Simplify
12 cm : 60 mm

Answer:

\(A(t)=16(0.99948)^t\)

Step-by-step explanation:

The exponential function is modeled using the equation:

\(A(t)=A_o(1\pm r)^t\)

Where the plus sign indicates growth and the negative sign indicates exponential decay.

For an exponential function has a starting value of 16 and a decay rate of 0.52%.

\(A_0=16\\r=0.052\%=0.00052\)

This gives:

\(A(t)=16(1- 0.00052)^t\\A(t)=16(0.99948)^t\)

The function that models this situation is:

\(A(t)=16(0.99948)^t\)

Answer:

it is on ed it is 30

Step-by-step explanation:

Answer:

30 minutes

Step-by-step explanation:

Answer:

1. 57/16 or 3.5625 ounces of water

8 : 4.75

1 : 19/32  -----> divide both by 8

19/32x6=57/16 = 3.56 ounces

2. 2.4375 ounces of other ingredients

6-3.5625=2.4375

Answer:

E

Step-by-step explanation:

When is comes to a system of equations, the point where the lines intercept is the answer.

The graph of the proportional relationship would look like A line passes through the point (0, 0) and continues through the point (12, 3).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.

The given table is

x  12  8  24

y  3   2   6

The graph of the proportional relationship would look like.

A line passes through the point (0, 0) and continues through the point (12, 3).

In the ordered pair the first value represents the x axis  value and second value represents the y value. The ordered pair (12, 3) is coordinated with the values of x and y in the table.

Hence the graph of the proportional relationship would look like A line passes through the point (0, 0) and continues through the point (12, 3).

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The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

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Answer:

x=1 y=2

Step-by-step explanation:

Isolate x for 4x -y=2: X=2+y/4

Substitute x= 2+y/4

(2+y/4 )+3y=7

simplify 2+13y/4=7

Isolate y for 2+13y/4=7

y=2

Forx= 2+y/4

Substitute y = 2

x= 2+2/4

Simplify

X=1

Answer:

Step-by-step explanation:

Let's break down the expression step by step:

Nine raised to the power of 1/3:

9^(1/3) = ∛9 = 2.0801

Twenty-seven raised to the power of 1/2:

√27 = 5.1962

Two raised to the power of 1/6:

∛2 = 1.1225

Combining the previous results:

(2.0801 * 5.1962) / 1.1225

Three raised to the power of 1/3:

∛3 = 1.4422

Combining the final result:

(2.0801 * 5.1962) / 1.1225 * 1.4422

(2.0801 * 5.1962) / 1.1225 * 1.4422 ≈ 9.7085

Therefore, the value of the given expression is approximately 9.7085.

Step-by-step explanation:

to control fever a doctor recommend that a child should be given one mg of certain medicine for every 0. 07 kg body weight if the those is proportional to the body weight of the child then the quantity of medicine for a child of body weight to 24.92 kg

Answer:

The answer is number 2

Answer:

3.

Step-by-step explanation:

Since it states it needs to be cut into pieces, it's division, so since it's division we do KCF - keep change flip

We keep the first term, then we change the sign to a multiplication sign and flip the numerator and the denominator for the second term, so your equation would be :

6/8 × 4/1

6 times 4 would be 24, then we put 24 over 8, 24/8, - then you just divide 24 by 8 which would be 3. I hope this helps.

Answer:

77 cents

Step-by-step explanation:

Answer:

Let's use a system of equations to solve the problem:

x = number of cases of orange juice

y = number of cases of cranberry juice

From the problem, we know that:

x + y = 17 (Brett bought a total of 17 cases of juice)

15x + 8y = 192 (Brett paid a total of $192 for the juice)

We can solve for one of the variables in the first equation and substitute it into the second equation:

x + y = 17

x = 17 - y

15x + 8y = 192

15(17 - y) + 8y = 192

255 - 15y + 8y = 192

-7y = -63

y = 9

So Brett bought 9 cases of cranberry juice. We can substitute this value back into the first equation to find how many cases of orange juice he bought:

x + y = 17

x + 9 = 17

x = 8

Therefore, Brett bought 8 cases of orange juice.

Answer: sun are the main light source

Step-by-step explanation:

Answer:

What is sun ?

Answer:

5+r=6-r

-5 -5

r=1-r

+r +r

2r=1

÷2 ÷2

r=1/2

Answer:

37

-----

56

Step-by-step explanation:

Answer:

  (c)  0

Step-by-step explanation:

Each of the terms in the expression represents a different transformation of a different trig function. Expressing those as the same trig function can make it easier to find the sum.

__

We can start with the identity ...

  cos(x) = sin(x +π/2)

Substituting the argument of the cosine function in the given expression, we have ...

  cos(π/2 -θ) = sin((π/2 -θ) +π/2) = sin(π -θ) = -sin(θ -π)

__

The first term, sin(π +θ), is a left-shift of the sine function by 1/2 cycle, so can be written ...

  sin(π +θ) = -sin(θ)

The second term is the opposite of a right-shift of the sine function by 1/2 cycle, so can be written ...

  cos(π/2 -θ) = -sin(θ -π) = sin(θ)

Then the sum of terms is ...

  sin(π +θ) +cos(π/2 -θ) = -sin(θ) +sin(θ) = 0

The sum of the two terms is identically zero.

The number of buttons A will be equal to 11. And the number of buttons B will be  equal to 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Given that container of buttons contains a similar number of each kind of button it contains 220g of buttons.

The weight of the button is given as follows;

Button A=8 grams

Button B = 12 Grams

Consider x be the number of each button. Then the equation is;

8x + 12x = 220

20x = 220

x = 11

The number of buttons A is 11. And the number of buttons B is 11.

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Answer:

f(3r - 1) = -6r + 6

Step-by-step explanation:

To find f(3r - 1), we substitute 3r - 1 for x in the expression for f(x) and simplify:

f(x) = 4 - 2x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= -6r + 6

So, f(3r - 1) = -6r + 6.

Answer:

$1.26

Step-by-step explanation:

A 20% off means multiplying by 1-0.2=0.8

4.39*0.8=3.512

3.512-1=2.512

2.512-1.25=1.262

1.262 rounded to the nearest cent is $1.26

Answer:

350%

Step-by-step explanation:

First, there is a whole number in the ones place, so that number will be in the hundreds place of your percent. Then to find the percent of 0.5 you put the decimal part over 10:

5/10 = 1/2 = 50%

In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.

The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."

When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.

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The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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Answer:

153.3852

Step-by-step explanation:

After the decimal, you count the places. 3 is in the ones place, 8 in the tenths, 5 in the hundreths, and 1 in the thousandths. The thousandths place is what we are rounding, so we look at the next number, 9, which tells us to round the 1 up to 2

Answer:

153.385

Step-by-step explanation:

153.38519

153.38519

The digit to the right of the thousandth (the the one, which is bolded) is less than or equal to 4, which means we round down.

153.38519 ≈ 153.385

Hope this helps.

Answer: \(35x < 4-5x+3x^2\) is \(x < \frac{1}{3}\) or \(x > \frac{4}{3}\)

Step-by-step explanation:

A) To generate the table of values, we can substitute different values of x into the equation and solve for y.

x             y

-2        26

-1        12

0         4

1         2

2        10

To plot the graph of the function, we can use the table of values and plot the corresponding points on a graph with a scale of 4 for the y-axis and 2cm to 1 unit along the x-axis. The graph should look like a parabola opening upwards.

c) To solve for the root of the equation 4-5x+3x^2=0, we can use the graph and find the x-coordinate of the point where the graph intersects the x-axis. This point is also known as the x-intercept or the root of the equation. From the graph, we can see that the root is approximately x=0.83.

To solve the equation 3x^2 -5x=2, we can rearrange it to the form 3x^2 -5x-2=0 and factor it as (3x+1)(x-2)=0. This gives us two solutions: x=-1/3 and x=2.

To determine the range of values of x for which 35x​<4-5x+3x^2, we can rearrange the inequality to the form 3x^2-40x+4>0 and factor it as (3x-1)(x-4/3)>0. This means that either (3x-1) and (x-4/3) are both positive or both negative.

When (3x-1)>0 and (x-4/3)>0, we get x>1/3 and x>4/3, which means x>4/3.

When (3x-1)<0 and (x-4/3)<0, we get x<1/3 and x<4/3, which means x<1/3.

Therefore, the range of values of x for which 35x<4-5x+3x^2 is x<1/3 or x>4/3.

Answer:

A=40.8 B=8

Step-by-step explanation:

A Explanation

£7.20*3=£21.6

£9.60*2=£19.2

19.2+21.6=40.8

B Explanation

£9.60*3=£28.8

86.40-28.8=57.6

57.6/7.20=8

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer:

24

Step-by-step explanation:

Equation: x + 11 = 35

1. Subtract 11 from both sides

x + 11 = 35

  -11      -11

x = 24

Answer:

x is 24

Step-by-step explanation:

Let's write it down as an equation

If number x is increased by 11, we'll write is as x+11 and the result of that is 35, so x + 11 = 35

x + 11 = 35 implies that

x = 35 - 11

35 - 11 = 24

x = 24

Answer:

Step-by-step explanation:

I'll do the first part for you:

The number of 3/4 in 2 is \(=2/\frac{3}{4}\)

That is the division equation.  Rearrange it to make the multiplication equation.  keep...change...flip.  Change the division to a multiplication and flip the fraction:

The number of 3/4 in 2 =\(=2.\frac{4}{3}\)