A city has a population of 435,000. The population y increases by 5% each year.

a. Write an exponential function that represents the population after t years.

b. What will the population be after 11 years? Round your answer to the nearest thousand.

show work pleaseee

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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Given:

The volume of a cube = \((2+3p)^3\ \text{cm}^3\)

To find:

The total surface area of the cube in terms of p.

Solution:

Volume of a cube is:

\(V=a^3\)            ...(i)

Where, a is the side length.

It is given that,

\(V=(2+3p)^3\ \text{cm}^3\)         ...(ii)

On comparing (i) and (ii), we get

\(a=2+3p\text{ cm}\)

Now, the total surface area of a cube is:

\(A=6a^2\)

Where, a is the side length.

Putting \(a=2+3p\), we get

\(A=6(2+3p)^2\)

Therefore, the total surface area of the cube in terms of p is \(6(2+3p)^2\ \text{cm}^2\).

Answer:

24

Step-by-step explanation:

12 / 1/2 = 12 * 2/1 = 24/1 = 24

Answer:

this is the answer to the question, its 5.6 for sure

Answer:

Hello!

A' is (-4, 0)

B' is (-1, 4)

C' is (-1, -3)

Step-by-step explanation:

Here are the points and a graph showing the dilation in purple

Answer:

above sea level

Step-by-step explanation:

Answer:

( c ) x = 2.5

Step-by-step explanation:

\(3(17x - 6.5) = 108\)

divide both side of the equation by 3...

\(17x - 6.5 = 36\)

\(17x = 36 + 6.5\)

\(17x = 42.5\)

\(x = 2.5\)

hence the value of x is 2.5...

Answer:

C = 14

Step-by-step explanation:

\(C = x+y\)

\(2x + y \geq 20\)

\(2x + 3y\geq 36\)

\(x\geq 0\)

\(y\geq 0\)

If we graph the inequalities, the solution set of the constraints is the shaded area (see attached diagram).

The vertices of the shaded area are (0, 20), (6, 8) and (18, 0)

To determine the minimum value of C, substitute the values of x and y of each vertex into C = x + y:

at (0, 20):  C = 0 + 20 = 20

at (6, 8):  C = 6 + 8 = 14

at (18, 0):  C = 18 + 0 = 18

Therefore, the minimum value is at (6, 8) ⇒ C = 14

Answer:

Hi im not sure but if I was doing this this is what i would say

Step-by-step explanation:

a) since the pizza is split in 6th then the pizza would be 6/6th

b) 7/4 is equal to 1 2/4 ( not 100% simplified ) but 1 2/4 also equals to 6/6ths because 1 2/4 = 4+2=6 (not the best accurate explanation )

c) no slices are left over if joan ate 7/4th of the pizza XD

Answer:

76,105

Step-by-step explanation:

To show the given results, let's start with (a):
\((a) yˉ​TAxˉ=λyˉ​Txˉ\). Since A is a symmetric matrix, we know that A = A^T. Therefore, we have:
\(yˉ​TAxˉ = yˉ​(A^T)xˉ\) .

Now, we can use the property of eigenvectors and eigenvalues, which states that Axˉ = λxˉ:
\(yˉ​(A^T)xˉ = yˉ​(λxˉ)\). Next, we can distribute yˉ​ to both terms:
yˉ​(λxˉ) = λyˉ​xˉ  

Thus, we have shown that yˉ​TAxˉ=λyˉ​Txˉ. Moving on to (b):
(b)\(xˉTAyˉ​=μxˉTyˉ\)​  Similarly, we start with:
xˉTAyˉ = xˉ(A^T)yˉ

Again, using the property Axˉ = μxˉ:
\(xˉ(A^T)yˉ = xˉ(μyˉ)\). Now, we distribute xˉ to both terms:
xˉ(μyˉ) = μxˉyˉ.

Thus, we have shown that xˉTAyˉ​=μxˉTyˉ​. Lastly, let's prove (c):
(c)\(yˉ​TAxˉ=xˉTAy\)ˉ​ By comparing (a) and (b), we can see that:
yˉ​TAxˉ = λyˉ​Txˉ = xˉTAyˉ​.

Now, using the transitive property of equality, we have:
yˉ​TAxˉ = xˉTAyˉ

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Using the results derived in parts (a), (b), and (c), we have shown that if λ=μ, then yˉ​Txˉ=0, i.e. yˉ​T and xˉ are orthogonal. This conclusion is based on the fact that the equation yˉ​(xˉT-μxˉ)=0 holds when λ=μ.

(a) To prove that yˉ​TAxˉ=λyˉ​Txˉ, we start by expressing the eigenvector equation Axˉ=λxˉ in matrix form as follows:

Axˉ-λxˉ=0

Now, let's multiply both sides of this equation by yˉT from the left:

yˉTAxˉ-yˉTλxˉ=0

Using the property of matrix multiplication, we can rearrange the terms as follows:

yˉT(Axˉ)-yˉT(λxˉ)=0

Since matrix A is symmetric, we can interchange the order of multiplication in the first term:

yˉT(Axˉ)-(yˉTλ)xˉ=0

Now, we know that Axˉ=λxˉ, so we can substitute this into the equation:

yˉT(λxˉ)-(yˉTλ)xˉ=0

Simplifying the equation, we get:

λyˉTxˉ-λyˉTxˉ=0

This simplifies to:

0=0

Therefore, we have shown that yˉ​TAxˉ=λyˉ​Txˉ. In this step-by-step explanation, we used the eigenvector equation and properties of matrix multiplication to prove that yˉ​TAxˉ=λyˉ​Txˉ. We manipulated the equation by multiplying it from the left by yˉT and rearranged the terms using the properties of symmetric matrices.

(b) To prove that xˉTAyˉ​=μxˉTyˉ​, we start with the eigenvector equation Axˉ=λxˉ and multiply both sides by AyˉT from the right:

AxˉAyˉT=λxˉAyˉT

Since matrix A is symmetric, we can interchange the order of multiplication:

A(xˉAyˉT)=λxˉAyˉT

Now, we know that AyˉT is a column vector, so we can write it as yˉ. Taking the transpose of both sides, we get:

(A(xˉAyˉT))T=(λxˉAyˉT)T

Using the property of transpose, we have:

((AyˉT)T(xˉT))=(λxˉAyˉT)T

Simplifying the equation, we get:

(yˉAxˉT)=(λAyˉxˉT)

Now, we know that Axˉ=λxˉ, so we can substitute this into the equation:

(yˉλxˉT)=(λAyˉxˉT)

Cancelling out the common factor of λ, we get:

yˉxˉT=AyˉxˉT

Finally, we can take the transpose of both sides to get the desired result:

xˉTAyˉ​=μxˉTyˉ​

In this step-by-step explanation, we used the eigenvector equation and properties of matrix multiplication and transpose to prove that xˉTAyˉ​=μxˉTyˉ​. We manipulated the equation by multiplying it from the right by AyˉT and rearranged the terms using the properties of symmetric matrices.

(c) To prove that yˉ​TAxˉ=xˉTAyˉ​, we start with the equation we proved in part (a):

yˉ​TAxˉ=λyˉ​Txˉ

Now, let's transpose both sides of the equation:

(yˉ​TAxˉ)T=(λyˉ​Txˉ)T

Using the property of transpose, we have:

(xˉATyˉ​)=(λxˉTyˉ​)

Since matrix A is symmetric, we can interchange the order of multiplication in the first term:

(xˉTAyˉ​)=(λxˉTyˉ​)

Therefore, we have shown that yˉ​TAxˉ=xˉTAyˉ​.

In this step-by-step explanation, we used the equation we proved in part (a) and the property of transpose to prove that yˉ​TAxˉ=xˉTAyˉ​. We manipulated the equation by transposing both sides and rearranged the terms using the properties of symmetric matrices.

Using the above results, we can now prove that if λ=μ, then yˉ​Txˉ=0, i.e. yˉ​T and xˉ are orthogonal.

Suppose λ=μ. From part (a), we have:

yˉ​TAxˉ=λyˉ​Txˉ

From part (b), we have:

xˉTAyˉ​=μxˉTyˉ​

Since λ=μ, we can equate the two equations:

λyˉ​Txˉ=μxˉTyˉ​

Now, let's take the transpose of both sides:

(λyˉ​Txˉ)T=(μxˉTyˉ​)T

Using the property of transpose, we have:

xˉTyˉ​=μyˉ​Txˉ

Since λ=μ, we can rearrange the equation as:

xˉTyˉ​-μyˉ​Txˉ=0

Now, we can factor out yˉ​ from the left side and xˉ from the right side:

yˉ​(xˉT-μxˉ)=0

Since λ=μ, we have (xˉT-μxˉ)=0. Therefore, for yˉ​(xˉT-μxˉ)=0 to be true, yˉ​ must be orthogonal to (xˉT-μxˉ).

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Answer:

x = 30

Step-by-step explanation:

Put in proportions \(\frac{x}{45}\) = \(\frac{18}{27}\)

Cross multiply and get 27x = 45 x 18

OR...

27x = 810.

THEN...

divide by 27 on both sides to get 30

x = 30

Given info:-

A shop keeper offers a discount of 20% on all the articles at his shop and all makes a profit of 12%.

What is the CP of an article whose MP is Rs. 280 ?

Explanation:-

Given that

The Marked Price of an article (M) = Rs. 280

Discount on it = 20%

Discount (D) = MD/100

⇛ Discount = (280×20)/100

⇛ Discount = 28×2

⇛ Discount =56

Selling Price = Marked Price - Discount

⇛ Selling Price = 280-56

⇛ Selling Price = Rs. 224

Selling Price of the article = 224

Profit on it = 12%

We know that

Cost Price = (100×SP)/(100+g)

⇛ CP = (100×224)/(100+12)

⇛ CP = 22400/112

⇛ CP = 200

Therefore, The CP = Rs. 200

The Cost Price of the article = Rs. 200.

Formula:-

M = Marked Price

SP = Selling Price

g = gain or profit

Answer:

A= 4pi r

C = 2pi r

Step-by-step explanation:

answer:

103

step-by-step explanation:

**the steps are in the picture**

good luck :)

i hope this helps

brainliest would be highly appreciated

have a nice day!

The model suggests that increases in productivity lead to increases in income and consumption levels, while increases in the interest rate lead to decreases in consumption levels. The main drivers of these predictions are productivity growth and capital accumulation, which determine the consumer's lifetime income.

B.1: The value of lifetime wealth/income in terms of period 1 dollars can be calculated using the formula as follows: Lifetime income in period 1 dollars = 1 + (1 - R)/(1 + R) * 2= 1 + 0.95 * 2= $2.9 million

B.2: We know that consumption for each period is given by the following formula:

C1 = w1 - S And, C2 = w2 - C1

Where S is the amount saved.

Based on this,C1 = $72,500 and C2 = $47,500B.

3: The amount saved can be calculated using the following formula:

S = (1 + R) C1 - C1= $ 31,875

Since S is greater than zero, it shows that the consumer saved money.B.4: We will use the same formula to calculate consumption.C1 = w1 - S And, C2 = w2 - C1

If income in period 2 is $15,000, then we can calculate the consumption for period 2 as follows:

C2 = w2 - C1

= $15,000 - ($72,500)

= -$57,500

This means the consumer will have to borrow $57,500 to meet his consumption needs. C1 will remain the same.B.5: The Neoclassical Growth Model predicts that consumption depends on lifetime income, interest rate, and the consumer's rate of time preference. The model assumes that consumers prefer to consume in the present rather than the future and that income is determined by productivity and capital accumulation.

The model suggests that increases in productivity lead to increases in income and consumption levels, while increases in the interest rate lead to decreases in consumption levels. The main drivers of these predictions are productivity growth and capital accumulation, which determine the consumer's lifetime income.

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9/4 or 2 1/4

Step-by-step explanation:

Answer:

I'm pretty sure 8

Step-by-step explanation:

Equation of a line:

9x - 7y = -63

To find the x-intercept we have to substitute y = 0 into the equation, as follows:

9x - 7*0 = -63

9x = -63

Dividing by 9 at both sides of the equation:

9x/9 = -63/9

x = -7

To find the y-intercept we have to substitute x = 0 into the equation, as follows:

9*0 - 7y = -63

-7y = -63

Dividing by -7 at both sides of the equation:

-7y/(-7) = -63/(-7)

y = 9

Answer

x-intercept: −7; y-intercept: 9

The equivalent expression after combining the like terms is 8 + 9t

from the question, we have the following parameters that can be used in our computation:

5 + 9t + 3

Collect the like terms

So, we have

5 + 3 + 9t

Evaluate teh like terms

8 + 9t

Hence, the equivalent expression is 8 + 9t

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Given f(x) = 3x - 6 - 3x - 2 Find all the values of x where the tangent line to the graph of f(x) is perpendicular to the line y = -6x + 16. We have to find the derivative of the function f(x) first. f(x) = 3x - 6 - 3x - 2f(x) = -5x - 8f'(x) = -5Now, the slope of the tangent line to the graph of f(x) is -5.

Since the line y = -6x + 16 is perpendicular to the tangent line, its slope will be the negative reciprocal of -5.Now, the slope of the line y = -6x + 16 is -6. Therefore, -6 = -1/m, where m is the slope of the tangent line. m = 1/6 Now, the tangent line has a slope of 1/6 and passes through a point (x, f(x)). The equation of the tangent line is given by:y - (3x - 6 - 3x - 2) = (1/6)(x - x)y - 5x + 8 = (1/6)x - (1/6)x + C.

where C is the y-intercept. To find C, we use the point-slope form of the equation and substitute x = 1:y - 5(1) + 8 = (1/6)(1) + C= -17/6 + C= y - (3x - 6 - 3x - 2) = (1/6)(x - 1)y - 5x + 8 = (1/6)x - (1/6)(1) - 17/6y - 5x = (1/6)x - 23/6y = (1/6)x - 23/6 + 5xy = (1/6)x + (23 - 5x)/6 The slope of the tangent line is 1/6, and it passes through a point (x, f(x)).Therefore, the equation of the tangent line is:y = (1/6)x + (23 - 5x)/6To find all the values of x where the tangent line is perpendicular to the line y = -6x + 16, we need to solve the following equation:-6 = 1/6x + (23 - 5x)/6-36 = x + 23 - 5x-36 = -4x + 23-4x = -13x = 13/4Therefore, the only value of x where the tangent line is perpendicular to the line y = -6x + 16 is x = 13/4.Answer: x = 13/4

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Answer:

the answer is the option B 35

Step-by-step explanation:

first, add 4 and 3. you will get 7. Next, multiply 7 by 5 and you will get the answer :35

\(5(3 + 4) \\ 5(7) \\ 35\)

Answer:

30.2x+12.9y

Step-by-step explanation:

y is the dependent variable and x is the independent variable.

LOL Khan Academy

A) The value of p(x=5) is 0.2017

B) The value of p(x=8) is 0.1167

C) The expected value (mean) of x7.89.

A) We are required to find P(x = 5).P(x = 5) is the probability that 5 out of the 10 students selected chose the stated option.

Using the binomial distribution formula, we have

P(x = 5) = nCx px q(n - x)

where n = 10, x = 5, p = 45/57 = 0.789, and q = 1 - p = 1 - 0.789 = 0.211

Thus, P(x = 5) = (10C5) (0.789)5 (0.211)5= 0.2017 (rounded to four decimal places)

B) We are required to find P(x = 8).P(x = 8) is the probability that 8 out of the 10 students selected chose the stated option.

Using the binomial distribution formula, we have

P(x = 8) = nCx px q(n - x)

where n = 10, x = 8, p = 45/57 = 0.789, and q = 1 - p = 1 - 0.789 = 0.211

Thus, P(x = 8) = (10C8) (0.789)8 (0.211)2= 0.1167 (rounded to four decimal places)

C) We are required to find the expected value (mean) of x.

Using the binomial distribution formula, we have

E(x) = np

where n = 10, and p = 45/57 = 0.789

Thus, E(x) = 10 × 0.789= 7.89 (rounded to two decimal places)

Therefore, the expected value (mean) of x is 7.89.

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The value of x is 17

The congruent arcs are (b) PQ and SR

The radius is 12 units

The value of PQ is 4

The length YZ is 19 units

In this question, we make use of the property of congruent sides

So, we have

3x - 24 = x + 10

When evaluated, we have

2x = 34

Divide by 2

x = 17

By the definition of congruent arcs, congruent arcs are arcs that have equal measures

In this figure, the congruent arcs are PQ and SR i.e. (b) PQ and SR

The radius of the circle is calculated as

r² = (25 + r)² - 35²

When expanded, we have

r² = 625 + 50r + r² - 1225

So, we have

50r = 600

Divide both sides by 50

r = 12

In this question, we make use of the property of congruent sides

So, we have

PQ = SR

Where

SR = 4

When evaluated, we have

PQ = 4

The length of YZ in the circle is calculated as

YZ² = (9 + 8)² + 8²

So, we have

YZ² = 17² + 8²

When expanded, we have

YZ² = 289 + 64

So, we have

YZ² = 353

Take the square root of both sides

YZ = 19

Hence, the length YZ is 19 units

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Answer: It should be you lost 2.8 million dollars

Step-by-step explanation:

The value of the boolean variable x is 0

The boolean equation is given as:

x . 1 = 0

The above means that:

x and 1 = 0

The law of the and operator is that;

The output is 0 if both inputs are different.

One of the inputs is 1.

So, the other input is 0

Hence, the value of x is 0

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The value of S, which represents the length of each side of the square, is 4 miles.

To find the value of S, we need to determine the length of each side of the square. Given that the perimeter of the square is 16 miles, we can use the formula for the perimeter of a square, which is 4 times the length of a side.

Perimeter = 4 × S

Given that the perimeter is 16 miles, we can substitute this value into the equation:

16 = 4 × S

To solve for S, we divide both sides of the equation by 4:

16 ÷ 4 = S

4 = S

Therefore, S, which stands for the square's side lengths, has a value of 4 miles.

So, S = 4 miles.

This means that each side of the square measures 4 miles, and the square has equal sides and right angles at each corner.

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