simplify each of the following fractions :

25
__
30​

Answer:

On the 7th week, both Sam and Jill will have the same amount (360 dollars)

Step-by-step explanation:

Answer:

I think you've been wrong, you're ask, not answering

Answer:

Step-by-step

2/7

Given:

Initially the number of people at art museum = 250

Rate of increase = 3% per month

To find:

The number of people at art museum in the end of a year.

Solution:

The general exponential growth model is:

\(y=a\left(1+\dfrac{r}{100}\right)^t\)

Where, a is the initial value, r is the rate of increase in % and t is the time period.

We know that, 1 year = 12 months.

Putting a=250, r=3 and t=12, we get

\(y=250\left(1+\dfrac{3}{100}\right)^{12}\)

\(y=250\left(1+0.03\right)^{12}\)

\(y=250\left(1.03\right)^{12}\)

\(y=250(1.42576)\)

\(y=356.44\)

\(y\approx 356\)

The number of people at the end of a year is 356. Therefore, the correct option is D.

\(f( - 4) = - 122\)

And

\(g(5) = - 21\)

Step-by-step explanation:

Greetings !

For the first expression

\(f(x) = 2x {}^{3} + 6\)

plug in -4 at the variable x and solve the expression.

\(f( - 4) = 2( - 4) {}^{3} + 6\)

Follow the PEMDAS order of operations

calculate the exponents

\(( - 4) {}^{3} = - 64\)

Apply exponent rule

\(( - a) {}^{n} = - a {}^{n} . \: if \: n \: is \: odd\)

Thus,

\(( - 4) {}^{3} = - 4 {}^{3} = - 64\)

Multiply and divide (left to right )

\(2( - 64) = - 128\)

\( = - 128 + 6 \\ = - 122\)

Fairly follow the same. process for the second function

Hope it helps !!

Answer: B. XIX

Step-by-step explanation: If Sarah is 3 years older than Ben, she is 3 years older than 16. That means she is 19 years old. In Roman numerals, we need to think of it as she is 10+9 years old.

X represents 10.

IX represents 9 Because...

... in order to represent a number less than ten, we need to think about how much less than ten it is. Since 9 is one less than 10, you write it as IX since a smaller numeral in front of X represents subtraction.

So you combine the 10 and 9 to get XIX.

Answer:

pag times mo po sya tyaka download ka photo ma tsaka ma kipag up a9e

Answer:

6 times............ I think

Answer:

Step-by-step explanation:

x          -  age of a son three years ago

3x        -  age of a father three years ago

x + 3      -  age of the son now

3x + 3       -  age of the father now

x + 3 + 5       -  age of the son in five years time

3x + 3 + 5       -  age of the father in five years time

in five years time, the father will be twice as old as his son, so:

3x + 3 + 5 = 2(x + 3 + 5)

3x + 8 = 2x + 16

3x - 2x = 16 - 8

  x = 8

x + 3 + 4       -  age of the son in four years time

8 + 3 + 4 = 15

3x + 3 + 4       -  age of the father in four years time

3×8 + 3 + 4 = 31    

the sum of their ages in four years time:

15 + 31 = 46

The new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025

The correct equation to find the new tuition for the fall is: B. 1.15 • 3500 = x

Here's why: The problem states that there is a 15% increase in tuition, which means that the new tuition will be the current tuition plus 15% of the current tuition. Mathematically, we can represent this as:

new tuition = current tuition + 15% of current tuition

Using x to represent the new tuition, and 3500 to represent the current tuition, we can write this equation as:

x = 3500 + 0.15(3500)

Simplifying the right side, we get:

x = 3500 + 525

x = 4025

Therefore, the new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025

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The coordinates of K are (3, 1).

What is the coordinate point?

The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y-axis. The coordinates of a given point represent how far along each axis the point is located.

Point K is 1/n of the way from J(4,5) to L(0,-7). To find the coordinates of K, we can use the concept of linear interpolation.

Given two points J(x1,y1) and L(x2,y2) and a value of t, such that 0<=t<=1, the coordinates of the point K(x,y) that is t of the way from J to L is given by:

x = (1-t)x1 + tx2

y = (1-t)y1 + ty2

In this case, we know that n=4 and t = 1/4.

So the x and y coordinates of K are:

x = (1-1/4)x1 + (1/4)x2 = (3/4)x1 + (1/4)x2 = (3/4)(4) + (1/4)(0) = 3

y = (1-1/4)y1 + (1/4)y2 = (3/4)y1 + (1/4)y2 = (3/4)(5) + (1/4)(-7) = 1

Hence, the coordinates of K are (3, 1).

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Answer:

\(2^{12}\)

Step-by-step explanation:

\(4^3=(2^2)^3=2^6 \\ \\ 8^2=(2^3)^2=2^6 \\ \\ 2^6 \times 2^6=2^{6+6}=2^{12}\)

To find the missing value of x in a triangle, subtract the sum of the two angles from 180 degrees.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Having three edges and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C.

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

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Answer:

9x^2-24x+16

Step-by-step explanation:

(3x-4)(3x-4)

FOIL

9x^2-12x-12x+16

9x^2-24x+16

Based on the inscribed angle theorem, the measure of angle BED in the diagram given is: 57°.

The inscribed angle theorem states the measure of the inscribed angles subtended by the same arc are the same.

∠BCD and ∠BED are subtended by the same arc BD.

Therefore, based on the inscribed angle theorem, we have:

m∠BCD = m∠BED = 57°.

m∠BED = 57°

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Answer:

I think the answer is C.

Step-by-step explanation:

A triangle inside always has to add up to 180. So of you subtract 78 and 41 from 180 it wil give you 61

Step-by-step explanation:

30%of24

30÷100×24

7.2

To convert an annual interest rate to a daily interest rate based on simple interest, divide the annual interest rate by 365, the number of days in a year.

This way,

The daily interest rate is 0.05%

To get the simple interest in a 30 day period, we use the formula for simple interest and get:

The interest for a 30 day period is $23.15

The value of the given expression 6/(y-z) - 2/(y-z) is 4/(y-z). Option 3 is the correct answer.

In algebra, like terms are those in which the same variable(s) are raised to the same power (s). Because they both have the same variable (y) raised to the same power, the expressions 2xy and -5y are similar (1). When combining terms that have similar coefficients, it's important to preserve the exponent and variable constants.

The given expression is 6/(y-z) - 2/(y-z).

Simplifying the expression by combining the like terms we have:

(6 - 2)/(y-z) = 4/(y-z)

Hence, the value of the given expression is option 3 4/(y-z).

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Answer:

Mr Nelson will sell 115 more bottles of water than popcorn. First, you find the rate of popcorn and water being sold. That will be 147 bags divided by 3 and 216 bottles divided by 3. You get 49 bags and 72 bottles. You subtract those two numbers, 72-49=23. 23 is the number more waters sold than the popcorn. Finally, you multiply 23 by 5 days and you get 115. So it's 115 more waters sold than popcorn.

Step-by-step explanation:

Answer:

21×5 = 105.

14×5=70.

105-70 =35

function of f(2) is f(2) = 3(2) + 15 = 21.

Given the function f(x) = 3x + 15, we want to find the value of f(2). To do this, we substitute 2 in place of x in the function.

When we replace x with 2, we get f(2) = 3(2) + 15.

Now, we simplify the expression by performing the multiplication first. Multiplying 3 by 2 gives us 6.

So, we have f(2) = 6 + 15.

Finally, we perform the addition to get the final result. Adding 6 and 15 gives us 21.

Therefore, f(2) = 21, which means that when we plug in 2 for x in the function f(x) = 3x + 15, the result is 21.

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The angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.

In physics, angular velocity or angular speed, also recognized as angular frequency vector, is a pseudovector portrayal of how fast the angular position or orientation of an object changes over time.

So, angular velocity will be:

mg(h sinθ) = 1/2 Iω² + 1/2mv²

I of solid sphere = 2/5 mr²

Hence,

mg(h sinθ) = 1/2 (2/5 mr²) ω² + 1/2 mv²

Now remove the mass:

g h sin θ = 1/5 r² ω² + 1/2 v²

ω = v/r, v = ωr

Now, calculate angular velocity as follows:
g h sin θ = 1/5 r² ω² + 1/2 (ωr)²

g h sin θ = (7/10) r² ω²

ω² = 10 g h sin θ/7 r²

ω = √10 g h sin θ/7 r²

  = √10 (9.8) (2.1) sin 25° / 7 (0.04)²

  = 88.1 rad/s

Therefore, the angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.

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Complete question:
An 8.0 cm diameter, 400 g sphere is released from rest ta the tip of a 2.1 m long, 25-degree incline. It rolls, without slipping, to the bottom. What is the sphere's angular velocity at the bottom of the incline?

Ans:

B. The graph will have a vertical asymptote at x=π.

D. The graph will have a vertical asymptote at x=2π.

E. The graph will go through the point (π/4, 1).

M. The graph will go through the point (π/3, √3/3).

Sorry, I know I'm late :'>

but to whoever else needs this, good luck~! You got this >:)

♡ Have a wonderful day

The formula for the distributive property is: a(b+c) = ab + ac.

When performing arithmetic operations, the numbers in mathematics should adhere to the characteristic quality. The many qualities include those that are associative, commutative, distributive, inverse, identity, and so on. The ability to multiply a number by a set of numbers that are added together is known as the distributive property.

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Thus, The formula for the distributive property is: a(b+c) = ab + ac.

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a) Dos ángulos rectos. SPQ Y SRQ

b) Dos ángulos agudos. QSR Y PQS

c) Dos ángulos suplementarios. NO HAY

d) Dos ángulos complementarios RSQ+PSQ=90°

e) Dos rectas paralelas. PQ║ SR ( ARIBA DE PQ Y SR LLEVA LINEA SEPARAD NO LINEA JUNTA)

f) Dos rectas perpendiculares PS⊥RS (LLEVA LINEA ARRIBA DE LAS DOS LETRAS LINEA SEPARADA)

g) Una recta transversal RS (LLEVA LINEA ARRIBA)

Answer:

y = 2x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (1, 7 ) and (x₂, y₂ ) = B (- 3, - 1 )

m = \(\frac{-1-7}{-3-1}\) = \(\frac{-8}{-4}\) = 2 , then

y = 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 7 )

7 = 2(1) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = 2x + 5 ← equation of line

The rate at which the diameter decreases when the diameter is 10 cm is -0.00798 cm/min.

To find the rate at which the diameter decreases, we can use the relationship between the surface area and the diameter of a sphere.

The surface area of a sphere is given by the formula:

A = \(4\pi r^2\), where A is the surface area and r is the radius (which is half the diameter).

Differentiating both sides of the equation with respect to time t, we get:

dA/dt = 8πr(dr/dt).

We are given that the surface area decreases at a rate of \(1 cm^2/min\), so dA/dt = \(-1 cm^2/min\). We want to find dr/dt when the diameter is 10 cm, which means the radius is r = 10/2 = 5 cm.

Substituting these values into the equation, we have:

-1 = 8π(5)(dr/dt).

Simplifying, we get:

-1 = 40π(dr/dt).

Now, solving for dr/dt:

dr/dt = -1 / (40π).

Using a calculator, this evaluates to approximately -0.00798 cm/min.

Therefore, when the diameter is 10 cm, the rate at which the diameter decreases is approximately -0.00798 cm/min. Note that the negative sign indicates the decrease in diameter.

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