If p varies directly with T and p =105 when T=400.Find p when T =500

Answer:

3053.5517 cm^3 ; 1/8

Step-by-step explanation:

Given the following :

Volume (V) of sphere = (4/3)πr^3 where r = radius

Diameter of sphere = 18 ; radius(r) = diameter / 2 = 18/2 = 9cm

V = (4/3) × π × 9^3

V = 1.3333 × π × 729

V = 3053.5517 cm^3

When diameter(d) is reduced to half

d = d/2

Volume (V1) of sphere with diameter 'd' =

V1 = (4/3)π(d/2)^3

Volume (V2) of sphere with diameter 'd' reduced to half, d = d/2, d/2 * 1/2 = d/4

V2 = (4/3)π(d/4)^3

V1 / V2 = [(4/3)π(d/2)^3] / [(4/3)π(d/4)^3]

V1 / V2 = (d/2)^3 / (d/4)^3

V1 / V2 = [d^3 / 2^3] / [d^3 / 4^3]

V1 / V2 = 8 / 64

V1 / V2 = 1 / 8

Answer:

first blank is 972

second blank is 1/8

yup

Step-by-step explanation:

Answer:

n = 24

Step-by-step explanation:

Given the fraction:

[tex]$\frac{n}{n+101}$[/tex]

To find:

Smallest positive integer [tex]$n$[/tex] such that the fraction is equal to a terminating decimal.

Solution:

The rule that a fraction is equal to a terminating decimal states that, the denominator must contain factors of only 2 and 5.

i.e. Denominator must look like [tex]2^m\times 5^n[/tex], only then the fraction will be equal to a terminating decimal.

Now, let us have a look at the denominator, [tex]n+101[/tex]

Let us use hit and trial method to find the value of [tex]n[/tex] as positive integer.

n = 1, denominator becomes 102 = [tex]2 \times 3 \times 17[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 4, denominator becomes 105 = [tex]5 \times 3 \times 7[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 9, denominator becomes 110 = [tex]2 \times 5 \times 11[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 14, denominator becomes 115 = [tex]5 \times 23[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 19, denominator becomes 120 = [tex]5 \times 3 \times 2^3[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 24, denominator becomes 125 = [tex]2^0 \times 5 ^3[/tex] It is of the form [tex]2^m\times 5^n[/tex].

So, the answer is n = 24

Answer:

x = 3

Step-by-step explanation:

j(x) = 4/5(-5) + 7

= -4 + 7

= 3

Answer:

15

Step-by-step explanation: -4/5 x has to be -12 because -12+7 equals 5. Since we want to figure out x, we have to flip -4/5 x to 4/5x which would change the -12 to 12. What is a fourth of 12? It is three. 12+3 equals 15. This is the first right answer on all of the internet for this question!

Answer:

Step-by-step explanation:

Adding both equations

4x+5y+5y-4x=19+38

10y = 57

y= 5.7

Subtracting equation i from ii

5y-4x-4x-5y=38-19

-8x=9

x= -0.9

Answer:

For "Negative 23 greater-than x" , highlight the left half of the number line starting at -23 and use a parenthesis ) on -23.

For "x greater-than-or-equal-to negative 23", highlight the right half of the number line starting at -23, and use a square bracket [ on -23.

Step-by-step explanation:

Start by locating the number -23 on the number line. Please see attached image to accompany the explanation.

In the first case:  "Negative 23 greater-than x" , which is expressed mathematically as:

[tex]-23 >x[/tex]

notice that "x" has to be strictly smaller than the number -23, therefore those sought x values must reside to the left of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself shouldn't be considered as part of the set, that symbol is by convention a parenthesis ).

In the second case: "x greater-than-or-equal-to negative 23", which is expressed mathematically as:

[tex]x\geq -23[/tex]

notice that "x" has to be greater than or equal to the number -23, therefore those sought x values must reside to the right of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself should be considered as part of the set, that symbol is by convention a square bracket [.

Answer:

the answer is A

Step-by-step explanation:

Answer:

9.1 hours

Step-by-step explanation:

Given

Sally

Speed = 66mph

Keith

Speed = 75mph

Time = 8 hours

Required

Determine how long Sally has traveled

To solve this, we make use of Speed formula.

Speed = Distance/Time

Make Distance the subject of formula

Distance = Speed * Time

For Sally:[Substitute 66mph for speed]

Distance = 66 * Time ------ Equation 1

For Keith [Substitute 75mph for speed and 8 hours for Time]

Distance = 75 * 8

Distance = 600m----- Equation 2

From the question, we understand that Keith caught up; this implies that they've both traveled the same distance.

Hence;

Equation 1 = Equation 2

66 * Time = 600

Time = 600/66

Time = 9.1 hours

Hence, Sally has traveled 9.1 hours

Write it out as an equation:

(48 /(5+(11-8))) -7

Simplify:

(48/(5+3))-7

(48/8)-7

6-7 = -1

The answer is -1

Answer:

fifth option

Step-by-step explanation:

Given

- 2(x - 5) ≤ 6x + 18 ← distribute left side

- 2x + 10 ≤ 6x + 18 ( subtract 6x from both sides )

- 8x + 10 ≤ 18 ( subtract 10 from both sides )

- 8x ≤ 8

Divide both sides by - 8, reversing the sign as a result of dividing by a negative quantity, thus

x ≥ - 1

Answer:  D. (-2, -1)

Step-by-step explanation:

Here we do two reflections to the point (-1, 2).

First, we do a reflection over the line x = y.  Remember that a reflection over a line keeps constant the distance between our point and the given line, so we have that for a pint (x, y), the reflection over the line y = x is:

Ry=x (x, y) = (y, x)

so for our point, we have:

Ry=x (-1, 2) = (2, -1)

Now we do a reflection over the y-axis, again, a reflection over a line keeps constant the distance between our point and the given line, so if we have a point (x,y) and we do a reflection over the y-axis, our new point will be:

Ry-axis (x,y) = (-x, y)

Then in our case:

Ry-axis (2, -1) = (-2, -1)

The correct option is D.

Answer:

Below

Step-by-step explanation:

All figures are squares. The area of a square is the side times itself

Let A be the area of the big square and A' the area of the small one in all the 5 exercices

51)

● (a) = A - A'

A = c^2 and A' = d^2

● (a) = c^2 - d^2

We can express this expression as a product.

● (b) = (c-d) (c+d)

■■■■■■■■■■■■■■■■■■■■■■■■■■

52)

● (a) = A-A'

A = (2x)^2 = 4x^2 and A'= y^2

● (a) = 4x^2 - y^2

● (b) = (2x-y) ( 2x+y)

■■■■■■■■■■■■■■■■■■■■■■■■■■

53)

● (a) = A-A'

A = x^2 and A' = y^2

● (a) = x^2-y^2

● (b) = (x+y) (x-y)

■■■■■■■■■■■■■■■■■■■■■■■■■■

54)

● (a) = A-A'

A = (5a)^2 = 25a^2 and A' =(2b)^2= 4b^2

● (a) = 25a^2 - 4b^2

● (a) = (5a-2b) (5a+2b)

■■■■■■■■■■■■■■■■■■■■■■■■■■

55)

● (a) = A - 4A'

A = (3x)^2 = 9x^2 and A'= (2y)^2 = 4y^2

● (a) = 9x^2 - 4 × 4y^2

● (a) = 9x^2 - 16y^2

● (a) = (3x - 4y) (3x + 4y)

Answer:

Step-by-step explanation:

-d - 4 = -8

-d = -4

d = 4

Answer:

d= 4

Step-by-step explanation:

4d - 4 = 5d – 8

Subtract 4d from each side

4d-4d - 4 = 5d-4d – 8

-4 = d-8

Add 8 to each side

-4+8 = d-8+8

4 =d

Answer:

less than or equal to it hope this helps you!

Answer:

5(12 : 3) -8

Step-by-step explanation

when you solve the first half of the equation you get 1.

so 9-1 is 8.

Answer:

f(x) = 5 * ( 8/5) ^x

Step-by-step explanation:

f(x) = a b^x

Let x = 0

5 = a * b^0

5 = a*1

a = 5

Let x = 1

8 = 5 * b^1

Divide each side by 5

8/5 = b

f(x) = 5 * ( 8/5) ^x

Answer:

(0,-3)

Step-by-step explanation:

You can plug in x and y into the equations to see if it works.

(-1,5)

2(-1)-(-5)=-2+5=3 Yes

(-1)+2(-5)=-1-10=-11 No

So (-1,5) Does NOT work.

(0,3)

2(0)-(-3)=0+3=3 Yes

(0)+2(-3)=0-6=-6 Yes

So (0,-3) DOES work.

Answer:

1. Tan θ = √11/5

2. Cosec θ = 6√11 /11

3. Cos θ = 5/6

Step-by-step explanation:

Let the side opposite to angle θ be y.

The value of y can be obtained by using the pythagoras theory as follow:

b² = 6² – 5²

b² = 36 – 25

b² = 11

Take the square root of both side.

b = √11

1. Determination of Tan θ

Tan θ =?

Opposite = √11

Adjacent = 5

Tan θ = Opposite /Adjacent

Tan θ = √11/5

2. Determination of Cosec θ.

We'll begin by calculating the Sine θ. This is illustrated below:

Sine θ =?

Opposite = √11

Hypothenus = 6

Sine θ = Opposite /Hypothenus

Sine θ = √11/6

Now, we shall determine Cosec θ as follow:

Cosec θ = 1/Sine θ

Sine θ = √11/6

Cosec θ = 1 ÷ √11/6

Cosec θ = 1 × 6/√11

Cosec θ = 6/√11

Rationalise the denominator

Cosec θ = 6/√11 × √11/√11

Cosec θ = 6√11 /11

3. Determination of Cos θ.

Cos θ =?

Adjacent = 5

Hypothenus = 6

Cos θ = Adjacent / Hypothenus

Cos θ = 5/6

square ?

although this statement doesn't make any sense.

Answer:

Square!

Step-by-step explanation:

A rectangle is a parallelogram with all its interior angles being 90 degrees. A rhombus is a parallelogram with all its sides equal. This means that for a rectangle to be a rhombus, its sides must be equal. When this is satisfied, we have a square.

Hope helped.. If yes mark me BRAINLIEST

TYSM!

Answer:

  842, 743, 394, 305, 836

Step-by-step explanation:

We arbitrarily chose the ones digit to start with as 2. (It must be 5 or less.) The other two digits are chosen by a random number generator, as shown in the attached.

The 5 three-digit numbers we chose are ...

  842, 743, 394, 305, 836

Answer:

The only criteria the question gives are that there must be 5 numbers, and the numbers must have 3 digits. The ones digit in the numbers should go up by 1.

So, we can have 111, 112, 113, 114, and 115.

Hope this helps!

Answer:

Marie´s error was not to consider the number 8:

4x - 8 = 36

it´s equal to:

(4x-8)/4 = 36/4

4x/4 - 8/4 = 36/4

x - 2 = 9

x = 9+2

x = 11

probe:

4*11 - 8 = 36

44 - 8 = 36

Marie did not add 8 on the right-hand side so by considering it the solution of the given equation will be 11.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given equation,

4x - 8 = 36

Marie add +8 on the left-hand side but forgot to add it to the right-hand side.

Thus, add +8 on the left as well as the right-hand side.

4x - 8 + 8 = 36 + 8

4x = 44

x = 11

Hence "Marie did not add 8 on the right-hand side so by considering it the solution of the given equation will be 11".

For more about the equation,

brainly.com/question/10413253

#SPJ2

Answer:

n = 5

Step-by-step explanation:

To start off, we know that whenever the bases are the same, their exponents are equal to each other. Therefore, since both of the numbers bases are the same (both are z), we know that they will be equal.

The n can be distributed to the [tex]z^2[/tex] so that it now reads to be:

[tex]z^2^n = z^{10}[/tex]

Exponents are equal, so:

2n=10

Divide the 2 on both sides:

n=5

Answer:

n =5

Step-by-step explanation:

z^2^n

We know that a^b^c = a^ (b*c)

z^(2n)

This is equal to z^10

Since the bases are the same, the exponents are the same

2n = 10

Divide by 2

2n/2 = 10/2

n = 5

Answer:

(- 1/2,5/3)

Step-by-step explanation:

Answer:

[tex]\huge\boxed{f = 5\ Hz}[/tex]

Step-by-step explanation:

Given:

Time period = T = 0.2 sec

Required:

Frequency = f = ?

Formula:

f = 1/T

Solution:

f = 1/0.2

f = 5 Hertz

Answer:

[tex] \boxed{\sf Frequency \ (f) \ of \ the \ wave = 5 \ Hz} [/tex]

Given:

Time Period (T) = 0.2 s

To Find:

Frequency (f) of the wave

Step-by-step explanation:

[tex] \sf Frequency (f) = \frac{1}{Time Period (T)} [/tex]

[tex] \sf f = \frac{1}{0.2} [/tex]

[tex] \sf f = \frac{1}{0.2} \times \frac{10}{10} [/tex]

[tex] \sf f = \frac{10}{2} [/tex]

[tex] \sf f = \frac{ \cancel{2} \times 5}{ \cancel{2}} [/tex]

[tex] \sf f = 5 \: Hz[/tex]

Answer:

∠T ≅ ∠A

Step-by-step explanation:

Since, ∆MTW ≅ ∆CAD

Therefore, ∠T ≅ ∠A (cpct)

Answer:

C. [tex]x[/tex] and $(x-6)$

Step-by-step explanation:

The roots of the quadratic equation are $0$ and $6$.

Hence the equation is $(x-0)(x-6)=x(x-6)$

Answer:

See below

Step-by-step explanation:

Answer:

the other factor is (x+7)

Step-by-step explanation:

Given x^2+11x+28

factor into

x^2+7x + 4x + 28

=x(x+7) + 4(x+7)

= (x+4)(x+7)

Answer: the other factor is (x+7)

Answer:

30

Step-by-step explanation:

6x

Replace 'x' with 5.

6(5) =

6 * 5 =

30

Hope this helps.

Answer:

30

Step-by-step explanation:

6 x 5 = 30

Answer:

c

Step-by-step explanation:

i did the quiz

Answer:

8(a + b)

Step-by-step explanation:

Sun of a and b = a + b

8 times of (a + b) = 8(a + b)

Answer:

The correct option is;

B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t

Step-by-step explanation:

The given parameters are;

The number of T-shirts, t, and shorts, s, Tim must design a day = 12

The maximum number of T-shirts and shorts Tim can design a day = 30

The maximum number of hours Tim can work = 18 hours

Therefore, we have;

The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs

Which gives;

s ≥ 12 - t

Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs

Which gives;

s ≤ 30 - t

The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24

The fraction of 36 minutes in 45 minutes = 36/45 = 0.667

Therefore we have;

The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts

Which gives;

s ≤ 24 - 0.66·t

The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.

Answer:

B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0

Step-by-step explanation:

Hope this helps!!

Answer: 15

Step-by-step explanation:

General terms in AP

f, f+d, f+2d, f+3d, ....  , where f= first term and d= common difference.

The given A.P. : 18, a, b, - 3

here, f= 18    

[tex]f+d= a ...(i)\\\\f+2d = b ...(ii)\\\\f+3d= -3 ...(iii)\\\\[/tex]

Put f= 18 in (iii) ,

[tex]18+3d=-3\\\\\Rightarrow\ 3d= -3-18\\\\\Rightarrow\ 3d= -21\\\\\Rightarrow\ d=-7[/tex]

Put f= 18 and d= -7 in (i) and (ii) , we get

[tex]a=18+(-7)=11\\\\b=18+2(-7)\\\\\Rightarrow\ b=18-14\\\\\Rightarrow\ b=4[/tex]

Now, [tex]a+b= 11+4=15[/tex]

Hence, the correct answer is "15".