Peter & Alex share a lottery win of £4450 in the ratio 4 : 1. Peter then shares his part between himself, his wife & their son in the ratio 1 : 6 : 3. How much more does his wife get over their son?

Answer:

(143/74, -65/148)

Step-by-step explanation:

We have the equations:

4x - 12y = 13

14x + 32y = 13

Let's use elimination, so multiply the first equation by 8 and the second equation by 3:

8 * (4x - 12y = 13)  ⇒  32x - 96y = 104

3 * (14x + 32y = 13)  ⇒  42x + 96y = 39

Add those two equations:

    32x - 96y = 104

+   42x + 96y = 39

________________

    74x  +  0y  =  143

Divide both sides by 74:

x = 143/74

Plug this into an equation to find y:

4x - 12y = 13

4 * (143/74) - 12y = 13

12y = 572/74 - 13 = -390/74

y = -65/148

The answer is (143/74, -65/148).

Answer:

x = 143/74

y = -65/148

Step-by-step explanation:

4x-12y= 13

4x = 13 + 12y

x = 13/4 + 3y

32y+14x=13

32y + 14(13/4 + 3y) = 13

32y + 91/2 + 42y = 13

74y = 13 - 91/2

74y = -65/2

y = -65/148

x = 13/4 + 3(-65/148)

x = 143/74

x = 143/74

y = -65/148

Answer:

[tex]A) t^4-1\\B)-2t^2+3t+4\\C)4t-7[/tex]

Step-by-step explanation:

When a polynomial is in standard form, it means that the terms are ordered from highest exponent to lowest exponent.

In the given options, A,B and C are ordered from the highest to the lowest and thus are in standard form.

The correct options are A,B and C.

The polynomials in standard form are:

- A [tex]\( t^4 - 1 \)[/tex]

- B [tex]\( -2t^2 + 3t + 4 \)[/tex]

- C [tex]\( 4t - 7 \)[/tex]

A polynomial is in standard form if its terms are written in descending order of their exponents. Let's evaluate each option:

- Option A: [tex]\( t^4 - 1 \)[/tex]

 - This polynomial is written in descending order of its exponents: [tex]\( t^4 \)[/tex](degree 4) and [tex]\(-1\)[/tex] (degree 0).

- Option B: [tex]\(-2t^2 + 3t + 4\)[/tex]

 - This polynomial is written in descending order of its exponents: [tex]\(-2t^2\)[/tex] (degree 2), [tex]\(3t\)[/tex] (degree 1), and [tex]\(4\)[/tex] (degree 0).

- Option C: [tex]\(4t - 7\)[/tex]

 - This polynomial is written in descending order of its exponents: [tex]\(4t\)[/tex] (degree 1) and [tex]\(-7\)[/tex] (degree 0).

-Option D: None of the above

 - Since options A, B, and C are already in standard form, option D is incorrect.

Complete question : Which polynomials are in standard form? Choose all answers that apply:

A t⁴ -1

B -2t² +3t+4

c 4t-7

D None of the above

Answer:

Area = 15 m²

Step-by-step explanation:

Area of A rectangle is length * breadth or height.

Length = 2 m

Height = 7.5 m

So the area = 2*7.5

Area = 15 m²

Answer:

12

Step-by-step explanation:

if the term to term rule is to divide by two and the third term in the sequence is 3, you work backwards by multiplying by 2

So 3x2=6

6x2= 12

Thus the first number is 12.

working forward again, you can check your answer. Divide 12 by 2, then divide 6 by 2 and you get 3, the third term if the sequence

The first term of the sequence will be 12.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The term to term rule is divide by 2 the third term of the sequence is 3.

Now,

Since, The term to term rule is divide by 2 the third term of the sequence is 3.

So, We get the second number by multiply the 2 in the third number 3.

Second number = 2 x 3

                         = 6

And, We get the first number by multiply the 2 in the second number 3.

So, First number = 6 x 2

                          = 12

Thus, The first term of the sequence will be 12.

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Final answer:

The largest volume among the rectangular prisms is 75 cm³, corresponding to the prism with dimensions l = 5 cm, w = 3 cm, and h = 5 cm.

Explanation:

To determine which rectangular prism has the largest volume, we must calculate the volume of each given prism. The volume (V) of a rectangular prism is calculated by multiplying its length (l), width (w), and height (h): V = l × w × h.

For the first prism, V = 4 cm × 5 cm × 3 cm = 60 cm³

For the second prism, V = 6 cm × 3 cm × 3 cm = 54 cm³

For the third prism, V = 2 cm × 6 cm × 6 cm = 72 cm³

For the fourth prism, V = 5 cm × 3 cm × 5 cm = 75 cm³

By comparing the volumes calculated, the prism with dimensions w = 3 cm, l = 5 cm, and h = 5 cm has the largest volume, which is 75 cm³.

Answer:

I think it's 100°

Step-by-step explanation:

Answer:

direct distance = 65,644.07 feet

horizontal distance = 65,154.77 feet

Step-by-step explanation:

The angle of depression is the angle that the airplane does with the horizontal plane.

So, if this angle is 7° and the airplane is at an altitude if 8000 feet, we can find the direct distance and the horizontal distance using the tangent and the sine relations of the angle.

In the tangent of the angle, the opposite side will be the height of the airplane, and the adjacent side will be the horizontal distance (hd), so:

tangent(7) = 8000 / hd

hd = 8000 / tangent(7) = 65,154.77 feet

In the sine of the angle, the opposite side will be the height of the airplane, and the hypotenusa will be the direct distance (d), so:

sine(7) = 8000 / d

d = 8000 / sine(7) = 65,644.07 feet

Answer:

[tex]t \approx 750550.12\,yr[/tex]

Step-by-step explanation:

The time constant of the isotope is:

[tex]\tau = \frac{1.3\times 10^{9}\,yr}{\ln 2}[/tex]

[tex]\tau \approx 1.876 \times 10^{9}\,yr[/tex]

The decay of the isotope is described by the following model:

[tex]\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]

Now, the time is cleared in the equation:

[tex]t = -\tau \cdot \ln \frac{m}{m_{o}}[/tex]

[tex]t = - (1.876\times 10^{9}\,yr)\cdot \ln 0.9996[/tex]

[tex]t \approx 750550.12\,yr[/tex]

The rock from Maui with 99.96% of its parent K-40 remaining is significantly younger than 1.3 billion years, the half-life of K-40. The precise age calculation would yield a time much less than the half-life, indicating the rock's relative youth.

The age of a rock that has 99.96% of its parent K-40 remaining can be calculated using the half-life of K-40, which is 1.3 billion years. Since such a small percentage (0.04%) of K-40 has decayed to form Ar-40, the rock sample from Maui is very young relative to the half-life of K-40. We can estimate the age of the rock by using the concept of half-lives in radioactive decay.

The formula for radioactive decay is: N(t) = N0 (1/2)^(t/T), where N(t) is the amount of the parent isotope remaining, N0 is the initial amount of the parent isotope, t is the time that has elapsed, and T is the half-life of the isotope.

In the case of Maui's rock, with N(t)/N0 being approximately 0.9996 (or 99.96/100), we can set up the equation as follows: 0.9996 = (1/2)^(t/1.3 billion years). Solving for t gives an age that is much less than 1.3 billion years, indicating that the rock is relatively young and has experienced only a fraction of a half-life period.

However, because the amount of decay is so small, it would fall within the uncertainties of practical measurement and thus would only give us an approximation that the age of the rock is significantly less than one half-life, or markedly younger than 1.3 billion years.

To find how many times greater 3 x [tex]10^8[/tex] is than 6 x [tex]10^5[/tex], divide 3 x [tex]10^8[/tex] by 6 x [tex]10^5[/tex], resulting in 500. Thus, 3 x [tex]10^8[/tex] is 500 times greater than  6 x [tex]10^5[/tex]

The question asks how many times greater is 3 x [tex]10^8[/tex] than 6 x [tex]10^5[/tex]. To compare the two values, we divide the larger number by the smaller number:
( 3 x [tex]10^8[/tex] ) / (6 x [tex]10^5[/tex]) = (3/6) x ([tex]10^8/10^5[/tex]) = 0.5 x [tex]10^3[/tex]

Since [tex]10^3[/tex] is equal to 1000, multiplying 0.5 x 1000 gives 500. Therefore, 3 x [tex]10^8[/tex] is 500 times greater than 6 x [tex]10^5[/tex].

Answer:

Step-by-step explanation:

Next time, please share the possible answer choices.

A quadratic function with one real zero actually has TWO real, identical zeros.  The vertex of the graph lies on the x-axis (touching it in only one place).

Answer:

a

Step-by-step explanation:

Answer:

1695.6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Looking at the function, we have;

V(t) = 1,000(1.06)^t

Mathematically, the amount earned on an investment that offers a particular constant percentage return to a particular number of years can be written as;

V = I(1 + r)^t

where V is the value of the investment after some certain number of years

I is the initial amount invested

r is the constant percentage increase

and t is the number of years.

Let’s now re-write what we can deduce in the question.

This is;

V(t) = 1000(1 + 0.06)^t

Thus what this 0.06 represents is r which is the constant interest rate

Answer:

B

Step-by-step explanation:

1 3/8 + 1 2/6 is equal to 2 17/24ths round up and you get 3 pizzas. 5- 3 is 2.

Answer: The price for the product is R$5.

Step-by-step explanation: Suppose the unit price of the product is X.

T is all the money I have.

In the first option, 20 units spend all my money, so:

T = 20x

In the second option, if I buy 14 of it, I have a remaining of R$30, so:

T = 14.x + 30

To determine the unit valor:

20x = 14x + 30

20x - 14x = 30

x = [tex]\frac{30}{6}[/tex]

x = 5

The product costs R$5.

Answer:

O valor unitário deste produto é de R$ 5.

Step-by-step explanation:

Ao comprar 14 unidades do produto, restam 30 Reais, ao comprar 20 unidades, não resta dinheiro, podemos afirmar que para comprar 6 unidades são necessários 30 Reais.

Portanto, para determinar o valor unitário do produto, devemos dividir os 30 Reais da troco pelas 6 unidades que não foram compradas.

Portanto, como 30/6 resulta em 5, esse é o valor unitário do produto. Cada produto vale 5 Reais.

Answer:

69 ounces of water

Step-by-step explanation:

Answer:

Step-by-step explanation:

its 69 ounces.  

i did the test and got 100% it works :)

Answer: 0.0

Step-by-step explanation:

Answer:

y=−2/3x+3

Step-by-step explanation:

I graphed the point and the equation given below. I used the same slope in the new equation as the original equation. The y-intercept is 3 because the line goes through (0,3).

Thus option C :  [tex]y = -\dfrac{2}{3}x + 3[/tex]  is correct.

Given that:

Equation of considered straight line:

[tex]y = -\dfrac{2}{3}x + 53[/tex]

Let the equation of the straight line that has to be found is given by:

[tex]y = mx + c[/tex]

It is given that the line is parallel to previous straight lines.

Which means  that slope of both the lines are same

or

[tex]m = -\dfrac{2}{3}[/tex]

Now since the second line passes through (-3,5), thus we have:

[tex]5 = -\dfrac{2}{3}\times -3 + c\\or\\c = 3[/tex]

Thus the needed equation of straight line is given by:

[tex]y = -\dfrac{2}{3}x + 3[/tex]

Thus option C :  [tex]y = -\dfrac{2}{3}x + 3[/tex]  is correct.

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Answer:

5.5lb of strawberries cost $10.78

Step-by-step explanation:

We can use ratios to solve this problem.

 lb : $$$

0.5 : 0.98

  5 : 9.8

5.5 : 10.78

5.5lb of strawberries cost $10.78

You can also divide 5.5 by 0.5 (pounds) and multiply the quotient by how much a 0.5 pound of strawberries cost.

To find the total cost of 5.5 pounds of strawberries, determine the cost of one pound by doubling the cost for a half-pound. Then multiply the cost of one pound by the quantity of pounds purchased to get the total cost, which is $10.78.

The question asks us to calculate the total cost of 5.5 pounds of strawberries when given the price for a half-pound. The first step is to determine the cost of one pound of strawberries by doubling the cost of the half-pound.

If a 1/2 pound of strawberries costs $0.98, then one pound would cost $1.96 (since 0.98 x 2 = 1.96).

Next, to find out how much 5.5 pounds would cost, multiply the cost of one pound by 5.5:

5.5 pounds of strawberries x $1.96 per pound = $10.78.

Therefore, if you bought 5.5 pounds of strawberries, you would have spent $10.78.

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To calculate the surface area of a trapezoidal prism, find the area of each of the five faces (two trapezoids and three rectangles) and sum them up.

To find the surface area of a trapezoidal prism, we have to calculate the area of each face and then sum them up. There are two trapezoidal faces and three rectangular faces in a trapezoidal prism.

For the trapezoidal face, the formula to calculate the area is 0.5*(a+b)*h where 'a' and 'b' are the lengths of the parallel bases and 'h' is the height of the trapezoid. For the rectangular faces, the area is simply length times width.

After finding these, add them all up. This sum gives us the total surface area of the trapezoidal prism.

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Answer:

60%

Step-by-step explanation:

To know the discount, we must know how much that $ 18 represents of the original price, as follows:

18/45 = 0.4

That is, $ 18 is 40% of $ 45

Therefore, to calculate the discount we must subtract what represents 45%, that is, 100%

100% - 40% = 60%

In other words, the discount is 60%

Answer:

60

Step-by-step explanation:

Answer:

y = -6 * x^3

Step-by-step explanation:

We can model the new function as:

f(x) = ax^3

the function y = x^3 have positive values of y for positive values of x, and negative values of y for negative values of x.

As the negative values of x have positive values of y and vice-versa, the first change is to put a negative sign in front of x^3, so we know that 'a' is negative.

Then, for x=1 we have y = -6, so:

-6 = a*1^3

a = -6

So the equation of the transformed function is:

y = -6 * x^3

Answer:

A

Step-by-step explanation:

Because think about it if there’s no one working in a business then there’s no work and no one gets paid in their business that’s how technology affects places where people work.

The answer is option C - More people are working from a remote location rather than an office building.

Technology has enabled a significant shift in the way people work, allowing many to perform their tasks remotely from locations outside of traditional office settings. With advancements in communication technology, internet connectivity, and collaboration tools, individuals can now work from virtually anywhere with an Internet connection. This trend towards remote work has been accelerated by factors such as the COVID-19 pandemic, which necessitated remote work arrangements for many organizations.

As a result, more people are opting to work from home, co-working spaces, or other remote locations rather than commuting to and working in traditional office buildings. This shift has several implications, including increased flexibility for workers, reduced commuting time and expenses, and the ability for companies to tap into talent from diverse geographical areas without the need for physical relocation.

While some individuals still prefer or require the structure and social interaction of a traditional office environment, the rise of remote work options has fundamentally changed the landscape of where and how people work.

Answer:

[tex]\frac{x+5}{x+3}[/tex]

Step-by-step explanation:

hope this helps!

Answer:

C - 5/y+5

Step-by-step explanation:

edge 2020

Answer:

1

Step-by-step explanation:

The radius is half the size of the diameter.

2 / 2 = 1

Answer:

h  = 9 units of length

Step-by-step explanation:

Volume of a circular right cone is:

V(c)  = (1/3)*Area of the circular base * h

Where h is the height of the cone, then

V(c)  =  (1/3) * π * r² * h

And  we have that  V(c) = 108*π

Then:

108 * π  =  (1/3) * π * r² * h                  (1)

We know diameter of the circular base is 12 units, according to that

r =  d/2     ⇒  r = 12/2     r = 6 units

Then:

108 * π  [ cubic units ]  =  (1/3) * π * (6)² * h  [square units] [ units of length]

When simplifying we have to take into account that in order to keep last equation h needs to have units of length  

Therefore:

108  =  (1/3) * 36 * h

h = ( 108* 3 )/ 36

h  = 9 units of length

Answer:

The answer is C. 103

Step-by-step explanation:

180 - 110 = 70

So, the measurement of angle z is 70.

Since parallelograms have a sum of 360°, then...

360 - (100 + 87 + 70)

360 - 257

103

YO MY N E  G G GA ITS 40 RACKS ON KEEP IT A ON GANG FORREAL MY N I 6 G A F5CK 12

Answer:

2,316 cu inch

Step-by-step explanation:

.

We have been given a graph that shows a line of best fit for data collected on the cost of hardwood flooring, from different vendors, as a function of area. We are asked to find the equation of line of best fit.

First of all, we will find the slope of line using point (0,0) and (400,1500) using slope formula.

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

[tex]m=\frac{1500-0}{400-0}[/tex]

[tex]m=\frac{1500}{400}[/tex]

[tex]m=\frac{15}{4}[/tex]

So the slope of line is [tex]\frac{15}{4}[/tex].

We can see that line starts at origin (0,0), so y-intercept will be 0.

Now we will slope-intercept form of equation [tex]y=mx+b[/tex], where m represents slope and b represents the y-intercept.

[tex]y=\frac{15}{4}x+0[/tex]

[tex]y=\frac{15}{4}x[/tex]

Therefore, our required equation would be [tex]y=\frac{15}{4}x[/tex] and option B is the correct choice.

Answer:

C

Step-by-step explanation: