In the Two Period Consumer model, the Net Effect from a decrease in the interest rate for a net borrower is:
Group of answer choices
C1↓; C2?; Savings ↑
C1↑; C2?; Savings ↓
C1↑; C2↓; Savings ↓
C1?; C2↓; Savings ?
C1?; C2↑; Savings ?

The volume of the largest right circular cone that can be inscribed in a sphere of radius 18 cm is approximately 11622.85 cubic centimeters.

To find the largest right circular cone that can be inscribed in a sphere of radius 18 cm, we need to find the cone with the largest possible volume that can fit inside the sphere.

Let's assume that the apex of the cone is at the center of the sphere. Since the cone is a right circular cone, the base of the cone will lie on the surface of the sphere, forming a circle with radius equal to the radius of the sphere, which is 18 cm.

Let's call the height of the cone "h" and the radius of the base of the cone "r". Then we can use the Pythagorean theorem to relate the height, radius, and slant height (which is equal to the radius of the sphere):

r^2 + h^2 = (18 cm)^2

The volume of a cone can be expressed as V = (1/3)πr^2h. We want to maximize this expression subject to the constraint above. We can use the constraint to eliminate one of the variables in the volume expression, then differentiate with respect to the remaining variable and set the derivative equal to zero to find the maximum.

From the constraint, we can solve for h^2:

h^2 = (18 cm)^2 - r^2

Substituting into the volume expression, we get:

V = (1/3)πr^2(18 cm - sqrt(r^2 + h^2))

Simplifying this expression, we get:

V = (1/3)πr^2(18 cm - sqrt((18 cm)^2 - r^2))

Differentiating with respect to r, we get:

dV/dr = (1/3)π(36 cm)r - (1/3)πr^3/sqrt((18 cm)^2 - r^2)

Setting this equal to zero and solving for r, we get:

r = (18 cm)/sqrt(2)

Substituting this value of r back into the expression for h, we get:

h = (18 cm)/sqrt(2)

Finally, substituting these values of r and h into the expression for the volume, we get:

V = (1/3)π((18 cm)/sqrt(2))^2((18 cm) - sqrt(((18 cm)/sqrt(2))^2 + ((18 cm)/sqrt(2))^2))

Simplifying this expression, we get:

V ≈ 11622.85 cubic centimeters

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Answer:

Step-by-step explanation:

No, the most popular class for members in the sample is not guaranteed to be the most popular class for all members. This is because the sample may not be representative of the entire population of members at the fitness center.

The sample may be biased, meaning it does not accurately represent the entire population. For example, the sample may include mostly young adults who prefer high-intensity workouts, while the overall population may have a more diverse age range and preferences for different types of classes.

Additionally, the sample size may not be large enough to accurately represent the entire population. A small sample size may not provide enough data to make accurate predictions about the entire population.

Therefore, while a survey of a sample of members can provide useful information about the preferences of those surveyed, it cannot guarantee that the most popular class for the sample will be the most popular class for all members of the fitness center.

Answer:

B

Step-by-step explanation:

28+25+29+18 = 100

red = 25

25/100     =    1/4

The required empirical probability is 1/4 which gets the color of red P(R).

The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

A spinner has 4 equal sectors colored yellow, blue, green, and red. If in 100 spins we get

28 blue (B), 25 red (R), 29 green (G), and 18 yellow (Y) outcomes

To find the empirical probability of getting a red outcome, we need to divide the number of red outcomes by the total number of spins:

P(R) = 25 red outcomes / 100 spins

Apply the division operation, and we get

P(R) = 1/4

Hence, the required empirical probability is 1/4

Therefore, the correct answer is 1/4 or option B.

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Answer:

If a polygon has 3 sides, then the polygon is a triangle.

Step-by-step explanation:

Bold = hypothesis

Italic = conclusion

Statement:

If p, then q.

Converse: If q, then p.

To find the converse, switch the hypothesis and conclusion.

Statement:

If a polygon is a triangle, then it  has 3 sides.

Now we switch the hypothesis and the conclusion to write the converse of the statement.

If it  has 3 sides, then a polygon is a triangle.

We fix a little the wording:

If a polygon has 3 sides, then it is a triangle.

Answer: If a polygon has 3 sides, then the polygon is a triangle.

The converse statement will be;

⇒ If a polygon has 3 sides, then the polygon is a triangle.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The statement is,

''If a polygon is a triangle, then it has 3 sides. ''

Now,

Since, The statement is,

''If a polygon is a triangle, then it has 3 sides. ''

We know that;

The converse of statement for p → q will be q → p.

Thus, The converse statement is find as;

⇒ If a polygon has 3 sides, then the polygon is a triangle.

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Hello, let's note A the matrix, we need to find \(\lambda\) such that A\(\lambda\)=\(\lambda\) I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as

\(\left|\begin{array}{cc}1-\lambda&3\\-3&1-\lambda\end{array}\right|\\\\=(1-\lambda)^2+9\\\\=\lambda^2-2\lambda+10\\\\=0\)

We just need to solve this equation using the discriminant.

\(\Delta=b^2-4ac=2^2-40=-36=(6i)^2\)

And then the eigenvalues are.

\(\lambda_1=\dfrac{2-6i}{2}=\boxed{1-3i}\\\\\lambda_2=\boxed{1+3i}\)

To find the basis, we have to solve the system of equations.

\(A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}\)

\(A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}\)

Thank you

Answer:

y=4x because the y values are bigger than the x values by 4 times

Answer:

Y=4x

When x is 0, y is 0 so there's no y intercept

It goes up 4 every time

Answer:

Step-by-step explanation:

First confirm that x = 1 is one of the zeros.

f(1) = 2(1)^3 - 14(1)^2 + 38(1) - 26

f(1) = 2 - 14 + 38 - 26

f(1) = -12 + 38 = + 26

f(1) = 26 - 26

f(1) = 0

=========================

next perform a long division

x -1  || 2x^3 - 14x^2 + 38x - 26 || 2x^2 - 12x + 26

         2x^3 - 2x^2

         ===========

                   -12x^2 + 28x

                    -12x^2 +12x

                    ==========

                                 26x -26

                                 26x - 26

                                ========

                                     0

Now you can factor 2x^2 - 12x + 26

                                2(x^2 - 6x + 13)

The discriminate of the quadratic is negative. (36 - 4*1*13) = - 16

So you are going to get a complex result.

x = -(-6) +/- sqrt(-16)

    =============

                2

x  = 3 +/- 2i

f(x) = 2*(x - 1)*(x - 3 + 2i)*(x - 3 - 2i)

The zeros are

1

3 +/- 2i

Apply the long division to find that there is only 1 real root

parallel structure is used correctly in :

Eggs, flour, and sugar are needed to bake the pie crust.

In grammar, parallelism, also referred to as parallel structure or parallel construction, is the distribution of identical phrases or clauses with the same grammatical structure within one or more sentences.

The use of parallel structure is more of a stylistic option than a strict rule because it aids in the patterning of sentence elements.

The use of parallelism has an impact on reading and may facilitate text processing.

The rhythm and grammatical balance of a sentence are both guaranteed by using parallel construction.

However, if this structure is not used when creating a sentence with two or more pieces of information, the sentence will have a disruption in rhythm or grammatical imbalance.

Therefore, the correct answer is:

Eggs, flour, and sugar are needed to bake the pie crust.

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Answer:

(1,2)

Step-by-step explanation:

x+4y = 9

2x -4y= -6

Add the equations together

x+4y = 9

2x -4y= -6

-------------------

3x +0y = 3

3x=3

Divide by 3

3x/3 = 3/3

x=1

Now find y

x+4y = 9

1 +4y =9

Subtract 1 from each side

4y = 8

Divide by 4

4y/4 = 8/4

y =2

Since Kyle invested $500 and received $650 after three years, the value of Kyles's interest rate is 43.3%.

Given the following data:

To calculate the value of Kyles's interest rate:

Mathematically, simple interest is given by the formula:

\(S.I = \frac{PRT}{100}\)

Where:

Making R the subject of formula, we have:

\(R = \frac{100S.I}{PT}\)

Substituting the given parameters into the formula, we have;

\(R = \frac{100 \times 650}{500 \times 3}\\\\R = \frac{65000}{1500}\)

Interest rate, R = 43.3%

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hi

-16t²+250 = 75

-16t² = 75 -250

-16t² = -175

  t² = -175 /-16

 t² = 175/16

Here there si two solutions :  t = \(\sqrt{175/16}\)   and  t =  - \(\sqrt{175/16}\)

However, as time cannot rewind,  we will  keep only positive solution

So t = \(\sqrt{175/16}\)

in seconds  it will be  :  3.3 seconds

Answer:

DAC=18(corresponding angles)

EAD= 162 degrees

Step-by-step explanation:

DAC=18(corresponding angles)

EAD=180-18(angles on a straight line)

EAD= 162 degrees

Answer:

Here, we have,

<HBA=18°

<DAC=?

<EAD=?

Now,

i)<DAC=<HBA=18°[being corresponding angle]

ii)<EAD+<DAC=180°[being straight angle]

or, <EAD+18°=180°

or, <EAD=180°-18°

or, <EAD=162°

Thus, <DAC=18° and<EAD=162°.

Answer:

geometric progression

Step-by-step explanation:

RICHIE! ANSWER MY COMMENTS!

Answer:

  x = 16/7 = 2 2/7

Step-by-step explanation:

In the similar triangles, ...

  DE/DA = BC/BA

  4/7 = x/4 . . . . . . . . substitute the numbers given

  x = 16/7 = 2 2/7 . . . . multiply by 4

Answer:

The range is 10

Explanation:

The range of scores is the difference between the lowest and the highest score.

Given that the scores are: 12, 10, 14, 16, 20, and 18

The lowest score is 10, and the highest score is 20

Range = 20 - 10

= 10

To simplify an expression means to write it in the simplest way possible. Ideally, there would be no parentheses and everything has been 'expanded'.

We're given:

\(5 (4x+3)-2\)

Open up the parentheses by multiplying each term by 5:

\(=5*4x+5*3-2\\=20x+15-2\\=20x+13\)

\(20x+13\)

Answer:

34 degrees

Step-by-step explanation:

34 degrees

the angle is 90 degrees

90-56=34

======================================================

Explanation:

Refer to the diagram below. I've added the variable y as the base angles to the isosceles triangle on the left.

Recall that the angles opposite the congruent sides are the base angles. The base angles of any isosceles triangle are the same measure.

Let's solve for y

y+y+56 = 180 .... all angles in a triangle add to 180

2y+56 = 180

2y = 180-56

2y = 124

y = 124/2

y = 62

I've also added the variable z, which is adjacent to one of the y angles.

Since y and z combine to form a straight angle, this means the two angles add to 180

y+z = 180

z = 180-y

z = 180-62

z = 118

Now focus on the isosceles triangle on the right. It has angles x, x, and z = 118.

x+x+z = 180

x+x+118 = 180

2x+118 = 180

2x = 180-118

2x = 62

x = 62/2

x = 31

Answer:

240 ft²

Step-by-step explanation:

Surface area of a rectangular prism is,

2(lw+wh+hl)

= 2(7×6+6×6+6×7)

= 240 ft²

The factored form is (5x+2)(x-4).

What is factorization?

A number, matrix, or polynomial may be broken up or decomposed into factors that, when multiplied together, produce the original number, matrix, etc. This process is known as factorization or factoring.

Here, we have

Given:  5 x squared minus 18 x minus 8

we have to find the factored form.

= 5x² - 18x - 8

= 5x² - 20x + 2x - 8

= 5x(x-4) + 2(x-4)

= (5x+2)(x-4)

Hence, the factored form is (5x+2)(x-4).

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Answer:

1540 cm³

Step-by-step explanation:

V= blh= 14 cm * 22 cm * 5 cm = 1540 cm³

Answer:

1540 cm³

Step-by-step explanation:

This is because the formula for volume is l*w*h so 5*22*14 is 1540

brainliest please

The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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Answer:

116370.197$

Step-by-step explanation:

Jimmie invested $13,000 at 5.23% compounded monthly.

Jimmie's account balance (B) after 42 years:

B = principal x (1 + rate)^time

  = 13000 x (1 + (5.23/100)/12)^(42 x 12)

  = 116370.197$

The value of f(12) for the function f(x) = (x - 4)/16 is 0.5.

Here we have been given the function

f(x) = (x - 4)/16

This function models the expression (x - 4)/16. This implies that we will get a different value of f(x) for every different value of x.

Now here we have been given to find the value of f(12). This implies that we need to find the value of f(x) = (x - 4)/16 when the value of x is 12.

Hence, to find f(12) we need to replace x with 1 in the function. This will give us

(12 - 4)/16

= 8/16

= 0.5

Therefore, f(12) is 0.5

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Answer:

\(y = \frac{-1}{5}x -4\)

Step-by-step explanation:

\(x + 5y = -20\\\\5y = -x - 20\\\\y = \frac{-1}{5}x - 4\)

Answer:

Same Line

Step-by-step explanation:

The solutions are all the same when both of them are asked to be solved. When you graph it, you get the same line, not intersecting, not perpendicular, its the same line.

Therefore the Answer is Same Line

The given two equations 6x - 15y = 15 and y = (2/5)x - 1 represent that both are identical to each other.

The equation is defined as a mathematical assertion with at least two terms that contain variables or integers that are equal.

We have been given two equations as

6x - 15y = 15 and y = 2/5x - 1

⇒ 6x - 15y = 15

Divided by 3 both sides of the equation

⇒ 2x - 5y = 5

⇒ y = 2/5x - 1

Multiply by 5 both sides of the equation

⇒ 2x - 5y = 5

When both of them are required to be solved, the answers are identical. When you graph it, you get the same line—not one that is perpendicular or intersecting—but just one that is.

As a result, the answer is identical.

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The volume of a cuboid toy chest is equal to their product of the length,

width, and height.

Reasons:

The dimensions of the toy chest are;

Toy chest A;

Length = 5 feet

Width = 4 feet

Height = 2 feet

Toy chest B;

Length = 4 feet

Width = 2 feet

Height = 4 feet

Volume of Toy chest A = 5 ft. × 4 ft. × 2 ft. = 40 ft.³

Volume of Toy chest B = 4 ft. × 2 ft. × 4 ft. = 32 ft.³

The volume of the toy chest Mrs. Smith needs = 35 ft.³

The toy chest Mrs. Smith should purchase is Toy chest A, that has a volume of 40 ft.³, which can store items that with a volume of 35 ft.³

The correct option is; Only toy chest A will provide the necessary storage space

Possible question options obtained from a similar question found online are;

Either toy chest have the storage space needed

Neither has the storage space needed

Only toy chest A

Only toy chest B

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