Two brothers are sharing a certain sum of money in the ratio 2/3 : 3/5, if the largest share was Gh¢500.00. How much was shared between them?​

Answer:

aef true and bcd false

hope u get well in your exams

Step-by-step explanation:

Given:

z be inversely proportional to the cube root of y.

When y =0.064, then z =3.

To find:

a) The constant of proportionality k.

b) The value of z when y = 0.125.​

Solution:

a) It is given that, z be inversely proportional to the cube root of y.

[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]

[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex]              ...(i)

Where, k is the constant of proportionality.

We have, z=3 when y=0.064. Putting these values in (i), we get

[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]

[tex]3=k\dfrac{1}{0.4}[/tex]

[tex]3\times 0.4=k[/tex]

[tex]1.2=k[/tex]

Therefore, the constant of proportionality is [tex]k=1.2[/tex].

b) From part (a), we have [tex]k=1.2[/tex].

Substituting [tex]k=1.2[/tex] in (i), we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]

We need to find the value of z when y = 0.125.​ Putting y=0.125, we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]

[tex]z=\dfrac{1.2}{0.5}[/tex]

[tex]z=2.4[/tex]

Therefore, the value of z when y = 0.125 is 2.4.

Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n}[/tex]

or

[tex]n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For the given case, it is given that:

[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]

Let the constant of proportionality be k, then we have:

[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]

It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:

[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]

Thus,  the constant of proportionality k is 1.2. And the relation between z and y is:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]

Putting value y = 0.0125, we get:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]

Thus, for the given relation between y and z, we have:

Learn more about proportionality here:

https://brainly.com/question/13082482

Answer:

1/3 = 1 serving

2/3 =2 servings

1 cup= 3 servings

so if one cup is 3 servings we can multiply 3 x 6 for an answer of 18 servings

Answer:

$389.73 in change

Step-by-step explanation

500-( (18.95 x 3)+(26.71 x 2) )=

500-(56.85+53.42)=

500-110.27=

389.73

Answer:

It is x=908.

Might be wrong tho so dont jump me

Answer: 908

Step-by-step explanation:

x/4 = 89 + 138

x/4 = 227

x = 227 x 4

x = 908

Answer:

Step-by-step explanation:

Think of it as if he paid for each ticket with one $20 bill.

He gets $3 change from each one so his total change is $(

Answer:

45

Step-by-step explanation:

45-5= 40

40*2= 80

Answer:

angle KPN=95 degree

Step-by-step explanation:

angle KPN = angle JPO (because they are vertically opposite angles)

Now,

angle JPO+angle LOP=180 degree(being co interior angles)

angle JPO + 85 =180

angle JPO =180-85

angle JPO =95

since angle JPO is equal to KPN ,angle KPN is 95 degree

Answer: its B.

Step-by-step explanation:

have a good day hope this help

Answer:

B.3

Step-by-step explanation:

just divide 6 by 2

Answer:

[tex]secA = \frac{65}{63}[/tex]

Step-by-step explanation:

[tex]cosec A = \frac{65}{16}\\\\sin A = \frac{1}{cosecA} = \frac{16}{65}\\\\cos^2 A = 1 - sin^2 A[/tex]

        [tex]= 1 - (\frac{16}{65})^2\\\\=\frac{4225-256}{4225}\\\\=\frac{3969}{4225}\\[/tex]

[tex]cos A = \sqrt{\frac{3696}{4225}} = \frac{63}{65}[/tex]

[tex]secA = \frac{1}{cosA} = \frac{65}{63}[/tex]

Answer:

9uv⁴

Step-by-step explanation:

9uv⁴(2v-3v+6)

Answer:

Factor out 9uv^4 from the expression

9uv^4(2uv - 3v + 6)

If you need more steps just ask :)

Answer:

Pedro vendió = 320 calendarios

Katrina vendió = 200 calendarios

Step-by-step explanation:

Dejemos que el número de calendarios

Pedro vendió = x

Katrina vendió = y

Pedro y su compañera Karina vendieron 520 calendarios en diciembre.

x + y = 520 .... Ecuación 1

Pedro vendió 120 calendarios más que su socio.

x = y + 120

Sustituimos y + 120 por x

y + 120 + y = 520

2 años = 520 - 120

2 años = 400

y = 400/2

y = 200 calendarios

Resolviendo para x

x = y + 120

x = 200 + 120

x = 320 calendarios

Por lo tanto,

Pedro vendió = 320 calendarios

Katrina vendió = 200 calendarios

Answer:

1/6 (simplified)

Step-by-step explanation:

It's 3/18, but in most cases you should simplify unless it says to not.

Answer:

The rocket hits the gorund after approximately 10.71 seconds.

Step-by-step explanation:

The height of the rocket y in feet x seconds after launch is given by the equation:

[tex]y=-16x^2+165x+69[/tex]

And we want to find the time in which the rocket will hit the ground.

When it hits the ground, its height above ground will be 0. Hence, we can let y = 0 and solve for x:

[tex]0=-16x^2+165x+69[/tex]

We can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = -16, b = 165, and c = 69.

Substitute:

[tex]\displaystyle x=\frac{-165\pm\sqrt{(165)^2-4(-16)(69)}}{2(-16)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{-165\pm\sqrt{31641}}{-32}=\frac{165\pm\sqrt{31641}}{32}[/tex]

Hence, our solutions are:

[tex]\displaystyle x_1=\frac{165+\sqrt{31641}}{32}\approx 10.71\text{ or } x_2=\frac{165-\sqrt{31641}}{32}\approx-0.40[/tex]

Since time cannot be negative, we can ignore the first answer.

So, the rocket hits the gorund after approximately 10.71 seconds.

Answer:

10.71

Step-by-step explanation:

the person below was correct!

Answer:

35 or A

Step-by-step explanation:

This is a combinations problem because the order doesn't matter (it's a council, not like president and v.p.). C(7, 3) is 7!/(4!*3!) = 7*6*5/3*2 = 35. Hope this helps! :)

Answer:

-1049

Step-by-step explanation:

Let's assume it's a arithmetic sequence

a_1 = -26

d = a_2-a_1 = -11

==> a_94 = a_1+93*d = -1049

Answer:

-1071

Step-by-step explanation:

Let the common difference be 'd'.

d is 11

Find the difference from a (first term) and 11

Then use (n-1)

Answer: Each fraction is greater than the previous fraction.

Step-by-step explanation:

The fractions given are:

2/3, 4/6, 8/12, 16/24

Note that

2/3 = 4/6 = 8/12 = 16/32

The Fractions are all equal. Each fraction is equivalent to 2/3

The pattern used here is:

2/3 × 2/2 = 4/6

4/6 × 2/2 = 8/12

8/12 × 2/2 = 16/24

16/24 × 2/2 = 32/48

Each fraction is equal to the previous fraction in the pattern multiplied by 2/2

Also, the next fraction in the pattern is 32/48.

The statement that "Each fraction is greater than the previous fraction" is incorrect. The fractions are all equal.

Step-by-step explanation:

Given

Two lines are [tex]4x+3y=6[/tex] and [tex]6x+2y=10[/tex]

Two lines [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex] will intersect when

[tex]\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}[/tex]

for the given lines

[tex]a_1=4,a_2=6,b_1=3,b_2=2[/tex]

[tex]\therefore \dfrac{4}{6}\neq \dfrac{3}{2}\\\\\dfrac{2}{3}\neq\dfrac{3}{2}[/tex]

Hence, lines are intersecting

Answer:

2

Step-by-step explanation:

she will have 2 arangments of one rose and two daisies.

Answer:

2

Step-by-step explanation:

group off the daisies and rose

2 Rose's

4 raises

in order to make it identical

group 1 consist of ( 1 rose and 2 daisies)

group 2 consist of (1 rose and 2 daises)

only 2 bouquets

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

╭═══════ღ❦ღ══╮

Os números em notação científica são os seguintes : -

1) 5,000,000,000,000 ⟹ [tex]\boxed{5 × 10^{12}}[/tex]

2) 0,000,007 ⟹ [tex]\boxed{7 × 10^{0}}[/tex]

3) 58,600,000,000,000 ⟹ [tex]\boxed{5.86 × 10^{13}}[/tex]

4) 0,000,005,874 ⟹ [tex]\boxed{5.874 × 10^{3}}[/tex]

╰══ღ❦ღ═══════╯

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# [tex]\large\boxed{RainbowSalt2^{2}2^{2}}[/tex] ღ

Answer:

zero

Step-by-step explanation:

everything is theoretically possible

Answer:

Step-by-step explanation:

The area of 1 face is s^2

The area of 6 faces is 6s^2

6s^2 = 433.5                 Divide by 6

s^2 = 433.5 / 6

s^2 = 72.25                   Take the square root of both sides

sqrt(s^2) = sqrt(72.25)

s = 8.5

Normally you would find the volume of parallelepiped by using L * W * H

Since L W and H are all equal in a cube, the volume = s^3

S^3 = 8.5^3 = 614.125

Answer:

[tex]\bar x = 260.1615[/tex]

[tex]\sigma = 70.69[/tex]

The confidence interval of standard deviation is: [tex]53.76[/tex] to [tex]103.25[/tex]

Step-by-step explanation:

Given

[tex]n =20[/tex]

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}[/tex]

[tex]\bar x = \frac{5203.23}{20}[/tex]

[tex]\bar x = 260.1615[/tex]

[tex]\bar x = 260.16[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

[tex]\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}[/tex][tex]\sigma = \sqrt{\frac{94938.80}{19}}[/tex]

[tex]\sigma = \sqrt{4996.78}[/tex]

[tex]\sigma = 70.69[/tex] --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

[tex]c =0.95[/tex]

So:

[tex]\alpha = 1 -c[/tex]

[tex]\alpha = 1 -0.95[/tex]

[tex]\alpha = 0.05[/tex]

Calculate the degree of freedom (df)

[tex]df = n -1[/tex]

[tex]df = 20 -1[/tex]

[tex]df = 19[/tex]

Determine the critical value at row [tex]df = 19[/tex] and columns [tex]\frac{\alpha}{2}[/tex] and [tex]1 -\frac{\alpha}{2}[/tex]

So, we have:

[tex]X^2_{0.025} = 32.852[/tex] ---- at [tex]\frac{\alpha}{2}[/tex]

[tex]X^2_{0.975} = 8.907[/tex] --- at [tex]1 -\frac{\alpha}{2}[/tex]

So, the confidence interval of the standard deviation is:

[tex]\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }[/tex] to [tex]\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }[/tex]

[tex]70.69 * \sqrt{\frac{20 - 1}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{20 - 1}{8.907}[/tex]

[tex]70.69 * \sqrt{\frac{19}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{19}{8.907}[/tex]

[tex]53.76[/tex] to [tex]103.25[/tex]

Answer:

Last image.

Step-by-step explanation:

So, we know that the orginal graph is of [tex]\sqrt[7]{x}[/tex]

We need to find the graph of [tex]-\sqrt[7]{x}-8[/tex]

First off, we see a negative in front of the root.

This means that all the values will be flipped across the x axis.

This removes the first two answer graphs, for they are of the postive root.

Next, we have a -8 following the root.

So, when another number is inside of the root(example: [tex]\sqrt[7]{x-6}[/tex]) You are going to add 6 to the x axis, basically shifting everything to the right(postive). If it was a postive 6 inside the root, we would move it left(negative)

This is not what is being done in our graph, I just wanted to explain this for future graphing.

Now, when a number is outside the root, such as the one above, then it shifts the y axis. In this case we have a -8 outside the root. This means that the graph will be shifted down(negative) by 8.

This eliminates the 3rd graph image, leaving the last graph answer shown below.

Hope this helps!

Answer:

Peter needs to get 36 problems correct to get 12 stars

Step-by-step explanation:

for every 3 correct answers, Peter gets 1 star

1/3

if he wants 12 stars he will have to get 'x' amount of questions correctly

considering this is constant, 1/3 will have to equal 12/x

[tex]\frac{1}{3} = \frac{12}{x} \\\\1x = 36\\[/tex]

1x = x, so you don't need to do anything to 36

therefore the answer is that you need to get 36 problems correct to get 12 stars

Answer: [tex]\dfrac{49}{50}[/tex]

Step-by-step explanation:

Given

Length of the stick is [tex]2y\ m[/tex]

A piece of [tex]4y\ cm[/tex] is cut

We know, 1 m=100 cm

So, [tex]2y\ m[/tex] in cm is [tex]200y\ cm[/tex]

Remaining length after cut is

[tex]\Rightarrow 200y-4y=196y[/tex]

Fraction of length that is left after the cut is

[tex]\Rightarrow \dfrac{196y}{200y}\\\\\Rightarrow \dfrac{49}{50}[/tex]

Thus, [tex]\frac{49}{50}[/tex] fraction of original stick remains after cut