Calculate capital if assets are £451,100, liabilities are £20,500, income is £351,200 and expenses are £270,600.

The solution is

a) The ascending order is 32 % < 2 1/2 < √9 < π

b) The ascending order is -4 < -3.4 < -3 < -2 1/2 < π

c) The ascending order is -5/8 < 0 < 250% < 3.4

What is Ascending Order?

When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.

Given data ,

A)

32 % , π , 2 1/2 , √9

32 % = 32 / 100

        = 0.32

π = 3.14

2 1/2 = 2.5

√9 = 3

So , arranging the numbers in ascending order we get ,

0.32 < 2.5 < 3 < 3.14

Hence , the ascending order is 32 % < 2 1/2 < √9 < π

B)

-3.4 , -4 , -3 , -2 1/2 , π  

Hence , the ascending order is -4 < -3.4 < -3 < -2 1/2 < π

C)    

250 % , 3.4 , -5/8 , 0

250 % = 2.5

-5/8 = -0.625

So , arranging the numbers in ascending order we get

-0.625 < 0 < 2.5 < 3.4

Hence , the ascending order is -5/8 < 0 < 250% < 3.4

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The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).

A(x₁,y₁) = (-8,4)

B(x₂,y₂) = (-1,3)

C(x, y ) = (x ,0)

equation of a line is given as:

y - y₁ = (y₂ - y₁)/ (x₂ - y₁) (x - x₁)

y - 4  = (3 - 4)/(-1 + 8)(x + 8)

y - 4 = -1/7(x + 8)

7(y - 4) = -1(x + 8)

7y - 28 = -x + 8

x + 7y - 36 = 0

when y = 0 then the value of x is given as:

x + 7y- 36 = 0

x + 7(0) - 36 = 0

x = 36

point C on the x-axis (x , 0) = (36,0)

The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).

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The rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.

The surface area of a sphere with radius r is given by4π[tex]r^{2}[/tex]

Given;

S = surface area at time t,  and r = radius at time t

radius of a spherical ball is increasing at a rate of 2 cm/min

radius: 6cm

Area of a sphere is A = 4π[tex]r^{2}[/tex]

Step 1: Differentiate area of a spherical ball

A = 4π[tex]r^{2}[/tex]

[tex]\frac{dA}{dt}[/tex] =[tex]\frac{d}{dt}[/tex](4π[tex]r^{2}[/tex])

=4π [tex]\frac{d}{dt}[/tex]([tex]r^{2}[/tex])

=4π2r [tex]\frac{dr}{dt}[/tex]

[tex]\frac{dA}{dt}[/tex] = 8πr

since we have that dr/dt = 2 cm/min. Thus, the radius of the ball is 6cm, we have;

[tex]\frac{dA}{dt}[/tex]= 8π(6)(2) =96π

So, the rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.

Note that measuring area unit is cm2/min

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Answer:

i think it 8h

Step-by-step explanation:

a.

The ratio of the number of students in 2006-2007 to the number of students in 2005-2006 is = 12,256 : 11,937

b.

Growth factor = (12256-11937)/11937

= 0.02672.

c.

Increase in percent = 100* (12256 - 11937)/11937

=  100 * 0.02672

= 2.672%

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Total Water Used by a standard flush in a week i.e. 7 days is 22.4 gallons.

What is Multiplication?

In mathematics, multiplying implies adding equal groups. The number of items in the group grows as we multiply.

Solution:

Given that,

The standard toilet uses 1.6 gallons of water per flush

Also, it is flushed twice a day

To Find, Total water used in a week i.e. 7 days

Since, flush uses 1.6 gallons water per flush

Total water used in a day is 2*1.6 = 3.2 gallons

This implies,

Total water used in 7 days = 7 * 3.2 = 22.4 gallons

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Using the given exponential function, it is found that:

a) The number of mosquitoes in the container after 5 days is of: 346.

b) The number of days until the container reaches the maximum capacity is of: 10 days.

The exponential function that models this problem is presented as follows:

P(t) = 24(4)^(0.385t).

Hence, after five days, the number of mosquitoes is of:

P(5) = 24(4)^(0.385 x 5) = 346 mosquitoes.

The number of days that it takes for the container to reach it's maximum capacity of 5000 is obtained solving the exponential function with logarithms as follows:

[tex]5000 = 24(4)^{0.385t}[/tex]

[tex](4)^{0.385t} = \frac{5000}{24}[/tex]

[tex](4)^{0.385t} = 208.3[/tex]

[tex]\log{(4)^{0.385t}} = \log{208.3}[/tex]

Applying the power property of logarithms, we have that:

[tex]0.385t\log{4} = \log{208.3}[/tex]

[tex]t = \frac{\log{208.3}}{0.385\log{4}}[/tex]

t = 10 days.

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Using the z-distribution to test the hypothesis, it is found that:

1. You would not like to continue the game, as in each trial you are losing.

2. The p-value is of 0.0023.

3. The low p-value means that there is enough evidence to conclude that the coin is biased.

At the null hypothesis, it is tested if there is not enough evidence that the coin is biased, that is, the proportion of heads is of 0.5, hence:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the coin is biased, that is, it has a proportion of heads lower than 0.5, hence:

[tex]H_1: p_1 < 0.5[/tex]

The test statistic is given by the equation as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the variables are listed and explained as follows:

The values of these parameters are given as follows:

[tex]\overline{p} = \frac{0}{8} = 0, n = 8, p = 0.5[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0 - 0.5}{\sqrt{\frac{0.5(0.5)}{8}}}[/tex]

z = -2.83.

Using a z-distribution calculator, and considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -2.83, the p-value is of 0.0023.

Since this p-value is less than the standard significance level of 0.05, it means that there is enough evidence to conclude that the coin is biased towards tails.

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The shaded area under the standard normal curve is 2.58%.

According to z-score table,

Area for < 2.23 = 0.9871

Area for >2.23 = 1 - 0.9871

                        = 0.0129

Area for < 2.23 = 0.0129

Total area = 0.0129 + 0.0129

                 = 0.0258

Area percent = 0.0258*100

                      = 2.58%

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The compound interest is quaterly then answer is $266,022.2639 and when it is in continuously then answer is $275,579.4095

Quarterly compounding is what?

Compounding quarterly is the term used to describe the amount of interest that is earned on a quarterly basis on a savings account or investment where the interest is also reinvested. As most banks offer interest income on the deposits, which compounds quarterly, this information is useful in computing the fixed deposit income. It can also be used to figure out any revenue from money market instruments or other financial products that pay quarterly income.

What Does Constant Compounding Mean?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. While this is not attainable in practice, the concept of continually compounded interest is crucial in finance. Given that most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.

a) A = P(1 + r/n)nt  

P = $25000

r = 12% = 0.12

t = 20 years

n = 4

A = 25000(1 + 0.12/4)(4)(20)

A = $266,022.2639  (Answer)

b) A = Pert

P = $25000

r = 12% = 0.12

t = 20 years

A = 25000e(0.12)(20)

A = $275,579.4095   (Answer)

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Answer:

yes yes ...................

Answer:

y=-2x-2

Step-by-step explanation:

If the endpoints of the line segment are (7,4) and (-9,-4), that means that the slope will be:

[tex]\frac{-4-4}{-9-7}[/tex] = [tex]\frac{-8}{-16}[/tex]=[tex]\frac{1}{2}[/tex]. For the perpendicular bisector to be perpendicular to the line, it must have a perpendicular slope, which will be the negative reciprocal of [tex]\frac{1}{2}[/tex], which is -[tex]2[/tex]. The perpendicular bisector must also go through the midpoint of the segment, which is (-1, 0) because -1 is the average of 7 and -9 and 0 is the average of 4 and -4.

Now we find the equation!

y=mx+b. Plug in -[tex]2[/tex]     as the "m", or slope:

y=-[tex]2[/tex]x+b

Now, plug in the point (-1, 0):

0=-[tex]2[/tex]*-1+b

0=[tex]2[/tex]+b

b=-[tex]2[/tex]

So, we have m=-[tex]2[/tex] and b=-[tex]2[/tex] and we can form our equation!

y=-[tex]2[/tex]x-[tex]2[/tex]

Hope this helps!! :D

The potential outliers, given the normal annual precipitation in the different U.S. cities are E. 59.4; 65.3.

Outliers in a data distribution are values or data points that are far from the other points in the data. These can be statistically significant when they distort measures of central tendency such as mean.

In this case, the potential outliers in the normal annual precipitation 59.4 and 65.3 because they are far from the highest annual precipitation (before them) of 47.2 inches. 9.2 inches is quite low but it is close to 12.3 inches and 13.6 inches and so is not an outlier.

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The fraction that represents 0.8 is 4/5 .

Fraction can be defined as a numerical quantity that is part of a whole number  . it is written in the form of a/b , where a is called the numerator and b is called the denominator .

For Example , 1/2 , 3/8 4/9 are all fractions .

In the question ,

it is given that the point is 0.8 ,

we need to convert this point in fraction ,

the point 0.8 in fraction can be written as 8/10 ,

= 8/10

simplifying further ,

we get

= 4/5

Therefore ,The fraction that represents 0.8 is 4/5 .

The given question is incomplete , the complete question is

What fraction is represented by 0.8 ?

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The answer is [14, 42].

The number 14 is even.

7 x 2 = 14

An even number, 42.

7 x 6 = 42

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The simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .

What is power function ?

A function having a single term that is the sum of a real number, a coefficient, and a variable raised to a fixed real number is called a power function. Consider functions for area or volume as examples (a number that multiplies a variable raised to an exponent is known as a coefficient). A power function is a function where y = x n, where n is any real constant number. In reality, many of our parent functions, including linear and quadratic functions, are power functions.

Here ,

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

To write in the form of f(x)= [tex]kx^p[/tex]

=> f(x) = [tex]\frac{-3}{2}* \frac{1}{x^5}[/tex]

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

b) g(x) = 5[tex]\sqrt[3]{x}[/tex]

Here we know that [tex]\sqrt[n]{a} = a^\frac{1}{n}[/tex] , then

=>g(x)=5[tex]x^\frac{1}{3}[/tex]

Hence the simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .

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The total middle school enrollment is 889 for the given city.

According to the question,

We have the following information:

Three middle schools in a city had enrollments of 296,315 and 278.

Now, the total middle school enrollment can be easily found by adding the enrollments in three middle schools of the city.

So, we have the following expression:

Total middle school enrollment = 296+315+278

(We already know that the digits are first added from the right hand side and then we move to the left hand side.)

Total middle school enrollment = 889

Hence, the total middle school enrollment is 889 for the given city.

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The 2.51 × 10⁻⁵ Watts/cm² sound intensity of the sound from the rocket engine has a decibel level of 114 dB

A decibel is a unit to measure the relative loudness of sound or to express the ratio electrical or acoustic power.

The intensity of the sound of the rocket engine = 2.51 × 10⁻⁵ Watts/cm²

Converting the unit of the sound intensity to Watts/m² gives;

1 cm² = 0.0001 m²

10,000 cm² = 1 m²

2.51 × 10⁻⁵ Watts/cm² = 10000 × 2.51 × 10⁻⁵ Watts/m² = 0.251 Watts/m²

The equation for the decibel from the power of sound is presented as follows;

[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{I}{I_0} \right)[/tex]

Where;

I₀ = 10⁻¹² W/m²

Which gives;

[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{0.251 }{10^{-12}} \right) = 113.9967373215 \approx 114[/tex]

The number of decibels for the power of the sound given to the nearest decibel by the rocket engine is 114 decibels

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The complete general form of the equation of the given sinusoidal function is y = 8sin[(27/2π)*(x - 4)] + c.

The general form of an equation for a sinusoidal function is presented below.

y = a×sin[b*(x - h)] + c

The variable "a" denotes the amplitude of the equation. The variable "T" represents the time period of the equation, and T = 2π/b. The variable "h" denotes the phase shift of the equation. The variable "c" denotes the vertical shift of the equation. The amplitude, period, and phase shift are 8, 27, and 4 units to the left, respectively. The general form of the equation of a sinusoidal function can be written as given below.

y = a×sin[b*(x - h)] + c

y = 8sin[(27/2π)*(x - 4)] + c

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Answer:

Step-by-step explanation:

Answer:

0.45833333333 or 11/23

Step-by-step explanation:

1 2/9*6/16 is simply 11/23, cross multiply and simplify

The differentiation of the given function is 12[tex]x^3[/tex](5[tex]x^2[/tex] +2).

In the given question we have to differentiate the given function with respect to x.

The given function is f(x) = [tex]2x^4(5x^2+3)[/tex]

Before differentiating the function we first simplify the given expression.

To simplify the expression we multiply the 2x^4 to each term under the bracket.

Now the function;

f(x) = [tex]2x^4\cdot5x^2+3\cdot2x^4[/tex]

As we know that if the base is same en power get added.

f(x) = [tex]10x^{4+2}+6x^4[/tex]

f(x) = [tex]10x^{6}+6x^4[/tex]

Now differentiating the function with respect to x.

f'(x) = d/dx([tex]10x^{6}+6x^4[/tex])

f'(x) = 10d/dx([tex]x^6[/tex]) + 6d/dx([tex]x^4[/tex])

As we know that d/dx of x^n =nx^(n-1). So

f'(x) = 10∙6 [tex]x^5[/tex] + 6∙4 [tex]x^3[/tex]

f'(x) = 60[tex]x^5[/tex]+24[tex]x^3[/tex]

Now taking 12x^3 common

f'(x) = 12[tex]x^3[/tex](5[tex]x^2[/tex] +2)

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The frequency distribution based on the information given is illustrated below.

What is the frequency distribution of table?

A frequency distribution table is the chart that summarizes all the data under two columns - variables/categories, and their frequency.

It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.

Given the above information the frequency distribution table is:

Cost of living[tex]\begin{table}[]\begin{tabular}{ll}Cost of living & Number of States \\85.0 - 94.9 & 9 \\95.0 - 104.9 & 5 \\105.0 - 114.9 & 0 \\115.0 - 124.9 & 2 \\125.0 - 134.9 & 2 \\135.0 - 144.9 & 1 \\145.0 = 154.9 & 1 \end{tabular}\end{table}[/tex]   Number of states

85.0 - 94.9             9

95.0 - 104.9         5

105.0 - 114.9         0

115.0 - 124.9         2

125.0 - 134.9         2

135.0 - 144.9         1

145.0 - 154.9         1

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Answer:

3y+3y-12

Step-by-step explanation:

we can add the coefficients of y to make 6y-12

And that is equivalent

Hopes this helps please mark brainliest

The inequality that describes this situation is f ≥ 5

How to calculate the inequality ?

Use the steps below to solve an inequality:

Step 1: Subtract all fractions by multiplying each term by the sum of all fractions' least common denominators.

Step 2: Simplify the inequality by merging like terms on each side.

Step 3: Add or subtract amounts to get the unknown and the numbers on either side.

As per the question it tells the High- fiber should have at least 5g of fiber per serving

f = Number of grams of fiber per serving of high-fiber food

∴ f ≥ 5

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Quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.

Given,

Quadratic equation passes through the points (-4,2) and (2,2)

(x₁, y₁) =(-4,2)

(x₂ ,y₂) = (2,2)

Here,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

⇒(y - 2) / (x + 4) = (2 -  2) / (2 + 4)

⇒ (y-2) / (x+4) =0

⇒y -2 =0

⇒y = 2

Quadratic equation formed from the given points (-4,2) and (2,2) is y =2.

Which represents the horizontal line and does not have any vertex.

Therefore, quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.

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The answer is option (a)

Hope this answer helps you