The population in England goes up by 1/5 every year. If the population was £20mil in 2008 what would be the population in 2010?

The answer of the given expression as a common fraction in lowest terms is  437/495  .

In the question ,

it is given that ,

the expression is 0.4overline 8 + overline 0.37 ,

that can be written as \(0.4\overline{8}\) + \(0.\overline{37}\)

On further simplifying the above expression further ,

we get ,

= (48 - 4)/90 + 37/99

= 44/90 + 37/99

taking the LCM of 90 and 99 as 990 and solving further ,

we get ,

= 484/990 + 390/990

= ( 484 + 390 )/990

= 874/990

in lowest form it is = 437/495 .

Therefore , the answer to the expression is  437/495  .

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both option (a) and option (b) represent equivalent expressions to 3(4h + 2k), while option (c) indicates that none of the given expressions are equivalent to 3(4h + 2k).

The expressions that are equivalent to 3(4h + 2k) are:

a) 3(2k + 4h)

b) 3(4k + 2h)

Both options (a) and (b) are correct.

In option (a), the terms inside the parentheses are rearranged, but the coefficients of h and k remain the same.

Similarly, in option (b), the terms inside the parentheses are rearranged, but the coefficients of h and k remain the same.

Therefore, both option (a) and option (b) represent equivalent expressions to 3(4h + 2k), while option (c) indicates that none of the given expressions are equivalent to 3(4h + 2k).

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The value of x is 10.

Given triangle is a right-angled triangle.

Let the lengths of not mentioned lengths be 2p(hypotenuse) and 2q (other side).

There are two triangles in the given picture.

Consider the smaller triangle.

Apply Pythagoras theorem to that i.e.,

\(p^{2}\) = \((3x)^{2} + q^{2}\)

(Here, total hypotenuse is 2p length and the smaller triangle has half of its length. So, length is p. Similarly in case of q)

\(p^{2} = 9x^{2} + q^{2}\)  (Equation 1)

Now, consider the large triangle.

Apply Pythagoras theorem to that i.e.,

\((2p)^{2} = (4x + 20)^{2} + (2q)^{2}\)

\(4p^{2} = (16x^{2} + 160x + 400) + 4q^{2}\)

Substitute \(p^{2}\) from Equation 1

\(4(9x^{2} + q^{2} ) = 16x^{2} + 160x + 400 + 4q^{2}\\\)

\(36x^{2} + 4q^{2} = 16x^{2} + 160x + 400 + 4q^{2}\)

\(36x^{2} = 16x^{2} + 160x + 400\)  (\(4q^{2}\) from both sides got cancelled)

\(20x^{2} - 160x - 400 = 0\)

Solving the quadratic equation,

\(20x^{2} - 200x + 40x - 400 = 0\)

\(20x(x - 10) + 40(x - 10) = 0\)

\((20x+ 40)(x - 10) = 0\)

So, 20x + 40 = 0 or x - 10 = 0

i.e., x = -2 or 1o

But \(x \neq -2\) because angles cannot be negative.

So, x is 10.

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Answer:

88 feet

Step-by-step explanation:

Use this formula

Circumference= 2*22/7*Radius

22/7 * 14=

2*44 =

88 feet

Find the distance from P to l.

Line I contains points (0, -3) and (7,4). Point P has coordinates (4,3)

Find the slope of line l

we have the points (0, -3) and (7,4)

m=(4+3)/(7-0)

m=7/7

m=1

Find the equation of the line perpendicular to the line l that passes through the point P

REmember that

If two lines are perpendicular, then the product of their slopes is equal to -1

therefore

the slope of the perpendicular line is

m=-1

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=P(4,3)

substitute

y-3=-1(x-4)

y-3=-x+4

y=-x+7

Find the equation of the line l

we have

m=1 (see the step 1)

and we have the point (0,-3) -----> y-intercept

so

the equation of the line l is

y=x-3

Find the intersection point line l and its perpendicular line

y=x-3 ------> equation A

y=-x+7 -----> equation B

solve the system of equations

Adds equation A and equation B

2y=-3+7

2y=4

y=2

Find the value of x

substitute in equation A

2=x-3

x=2+3

x=5

therefore

the intersection poin is (5,2)

Find the distance between point (5,2) and point P(4,3)

Remember that, this distance is the distance from P to l.

the formula to calculate the distance between two points is equal to

we have

(x1,y1)=(5,2)

(x2,y2)=(4,3)

substitute in the formula

therefore

teh answer is

Answer:

17 = x/18 and 23 = .84/n

Step-by-step explanation:

Answer:

17. x =18

23. n =0.84

Step-by-step explanation:

17.

\(\frac{6}{5} = \frac{x}{15} \\\\\frac{x}{15}=\frac{6}{5}\\\\\mathrm{Multiply\:both\:sides\:by\:}15\\\\\frac{15x}{15}=\frac{6\cdot \:15}{5}\\\mathrm{Simplify\:}\frac{15x}{15}:\quad x\\\\\mathrm{Simplify\:}\frac{6\cdot \:15}{5}:\quad 18\\\\x=18\\\)

23.

\(\frac{2}{0.21}=\frac{8}{n}\\\\ \mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\\\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\times \:d=b\times \:c\\\\2n=0.21\times \:8\\\\\mathrm{Simplify\:}0.21\times \:8:\quad 1.68\\\\2n=1.68\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2n}{2}=\frac{1.68}{2}\\\\Simplify\\\\n=0.84\)

To determine the magnitude of the resultant force acting on the object, we can use the Pythagorean theorem.

Let's denote the magnitude of the first force as F₁ = 100 N and the magnitude of the second force as F₂ = 150 N. Since the forces act at 90° to each other, they form a right triangle.

According to the Pythagorean theorem, the magnitude of the resultant force (F) is given by:

\(F = \sqrt{F_1^2 + F_2^2}\)

Substituting the given values:

\(F = \sqrt{100^2 + 150^2} \\\\= \sqrt{10000 + 22500} \\\\= \sqrt{32500} \\\\\approx 180.28 \, \text{N}\)

Therefore, the magnitude of the resultant force acting on the object is approximately 180.28 N, which corresponds to option b.

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Original Cost - $82

First part: Apply the 60% off discount

Convert first the 60% into decimal form

60% ÷ 100% = 0.6

Multiply it to the original cost to determine the discount

$82 ˣ 0.6 = $49.2

Subtract the discount to the original price, to determine the discounted price.

$82 - $49.2 = $32.8

Second part:

The discounted price is now $32.8 for which we will apply another 10% discount.

Again, convert 10% into decimal

10% ÷ 100% = 0.1

Multiply it to the discounted price, to determine the second discount.

$32.8 ˣ 0.1 = $3.28

Subtract the discount to the already discounted price.

$32.8 - $3.28 = $29.52

Therefore, the final sale price of the watch is at $29.52.

Answer:

C

Step-by-step explanation:

Hope I was able to help!! :)

The value of the derivative of the function g(x) at x = 1 will be 1/3. Then the correct option is A.

A function that may convert into another function is known as an inverse function or anti-function.

If the function is f(x) = sinx + 2x + 1.

Then the derivative of an inverse function g(x) of a function f(x) at a given value (a) will be

\(\rm g'(a) = \dfrac{1}{f'(g(a))}\)

The derivative of f(x) will be

f'(x) = cos x + 2

Then the given value of a will be

a = 1

g(x) = f⁻¹(x)

put x = 0, then we have

f(0) = sin 0 + 2(0) + 1

f(0) = 1

Put x = 1, in the function f⁻¹(x). Then we have

f⁻¹(1) = 0

and

g(1) = 0

Then put a = 1, then we have

\(\rm g'(a) = \dfrac{1}{f'(g(a))}\\\\g'(1) = \dfrac{1}{f'(g(1))}\\\\g'(1) = \dfrac{1}{f'(0)}\\\\g'(1) = \dfrac{1}{\cos 0 + 2}\\\\g'(1) = \dfrac{1}{1+2}= \dfrac{1}{3}\)

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Each campsite will receive 7.8 liters of water.

If the campers collect water from a stream and share it equally among 8 campsites, we need to determine how much water each campsite receives.

The total amount of water collected is given as 62.4 liters in a bucket. To find the amount of water per campsite, we divide the total amount of water by the number of campsites.

Dividing 62.4 liters by 8 campsites gives us 7.8 liters per campsite.

It's important to note that this calculation assumes an equal distribution of water among all the campsites. However, in practical situations, the division may not be exact due to factors such as spillage, uneven pouring, or variations in the bucket's actual capacity.

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First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

The rate of change means that the designer hourly charge is $55 per hour

Linear equation

A linear equation is in the form:

y = mx + b

Where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the total cost of hiring the designer after x hours.

From the table, using the point (0, 125) and (15, 950):

The rate of change means that the designer hourly charge is $55 per hour

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Therefore, the only claim that the interval would tend to refute is option E: The population mean is less than 125.

Based on the 90% confidence interval of 135 to 160, we can conclude that the population mean is likely to be within this interval with a 90% degree of confidence.

A. The claim that the population mean is more than 110 is not refuted by the confidence interval since the lower limit of the interval is above 110.

B. The claim that the population mean is less than 150 is not refuted by the confidence interval since the upper limit of the interval is above 150.

C. The claim that the population mean is between 140 and 150 is not refuted by the confidence interval since both values are within the interval.

D. The claim that the population mean is more than 140 is not refuted by the confidence interval since the lower limit of the interval is above 140.

E. The claim that the population mean is less than 125 is refuted by the confidence interval since the lower limit of the interval is above 125.

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Answer: 1 tablespoon

Step-by-step explanation:

In regression analysis , the error term ε is a random variable with expected value of 0.

What is regression analysis?

A set of statistical procedures known as regression analysis is used to estimate the relationships between a dependent variable and one or more independent variables.

Main Body:

In regression analysis, the model in the form is called regression model.

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as regression equation.

So the answer  to error term is 0.

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Answer

C

Step-by-step explanation:

2(-4) + 3

-8 + 3

-5

The emphasis is on the Counting and Cardinality standard in the early childhood years according to the National Council of Teachers of Mathematics.

The National Council of Teachers of Mathematics emphasizes the following standards in the early childhood years:

- Counting and Cardinality

- Operations and Algebraic Thinking

- Number and Operations in Base Ten

- Measurement and Data

- Geometry

The National Council of Teachers of Mathematics recognizes that all five math standards are important in the early childhood years. However, they place a particular emphasis on the standards related to counting and cardinality. This includes developing skills in counting, understanding numbers, and recognizing numerical relationships.

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If no deposits and withdrawals are made then the amount that will be in the account after 15 years is  $3642.84   .

In the question ,

it is given that ,

the amount invested is $1800 ,

the rate of interest = 4.7% = 0.047

time required is = 15 years

the continuous compounding formula is

y = P×\(e^{r \times t}\)

y = 1800*(\(e^{0.047 \times 15}\))

y = 1800*\(e^{0.705}\)

Simplifying further , we get

y = 1800*2.0238

y = 3642.84

Therefore , If no deposits and withdrawals are made then the amount that will be in the account after 15 years is  $3642.84   .

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Answer:

Equation: 3y - 6 = y + 7

y = 6.5

Step-by-step explanation:

Step 1: Write out equation

3y - 6 = y + 7

Step 2: Solve for y

2y - 6 = 7

2y = 13

y = 13/2 or 6.5

Answer:

19.2 m

Step-by-step explanation:

Since this is a right triangle, we can use the pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

12^2 + 15^2 = c^2

144 + 225 = c^2

369 = c^2

Taking the square root of each side

sqrt(369) =sqrt(c^2)

19.20937271=c

To the nearest tenth

19.2 = c

Answer:

Diagonal of rectangle walk = 19.2 meter (Approx.)

Step-by-step explanation:

Given:

Length of rectangle = 12 meter

Width of rectangle = 15 meter

Find:

Diagonal of rectangle walk

Computation:

Diagonal of rectangle = √l² + b²

Diagonal of rectangle walk = √Length of rectangle² + Width of rectangle²

Diagonal of rectangle walk = √12² + 15²

Diagonal of rectangle walk = √144 + 225

Diagonal of rectangle walk = √369

Diagonal of rectangle walk = 19.2093

Diagonal of rectangle walk = 19.2 meter (Approx.)

The IS relation is given by: Y = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places) in the numerical example of the IS-LM model.

To derive the IS relation, we need to equate aggregate demand (AD) to aggregate supply (AS). Aggregate demand consists of consumption (C), investment (I), government spending (G), and net exports (NX). In this case, we assume net exports to be zero.

Given:

C = 233 + 0.47YD

I = 143 + 0.22Y - 1,094i

G = 299

T = 239

Aggregate demand (AD) = C + I + G

Substituting the given equations into AD:

AD = (233 + 0.47YD) + (143 + 0.22Y - 1,094i) + 299

Simplifying:

AD = 233 + 143 + 299 + 0.47YD + 0.22Y - 1,094i

Combining like terms:

AD = 675 + 0.47YD + 0.22Y - 1,094i

Since we want an equation with Y on the left side, we need to express YD in terms of Y by substituting YD = Y - T.

AD = 675 + 0.47(Y - T) + 0.22Y - 1,094i

AD = 675 + 0.47Y - 0.47T + 0.22Y - 1,094i

Combining like terms again:

AD = (0.47Y + 0.22Y) + (675 - 0.47T - 1,094i)

AD = 0.69Y - 0.47T - 1,094i + 675

Comparing with the IS relation Y = a + bAD, we have:

Y = 0.69Y - 0.47T - 1,094i + 675

Rearranging terms to have Y on the left side:

Y - 0.69Y = -0.47T - 1,094i + 675

0.31Y = -0.47T - 1,094i + 675

Dividing both sides by 0.31:

Y = (-0.47T - 1,094i + 675) / 0.31

Now, we can calculate the intercept and slope terms:

Intercept term = (-0.47T - 1,094i + 675) / 0.31

Slope term = 1 / 0.31

Rounding these values to two decimal places, the IS relation is:

Y = Intercept term + Slope term = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places).

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Answer:

24.2 units²

Step-by-step explanation:

Given

A = \(\frac{1}{2}\) a( b + c)

Substitute the given values for a, b and c , that is

A = \(\frac{1}{2}\) × 4.4 × (8 + 3)

   = 2.2 × 11

   = 24.2

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Answer:

the answer is x = 2

Step-by-step explanation:

2x+2=4+1x

(2x-1x)+2= 4 +(1x-1x)

1x+2=4

1x(2-2)=(4-2

1x=2

2/1=x

x=2

Answer: X=2

I might be wrong

Answer:

C. 11/4

Step-by-step explanation:

We can make 2 into fourths: in one whole there are 4 fourths so in two wholes there are 8 fourths.

Then add the 3/4 to the 8/4 and we get 11/4.

C. 11/4

Answer:

43.3 cupcakes

Step-by-step explanation:

If shamans has 3&1/3 cups of flour to make cupcakes. If she needs 1/13 cup of flour to make one cupcake how many full cupcakes can she make

From the above question

1/ 13 cup = 1 cup cake

3 1/3 cups = x

Cross Multiply

1 /13 × X = 3 1/3 × 1

x = 10/3 ÷ 1 /13

x = 10/3 × 13/1

x = 130/3

x = 43.333333333 cupcakes