circle = πr²

The circle is defined as a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point which is the centre.

The angle at the center of a circle sums up to 360°.

To calculate the area of a circle, the formula that should be used is given as follows;

Area of a circle = πr²

radius of the circle = r units

area = π×r ×r

= πr² units ²

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Step-by-step explanation:

a.) you have to substitute f(5) into the formula

f(x) = 3x^2 + 5

you do this by inserting five into your x :

f(x) = 3x^2 + 5

f(5) = 3(5^2) + 5

= 3(25) + 5

= 75 + 5

f(5) = 80

b.) to solve for g(5) ,, you do the exact same but with the formulae g(x) = 11x - 10

g(x) = 11x - 10

g(5) = 11(5) - 10

= 55 - 10

g(5) = 45

. we can see that f(5) is the greater quantity ,, furthermore it is greater by 35 . =

f(5) = 80 g(5) = 45

80 - 45

= 35

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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Answer:

486 feet²

Step-by-step explanation:

assuming the room is shaped like a cube:

729/3 = 243

243 x 2 =486

Answer:

Step-by-step explanation:

3/5= 60%

3/4= 75%

21/25= 84%

13/20= 65%

The larger of the two consecutive even perfect squares is $15,536$.

Square is a four-sided shape that has four equal sides and four right angles. It is the most basic of all quadrilaterals and is a two-dimensional shape. A square has a line of symmetry that passes through the center and divides it into two equal halves. All four sides of a square are equal in length and all four angles are equal to 90 degrees.

To find this, we need to use the difference between the two squares and solve for the larger number. We know that the difference between the two squares is $268$, so we can write the following equation:

$15,536 - 268 = 15,268$

This equation tells us that the larger of the two squares is $15,536$.

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The larger of the two consecutive even perfect squares is 15,536.

Square is a four-sided shape that has four equal sides and four right angles. It is the most basic of all quadrilaterals and is a two-dimensional shape. A square has a line of symmetry that passes through the center and divides it into two equal halves. All four sides of a square are equal in length and all four angles are equal to 90 degrees.

To find this, we need to use the difference between the two squares and solve for the larger number. We know that the difference between the two squares is 268, so we can write the following equation:

So, 15,536 - 268 = 15,268

This equation tells us that the larger of the two squares is 15,536.

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Answer:

Step-by-step explanation:

80        40

___________

 100        50

is it like this pls don't mind how I snap it

We know that in statistics, the Type II error happens when the null hypothesis is false but fails to get rejected.

Type II error in this scenario will be when the researcher claim 65% of college students will graduate with debt is false but fails to be rejected.

A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null hypothesis that is actually false. A type II error produces a false negative, also known as an error of omission.

For example, a test for a disease may report a negative result when the patient is infected. This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect.

A Type II error can be contrasted with a type I error is the rejection of a true null hypothesis, whereas a type II error describes the error that occurs when one fails to reject a null hypothesis that is actually false. The error rejects the alternative hypothesis, even though it does not occur due to chance.

Given : The null hypothesis, , is: researchers claim that 65% of college students will graduate with debt.

Then , Type II error in this scenario will be when the researcher claim 65% of college students will graduate with debt is false but fails to be rejected.

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The height of the pyramid is equal to the slant height (90.3) divided by the square root of 2. Therefore, the height of the pyramid is 64.2.

To calculate the height of the pyramid, we must first use the Pythagorean theorem to find the length of the side of the pyramid. The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the slant height (90.3) and the other two sides are the base of the pyramid (21.8). Therefore, we can solve for the length of the side of the pyramid (x) by solving the equation \(90.3^2 = 21.8^2 + x^2\). After solving, we find that x = 64.2. Since the height of a pyramid is equal to the length of its side, the height of the pyramid is 64.2.

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The Mean Value Theorem for Integrals states that for a continuous function f on the interval [a, b], there exist numbers c1 and cz in [a, b] such that the average value of f over [a, b] is equal to f(c1) and f(cz) respectively.

The Mean Value Theorem for Integrals is an important result in calculus that relates the average value of a function over an interval to its value at a particular point within that interval.

The theorem states that if f is a continuous function on the interval [a, b], then there exist numbers c1 and cz in [a, b] such that the average value of f over [a, b] is equal to f(c1) and f(cz) respectively.

The first part of the theorem states that there is a number c1 in [a, b] such that the integral of f over [a, b] is equal to f(c1) multiplied by the length of the interval (b - a).

Similarly, the second part of the theorem states that there is a number cz in [a, b] such that the signed integral of f over [a, b] is equal to f(cz) multiplied by the length of the interval (b - a).

The third part of the theorem, known as the Second Mean Value Theorem for Integrals, states that if the signed integral of f exists over [a, b], then there is a number c in [a, b] such that the integral of f over [a, b] is equal to f(c) multiplied by the length of the interval (b - a).

The Mean Value Theorem for Integrals provides a connection between the values of a function and its integral, highlighting the existence of certain points within the interval where specific relationships hold.

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The volume of the cube expressed as a fraction will be 27x³y³ / 64.

Given that:

Volume, V = (0.75xy)³

It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of the cube expressed as a fraction is calculated as,

V = (0.75xy)³

V = (3xy/4)³

V = 27x³y³ / 64

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The probability of the sets are solved and

a) n(P U Q) = 85%

b) n(P ∩ Q) = 20%

c) n(only P) = 35%

d) n(only Q) = 30%

Given data ,

P and are the subsets of universal set U

And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%

Now , we'll use the formula for the union and intersection of sets:

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(only P) = n(P) - n(P ∩ Q)

n(only Q) = n(Q) - n(P ∩ Q)

We're given that:

n(P) = 55%

n(Q) = 50%

n(P U Q)' = 15%

To find n(P U Q), we'll use the complement rule:

n(P U Q) = 100% - n(P U Q)'

n(P U Q) = 100% - 15%

n(P U Q) = 85%

Now we can substitute the values into the formulas above:

(i)

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(P ∩ Q) = 55% + 50% - 85%

n(P ∩ Q) = 20%

(ii)

n(P ∩ Q) = 20%

(iii) n(only P) = n(P) - n(P ∩ Q)

n(only P) = 55% - 20%

n(only P) = 35%

(iv)

n(only Q) = n(Q) - n(P ∩ Q)

n(only Q) = 50% - 20%

n(only Q) = 30%

Hence , the probability is solved

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Answer: 20

Step-by-step explanation:

17 is closest to 20 :)

(sorry if this is wrong)

The value of y= 7/4 = 1.7

Steps for solving linear equations:

y=-3y+7

Add 3y to both sides

y+3y=7

Combine y and 3y to get 4y

4y=7

Divide both sides by 4

y=7/4

Thus, the answer is y=7/4 or 1.7

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The solution to the equation "16 more than s is at most -80" in interval notation is (-∞, -96].

To solve the equation "16 more than s is at most -80," we need to translate the given statement into an algebraic expression and then solve for s.

Let's break down the given statement:

"16 more than s" can be translated as s + 16.

"is at most -80" means the expression s + 16 is less than or equal to -80.

Combining these translations, we have:

s + 16 ≤ -80

To solve for s, we subtract 16 from both sides of the inequality:

s + 16 - 16 ≤ -80 - 16

s ≤ -96

The solution for s is s ≤ -96. However, since the inequality includes "at most," we use a closed interval notation to indicate that s can be equal to -96 as well. Therefore, the solution in interval notation is (-∞, -96].

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Answer:Answer:

D'F' = 28

Step-by-step explanation:

For the vertex D(1, 1)

D'(1 × 7, 1 × 7) = D'(7, 7)

For the vertex E(1, 5)

E'(1 × 7, 5 × 7) = E'(7, 35)

For the vertex F(5, 1)

F'(5 × 7, 1 × 7) = C'(35, 7)

Now to find the D'F':

we do:

y2 - y1 =

and

x2 - x1 =

Here are what the numbers mean

x1 = 7

y1 = 7

x2 = 35

y2 = 7

For the points above (7,7) and (35,7), in which (7,7) is Point 1 and (35,7) is Point 2:

Find the distance along the y-axis.

y2 - y1 = 7 - 7

7 - 7 = 0

Find the distance along the x-axis.

x2 - x1 = 35 - 7

35 - 7 = 28

Now we do: y² and x²

y² = 0² = 0

x² = 28² = 784

Next we add the y and x

0 + 784 = 784

And lastly, we do √x + y

Which is the same as: √0 + 784

√0 + 784 = 28

So the answer is 28

Step-by-step explanation: