topic: upper and lower bounds
why does there need to be a 5 placed at the end of 8.23, 8.24, 3.4 and 3.5?
Context cleared up in the picture provided:​

The angle that is marked as Q has a value of 30°

The cosine rule, also known as the law of cosines, is a mathematical formula used to calculate the length of a side or the measure of an angle of a triangle.

Cosine rule  useful in solving triangles when you know the lengths of two sides and the measure of the angle between them, or when you know the lengths of three sides.

By the use of the cosine rule, we have that;

7^2 = 12^2 + 14^2 - 2(12 * 14)Cos Q

49 = 144 + 196 -336CosQ

49- 340 =  -336CosQ

-291=  -336CosQ

Q = Cos-1 (-291/-336)

Q = 30

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a) The exponential growth function for a city's population that was 6.53 million in 2012 with an exponential growth rate of 2.79% per year is y = 6.53(1.0279)^t.

b) Based on the exponential growth function y = 6.53(1.0279)^t the population of the city in 2018 is 7.7 million.

c) The population of the city will be 10 million in 2028.

d) The doubling time for the population is 25 years.

An exponential growth function is one of the two exponential functions, including an exponential decay function.

An exponential growth function shows the relationship between two variables with an exponent and exhibits a constant rate of growth per period.

Population of the city in 2012 = 6.53million

Exponential growth rate = 2.79% per year

Let the number of growth years = t

a) y = 6.53(1.0279)^t

b) From 2012 to 2018, the number of years = 6 years

Population in 2018, y = 6.53(1.0279)^6

= 7.7 million

c) When the population will be 10 million = 15.5 years

10 = 6.53(1.0279)t

t = 15.5 years

= 16 years

= 2028

d) 13.06 = 6.53(1.0279)t

t = 25.189 years

= 25 years

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The polynomial equation of the smallest degree is f(u) = (u + 2)³(u - 1)²(u - 3)

Given that we have the graph of a polynomial

The degree of the graph is the number of times the graph intersect and/or crosses the x-axis

In this case, we have the following points at which the graph intersect and/or crosses the x-axis

When the multiplicities are added, we have

Degree = 3 + 1 + 2

Degree = 6

So, the degree is 6

In (a), we have

This means that

The zero at u = 1 has a multiplicity of 1

The equation is represented as

f(u) = (u - zero)^multiplicity

So, we have

f(u) = (u + 2)³(u - 1)²(u - 3)

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The values of the missing terms are 1) 24 and 2) 1.6.

Given are two similar figures, we need to find the value of x,

According to the definition of similar figures, the ratios of the corresponding sides are equal,

So,

1) GE / EF = RS / TR

5/6 = 20/x

5x = 120

x = 24

2) JH / LK = WX / ZY

3.84 / 2.04 = 3.2 / x

3.84x = 2.04 × 3.2

3.84x = 6.528

x = 1.7

Hence, the values of the missing terms are 1) 24 and 2) 1.6.

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According to the compound interest concept the total cost of the land today is $89,306.64, $86,249.94, $83,693.44 respective to the discount percentage.

To calculate the PV of the second payment of $48,000 due in three years, we need to use the formula for the present value of a single sum:

PV = FV / (1 + r)ⁿ

where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.

Using the given information, the FV is $48,000, the discount rate is 4%, 6%, or 8%, depending on the question, and the number of periods is three. Using a financial calculator, Excel, or present value tables, we can calculate the PV of the second payment:

For a discount rate of 4%:

PV = $48,000 / (1 + 0.04)³ = $41,306.64

For a discount rate of 6%:

PV = $48,000 / (1 + 0.06)³ = $38,249.94

For a discount rate of 8%:

PV = $48,000 / (1 + 0.08)³ = $35,693.44

Next, we need to add the PV of the second payment to the initial payment of $48,000 to get the total cost of the land today:

For a discount rate of 4%:

Total cost = $48,000 + $41,306.64 = $89,306.64

For a discount rate of 6%:

Total cost = $48,000 + $38,249.94 = $86,249.94

For a discount rate of 8%:

Total cost = $48,000 + $35,693.44 = $83,693.44

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The function that represents the fox population is P(t) = 6100 x [tex]1.06^{t}[/tex]

The fox population in 2008 is 9722.

The equation that would represent the population of the foxes is an exponential equation.

The form of the exponential equation would be

Future population = present population x [tex](1 + r)^{t}[/tex]

Where:

P(t) = 6100 x [tex](1 + 0.06)^{t}[/tex]

P(t) = 6100 x [tex]1.06^{t}[/tex]

Fox population in 2008 = 6100 x [tex]1.06^{8}[/tex] = 9722

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The standard deviation of the sample mean differences is, 16.98.

Since, We know that;

Standard deviation is defined to be the square root of the population variance of the vector. The sample standard deviation s is defined to the square root of the sample variance of the vector.

Here, The standard deviation of the sample mean differences should be calculated using the standard deviations of the two populations.

In order to see how they differ, we need to first subtract them from each other,

So, we get:

21.2 - 17.6 = 3.6

We then divide this number with the first standard deviation as follows:

⇒ 3.6/21.2 x 100

⇒ 16.98

Therefore, the standard deviation of the sample mean is, 16.98.

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Answer: 17/24 for both jobs

Step-by-step explanation:

The rate of each bus which leave a station at the same time are 76 mi/h and 68 mi/h respectively.

Given that,

Two buses leave a station at the same time and travel in opposite directions.

Let x be the distance travelled by the the first bus in 3 hours.

Then the distance travelled by the other bus in 3 hours = 432 - x

Rate of first bus = x/3 miles per hour

Rate of second bus = (432 - x) / 3 miles per hour

One bus travels 8 mi/h slower than the other bus.

x/3 - (432 - x) / 3 = 8

(x - 432 + x) / 3 = 8

2x - 432 = 24

2x = 456

x = 228

Rate of one bus = 228/3 = 76 mi/h

Rate of second bus = (432 - 228)/3 = 68 mi/h

Hence the rate of each bus are 76 mi/h and 68 mi/h respectively.

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The statement that is true about the ratios is:

There are 2 fewer geese than ducks on the pond.

Option A is the correct answer.

We have,

The ratio of ducks to geese on a pond is 3:2.

This means,

Number of ducks = 3x

Number of geese = 2x

And,

If the total number of ducks and geese = 10

So,

(3x + 2x) = 10

5x = 10

x = 2

Now,

Number of ducks = 3x = 3 x 2 = 6

Number of geese = 2x = 2 x 2 = 4

This means,

There are 2 fewer geese than ducks on the pond.

Thus,

The statement that is true about the ratios is:

There are 2 fewer geese than ducks on the pond.

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The Exponential model is y = 0.74 (1.79)ˣ

We have,

(10, 160) and (11, 250)

Using the Exponential model

y = abˣ

where a is the initial amount and be is the constant.

Now, the value of b is

= 250/ 140

= 1.79

Now, y = abˣ

140 = a (1.79)⁹

a = 0.74

So, the Exponential model is y = 0.74 (1.79)ˣ

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Answer:  the answer is 13 and one-half

Step-by-step explanation:

C

Step-by-step explanation:

The critical values of the function are x = 0 and x = 4.

The critical values of a function f(x) are the values of x for which f'(x) = 0.

In this problem, the function is:

f(x) = [tex]\frac{x^4}{5(x-2)^2}[/tex]

The derivative is found as follows, applying the quotient rule:

f'(x) = [tex]\frac{2x^3(x-4)}{5(x-2)^3}[/tex]

The zeros of the function are the zeros of the numerator, thus:

2x³(x-4) = 0

∴ x = 0, 4

Hence, the critical values of the function are x = 0 and x = 4.

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The base area of the cylinder is 78.54 ft².

The height of the cylinder is 2 ft.

The cylinder has a volume of 157.08 ft cube and the radius of the cylinder is 5 ft.

Therefore, the area of the base of the cylinder can be found as follows:

base area of the cylinder = πr²

base area of the cylinder = 3.1416 × 5²

base area of the cylinder = 3.1416 × 25

base area of the cylinder = 78.54 ft²

Therefore, let's find the height of the cylinder.

volume of the cylinder = πr²h

where

157.08 = 78.54 h

divide both sides by 78.54

h = 157.08 / 78.54

h = 2 ft

Therefore,

height of the cylinder = 2 ft

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The surface area of the composite figure is about 98.56 sq.cm

The composite figure is made up of a cylinder and a cuboid.

The formula for surface area of a cylinder is:

A = 2πr² + 2πrh

In this case, we only have top and not bottom. Thus:

A = πr² + 2πrh

A = π(1)² + 2π(1 * 6)

A = 37.7 sq.cm

Surface area of cuboid is:

A = 2(4 * 4) + 4(2 * 4) - π(1)²

A = 32 + 32 - π

A = 60.86 sq.cm

Total surface area = 37.7 sq.cm + 60.86 sq.cm

= 98.56 sq.cm

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Answer:

2(1/2)(11)(13) + 2(1/2)(10)(13.2) + 10(11)

= 143 + 132 + 110 = 385 square feet

B is the correct answer.

The sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of μ is given as follows:

n = 189 babies.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is defined as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]M = 0.4 \sigma = 2.8[/tex]

Then the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

0.4sqrt(n) = 1.96 x 2.8

sqrt(n) = (1.96 x 2.8/0.4)

n = (1.96 x 2.8/0.4)²

n = 189 babies. (rounded up).

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i) finite set, ii) infinite set, iii) infinite set, iv) infinite set, and v) finite set are the required solutions.

A Set is a collection of objects with similar properties. There are different types of set two of them are finite and infinite set.

Finite set- A set is called a finite set when the elements inside the set are countable or where we can know the starting and the ending of the elements. For example- A set of players in a cricket team.

Infinite set- A set is called an infinite set when the elements inside the set are uncountable or where the ending of the elements is not known. For Example- A set of positive numbers.

Here in the question the option (i) and (v) are finite sets because the no.of months in the year and no.of alphabets are countable or finite. Option (ii), (iii), and (iv) are infinite sets as no.of stars in the galaxy, even integers, and odd integers are uncountable.

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Answer:

the set of months in a year is finite

the set of star in the Galaxy is finite

the set of even integers is infinite

the set of odd integers is infinite

the set of alphabet is finite

Step-by-step explanation:

1) the set of month in a year is finite because they are limit and we can count them easily

2) the set of star in the galaxy is finite cause there are zillions of stars

3) the set of even integer is infinite because numbers are unlimit or infinite

4) the set of odd integers is infinite cause numbers are infinite ir they have not limit

5) the set of alphabet is finite because we can count them limitedly

The length of m∠WYX is equal to 12π units.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

16π = θ(π/360) × 8²

Central angle, θ = 0.5π

m∠WYX = 2π - m∠WX

m∠WYX = 2π - 0.5π

m∠WYX = 1.5π

Length of m∠WYX = (1.5π)/2π × 2πr

Length of m∠WYX = (1.5π)/2π × 2π(8)

Length of m∠WYX = 12π units.

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To draw the graph of y = g(-x), we need to replace x with -x in the original function.

If y = g(x) is given by the following graph:

(see attachment labeled "Attachment1")

Then y = g(-x) can be obtained by reflecting the graph of y = g(x) about the y-axis:

(see attachment labeled "Attachment 2")

Therefore, the graph of y = g(-x) is the reflection of the graph of y = g(x) about the y-axis.

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The real exchange rate is 0.75.

It is not possible to make a profit by buying apples in one country and selling them in another.

We have,

To find the real exchange rate, we need to compare the price of apples in the two countries in terms of their respective currencies.

In the U.S., a bushel of apples costs $15.00.

In Japan, the same apples cost 1,600 yen.

Using the exchange rate of 80 yen per dollar, we can convert the cost in yen to dollars:

1,600 yen / 80 yen per dollar

= $20.00

So, the price of a bushel of apples in Japan is equivalent to $20.00 in the U.S.

The real exchange rate is the ratio of the prices of the same goods in two different countries, taking into account the exchange rate.

In this case, the real exchange rate is:

Real exchange rate = Price in U.S. / Price in Japan

= $15.00 / $20.00

= 0.75

This means that it takes 0.75 U.S. dollars to buy the same goods in Japan which would cost 1 Japanese yen.

To determine if there is an arbitrage opportunity, we need to compare the real exchange rate with the actual exchange rate.

If the real exchange rate is greater than the actual exchange rate, there is an arbitrage opportunity for someone to buy the good in one country and sell it in another country for a profit.

However, if the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.

In this case,

The real exchange rate is 0.75, while the actual exchange rate is 80 yen per dollar, or 0.0125.

Since the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.

Therefore,

The real exchange rate is 0.75.

It is not possible to make a profit by buying apples in one country and selling them in another.

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The numeric value of the function graphed is given as follows:

f(-8) = 6.

The expression for the numeric value of the function in this problem is given as follows:

f(-8).

This means that the input is given as follows:

x = -8.

Passing a vertical line through x = -8, the value of y in which the vertical line crosses the graph is given as follows:

y = 6.

Hence the numeric value is given as follows:

f(-8) = 6.

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Answer:

n₁ = 198,610

P₁ = 27/198,610

n₂ = 196,877

P₂ = 104/196,877

q₁ = 1 - P₁

q₂ = 1 - P₂

Step-by-step explanation:

Answer:

56% Caesar

Step-by-step explanation:

The only salads sold were Caesar and it is majority

The solution to the inequality is:

0 < a  or a ≤ -5

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

We have: -1 -10a < -1 or 10 + 3a ≤ -5 and we want to solve for the variable "a".

-1 -10a < -1      or  10 + 3a ≤ -5

-10a < -1 + 1    or  3a ≤ -5 - 10

-10a < 0          or  3a ≤ -15  

a < 0/(-10)      or   a ≤ -15/3

a > 0              or   a ≤ -5

Since a a > 0  is the same as 0 < a. We can say:

0 < a  or a ≤ -5

Thus,  0 < a ≤ -5

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The monthly payments and total cost of interest depend on the interest rate and the length of the loan. Generally, a lower interest rate or a shorter loan term results in lower total interest costs.

To calculate the monthly payments, we can use the formula for the present value of an annuity:

[tex]PV = P * (1 - (1 + r)^{-n}) / r[/tex]

where PV is the present value of the loan, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments.

(a) 30 years, 5%:

PV = 0.9 * $90,000 = $81,000 (since she puts 10% down)

r = 0.05 / 12 = 0.0125(monthly interest rate)

n = 30 * 12 = 360 (number of monthly payments)

Using the formula, we get:

PV = $81,000

Monthly payment = $436.82

Total cost of interest = $57,255.85

(b) 30 years, 5.12%:

r = 0.0512 / 12 = 0.00427 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $439.88

Total cost of interest = $59,956.19

(c) 30 years, 6%:

r = 0.06 / 12 = 0.005 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $485.24

Total cost of interest = $95,687.34

(d) 15 years, 3.78%:

n = 15 * 12 = 180 (number of monthly payments)

r = 0.0378 / 12 = 0.00315 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $591.93

Total cost of interest = $34,147.07

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Answer:

180

Step-by-step explanation:

To find the lowest common multiple (LCM) of 36 and 30, we can use the prime factorization method:First, we can find the prime factorization of each number:36 = 2^2 * 3^230 = 2 * 3 * 5Next, we can take the highest power of each prime factor that appears in either number and multiply them together.The highest power of 2 is 2^2 = 4.The highest power of 3 is 3^2 = 9.The highest power of 5 is 5^1 = 5.Multiplying these together, we get:LCM(36, 30) = 2^2 * 3^2 * 5 = 180Therefore, the lowest common multiple of 36 and 30 is 180.

Answer: 180

Step-by-step explanation:

To find the lowest common multiple (LCM) of two numbers, we need to find the smallest number that is a multiple of both of them.

One way to do this is to find the prime factorization of each number and then take the product of all the prime factors, with each factor occurring as many times as it appears in the factorization of either number.

The prime factorization of 36 is 2^2 × 3^2, and the prime factorization of 30 is 2 × 3 × 5. Therefore, the LCM of 36 and 30 can be found by taking the product of the highest power of each prime factor that appears in either factorization:

LCM(36, 30) = 2^2 × 3^2 × 5 = 180

Therefore, the lowest common multiple of 36 and 30 is 180.