In 2004 there were 7,000000 people living alone in great Britain this is four time as many as in 1961, Calculate how many people lived alone in 1961. Express your answer in standard form

Answer:

w=4

Step-by-step explanation:

[tex]\large\bold{\underline{\underline{ 4( {x - 7})^{2} }}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]4x {}^{2} - 56x + 196[/tex]

Take [tex]4[/tex] as the common factor.

[tex] = 4( {x}^{2} - 14x + 49)[/tex]

[tex] = 4( {x}^{2} - 7x - 7x + 49)[/tex]

Taking [tex]x[/tex] as common from first two terms and [tex]7[/tex] from last two terms, we have

[tex] = 4 \: [ x(x - 7) - 7(x - 7) ][/tex]

Taking the factor [tex](x-7)[/tex] as common,

[tex] = 4(x - 7)(x - 7)[/tex]

[tex] = 4( {x - 7})^{2} [/tex]

[tex]\bold{ \green{ \star{ \red{Mystique35}}}}⋆[/tex]

Step-by-step explanation:

A

=

h

b

b

2

=

11

·

22

2

=

121

cm²

The area of the obtuse triangle with a height of 11 cm and a base of 22 cm is 121 cm².

To determine the area of an obtuse triangle, we can use the formula for the area of a triangle, which is given by:

Area = (1/2) * base * height

In this case, the height of the triangle is given as 11 cm and the base is given as 22 cm.

Substituting these values into the formula, we have:

Area = (1/2) * 22 cm * 11 cm

Calculating this expression, we get:

Area = (1/2) * 242 cm²

Simplifying further, we have:

Area = 121 cm²

The area of a triangle is calculated by multiplying half of the base by the height. In this case, the given height is 11 cm and the base is 22 cm. Substituting these values into the formula, the area of the obtuse triangle is calculated to be 121 cm².

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Answer:

9

Step-by-step explanation:

x = 1

y = 4

x + 2y = 1 + 8 = 9

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

9

Step-by-step explanation:

x + 2y

subtitute:

1 + 2(4)

simplify:

1 + 8 = 9

Answer:

i don't know how to work this

Answer:

x = [tex]\frac{3}{4}[/tex] , x = 20

Step-by-step explanation:

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

Multiply through by (x + 2)(3x - 5) to eliminate the fractions

2(3x - 5)² - 5(x + 2)² = 3(x + 2)(3x - 5) ← expand factors on both sides

2(9x² - 30x + 25) - 5(x² + 4x + 4) = 3(3x² + x - 10) ← distribute parenthesis

18x² - 60x + 50 - 5x² - 20x - 20 = 9x² + 3x - 30 ← simplify left side

13x² - 80x + 30  = 9x² + 3x - 30 ( subtract 9x² + 3x - 30 from both sides )

4x² - 83x + 60 = 0 factor by splitting the x- term

4x² - 80x - 3x + 60 = 0

4x(x - 20) - 3(x - 20) = 0

(4x - 3)(x - 20) = 0

Equate each factor to zero and solve for x

4x - 3 = 0 ⇒ 4x = 3 ⇒ x = [tex]\frac{3}{4}[/tex]

x - 20 = 0 ⇒ x = 20

Answer:

90g strawberry jelly

6 sponge fingers

315ml custard

135g tinned fruit

Step-by-step explanation:

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

Since those ingredients that are in the question say making a trifle for four people, let's divide each ingredient by four to find the ingredients for one person, and multiply by 3 to find the ingredients for 3 people.

So,

[tex]120/4=30[/tex]g strawberry jelly

[tex]8/4=2[/tex] sponge fingers

[tex]420/4=105[/tex]ml custard

[tex]180/4=45[/tex]g tinned fruit

There are the ingredients to make a trifle for one person.

-------------------->>>>

Now, let's multiply each of the ingredients for one person and multiply that by three to find the ingredients needed to make a trifle for four people.

[tex]30*3=90[/tex]g strawberry jelly

[tex]2*3=6[/tex] sponge fingers

[tex]105*3=315[/tex]ml custard

[tex]45*3=135[/tex]g tinned fruit

These are the ingredients needed to make a trifle for three people.

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

Hope this is helpful.

Answer:

17

Step-by-step explanation:

Answer:

Profit obtained by X =  Rs. 2,976.64

Profit obtained by Y = Rs. 2,545.58

Profit obtained by Z = Rs. 2,777.78

Step-by-step explanation:

Total capital for the first 6 months = Rs 5000 + Rs.4500 + Rs.6500 = Rs. 16,000

Total capital for the next 3 months = Rs. 16,000+ Rs 5000 = Rs. 21,000

Total capital for the last 3 months of the year = Rs. 21,000 + (Rs 4500 * 2) = Rs. 30,000

Share of profit of each partner is the sum of all the ratios of his capital to total capital of the business at each point in time multiply by the ratio of the numbers of months covered by each capital to 12 months and then multiply by RS.8300.

Profit obtained by X = ((Rs 5000 / 16,000) * (6 / 12) * Rs. 8300) +  ((Rs 10,000 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 10,000 / 30,000) * (3 / 12) * Rs. 8300) =  Rs. 2,976.64

Profit obtained by Y = ((Rs 4500 / 16,000) * (6 / 12) * Rs. 8300) +  ((Rs 4500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 13,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,545.58

Profit obtained by Z = ((Rs 6500 / 16,000) * (6 / 12) * Rs. 8300) +  ((Rs 6500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 6,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,777.78

Confirmation of total profit shared = Rs. 2,976.64 + = Rs. 2,545.58 + Rs. 2,777.78 = Rs. 8,300

Answer:

There is a non-removable discontinuity at x = 3

Step-by-step explanation:

We are  given that

[tex]f(x)=\frac{x^2+9}{x-3}[/tex]

We have to find true statement about given function.

[tex]\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}[/tex]

=[tex]\infty[/tex]

It is not removable discontinuity.

x-3=0

x=3

The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.

Therefore, x=3 is non- removable discontinuity of function f(x).

Hence, option B is correct.

Answer:

[tex]q = 3[/tex]

Step-by-step explanation:

[tex]3q−2=7[/tex]

[tex]3q=7+2[/tex]

[tex]3q=9[/tex]

[tex]q = 3[/tex]

Answer:

2, 3, 7 or 8

Step-by-step explanation:

Answer:

h = hamburgers sold

2h - 72 = 578

2h = 650

2       2

h = 325

There were 72 fewer cheeseburgers sold than hamburgers. That means cheeseburgers = 325 - 72

325 - 72 =  253

253 = cheeseburgers

325 = hamburgers

253 + 325 = 578

Hamburgers = 325

Hope this helps :)

Answer:

[tex]x = 0.143[/tex]

[tex]P(High\ |\ Cancer) = 0.215[/tex]

Not independent

Step-by-step explanation:

Given

See attachment for proper table

Solving (a): The missing probability

First, we add up the given probabilities

[tex]Sum = 0.242+0.047+0.079+0.391+0.098[/tex]

[tex]Sum = 0.857[/tex]

The total probability must add up to 1.

If the missing probability is x, then:

[tex]x + 0.857 = 1[/tex]

Collect like terms

[tex]x = -0.857 + 1[/tex]

[tex]x = 0.143[/tex]

Solving (b): P(High | Cancer)

This is calculated as:

[tex]P(High\ |\ Cancer) = \frac{n(High\ n\ Cancer)}{n(Cancer)}[/tex]

So, we have:

[tex]P(High\ |\ Cancer) = \frac{0.079}{0.242+0.047+0.079}[/tex]

[tex]P(High\ |\ Cancer) = \frac{0.079}{0.368}[/tex]

[tex]P(High\ |\ Cancer) = 0.215[/tex]

Solving (c): P(Leukemia) independent of P(High Wiring)

From the attached table

[tex]P(Leukemia\ n\ High\ Wiring) = 0.242[/tex]

[tex]P(Leukemia) = 0.242 + 0.391 =0.633[/tex]

[tex]P(High\ Wiring) = 0.242+0.047+0.079=0.368[/tex]

If both events are independent, then:

[tex]P(Leukemia\ n\ High\ Wiring) = P(Leukemia) * P(High\ Wiring)[/tex]

[tex]0.242 = 0.633 * 0.368[/tex]

[tex]0.242 \ne 0.232[/tex]

Since the above is an inequality, then the events are not independent

Answer:

B. x=4

Step-by-step explanation:

I hope this helps!

Answer:

90

Step-by-step explanation:

Answer:

408 cm²

Step-by-step explanation:

the total SA = (2×½×6×8) + (10+8+6)×15

= 48 + 360

= 408 cm²

The total surface area of the prism that has a triangular base of 10 cm, 8 cm, and 6cm and it is 15 cm long is 408 cm².

In order to create the triangle base, the three triangular sides slant upward. A pyramid with a triangular base is also known as a tetrahedron since it is made up of four triangles.

The shape of a pyramid's base is often used to describe it. A hexagonal pyramid has a base that is a hexagon, as does a triangular pyramid, for example. Pyramids with triangular bases are called triangular pyramids.

A triangle's area is equal to half the sum of its base and height, according to the formula for triangular bases. Whether it be a scalene triangle, an isosceles triangle, or an equilateral triangle, this formula can be used to determine their properties.

The total surface area of the prism calculations are,

b = 6 cm, h = 8 cm, l = 10 cm, and L = 15 cm

[tex]Total\ Surface\ Area = (2\times \frac{1}{2} \times b \times h) + (l+h+b) \times \\ L=(2\times \frac{1}{2} \times 6 \times 8) + (10+8+6) \times 15\\= 48 + 360\\= 408 cm^2[/tex]

Therefore, total surface area of the prism that has a triangular base of 10 cm, 8 cm, and 6cm and it is 15 cm long is 408 cm².

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Given:

AB formed by (-2,13) and (0,3).

CD formed by (-5,0) and (10,3).

To find:

Whether the segments AB and CD are parallel, perpendicular, or neither.

Solution:

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

AB formed by (-2,13) and (0,3). So, the slope of AB is:

[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]

[tex]m_1=\dfrac{-10}{2}[/tex]

[tex]m_1=-5[/tex]

CD formed by (-5,0) and (10,3). So, slope of CD is:

[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]

[tex]m_2=\dfrac{3}{10+5}[/tex]

[tex]m_2=\dfrac{3}{15}[/tex]

[tex]m_2=\dfrac{1}{5}[/tex]

Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.

[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]

[tex]m_1\times m_2=-1[/tex]

Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.

Hence, the segments AB and CD are perpendicular.

Answer:

AB is perpendicular to CD.

Step-by-step explanation:

AB formed by (-2, 13) and (0, 3)

CD formed by (-5, 0) and (10, 3)

Slope of a line passing through two points is

[tex]m= \frac{y''-y'}{x''- x'}[/tex]

The slope of line AB is

[tex]m= \frac{3- 13}{0+2} = -5[/tex]

The slope of line CD is

[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]

As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.

Step-by-step explanation:

4² = 16

5² = 25

16+25 = 41

41 is the answer.

Hope it helps! :)

Answer:

[tex]( {4}^{2} + {5}^{2} ) \\ (16 + 25) \\ = 41[/tex]

Answer:

3x²+12x-2x-8. = 0

3x(X+4)-2(X+4) = 0

(x+4)(3x-2) =0

[tex]x = (- 4) \: or \: x = \frac{2}{3} \: are \: the \: solutions[/tex]

Answer:

Step-by-step explanation:   7  1  16   37

8/1     8 divided by 1

16/2   16 divided by 2

24/3   24 divided by 3       I could go on, but won't

Answer:

I believe its the 1st answer.

Answer:

D

Step-by-step explanation:

-10 < -6 - 1

-10 < - 7 (ok)

-10 < -4 - 3

-10 < -7 (ok)

The answer is D (-2, -10)

Answer:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]p = 60\%[/tex]

[tex]n = 4[/tex]

Required

The distribution of x

The above is an illustration of binomial theorem where:

[tex]P(x) = ^nC_x * p^x *(1 - p)^{n-x}[/tex]

This gives:

[tex]P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}[/tex]

Express percentage as decimal

[tex]P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}[/tex]

[tex]P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}[/tex]

When x = 0, we have:

[tex]P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}[/tex]

[tex]P(x=0) = 1 * 1 *(0.40)^4[/tex]

[tex]P(x=0) = 0.0256[/tex]

When x = 1

[tex]P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}[/tex]

[tex]P(x=1) = 4 * (0.60) *(0.40)^3[/tex]

[tex]P(x=1) = 0.1536[/tex]

When x = 2

[tex]P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}[/tex]

[tex]P(x=2) = 6 * (0.60)^2 *(0.40)^2[/tex]

[tex]P(x=2) = 0.3456[/tex]

When x = 3

[tex]P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}[/tex]

[tex]P(x=3) = 4 * (0.60)^3 *(0.40)[/tex]

[tex]P(x=3) = 0.3456[/tex]

When x = 4

[tex]P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}[/tex]

[tex]P(x=4) = 1 * (0.60)^4 *(0.40)^0[/tex]

[tex]P(x=4) = 0.1296[/tex]

So, the probability distribution is:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]0 \to[/tex] Correct

[tex]1 \to[/tex] Defective

Required

The probability that the next is defective

The question is incomplete because the list of bottles that came out is not given.

However, the formula to use is:

[tex]Pr = Num ber\ o f\ d e f e c t i v e \div T o t a l\ b o t t l e s[/tex]

Take for instance, the following outcomes:

[tex]0\ 1\ 0\ 0\ 0\ 1\ 0\ 0\ 1\ 1\ 0\ 0\ 0\ 1[/tex]

We have:

[tex]Total = 14[/tex]

[tex]D e f e ctive = 9[/tex] --- i.e. the number of 0's

So, the probability is:

[tex]Pr = 9 \div 14[/tex]

[tex]Pr = 0.643[/tex]

Answer:

1/20

Step-by-step explanation:

000000000000100000

It is asking the probability of a defective bottle

there is one defective bottle out of 20

Answer:

The slope is 1.5

Step-by-step explanation:

To get the slope of the graph, we proceed to select any two points lying on the given line, and applying the slope formula

The two selected points are as follows;

(x1,y1) = (-4,0)

(x2,y2) = (-2,3)

m = (y2-y1)/(x2-x1)

m = (3-0)/(-2-(-4)

m = 3/2 = 1.5