which expressions are equivilant to 6^16?

Answer:

Customer A - 5 / 22.45 = $0.22 or 22 cents per quart

Customer B - 7 / 25.45 = $0.27 or 27 cents per quart

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\(6 = \frac{x + 2}{3} \\ \)

\( \frac{x + 2}{3} = 6 \\ \)

Multiply sides by 3

\(3 \times \frac{x + 2}{3} = 3 \times 6 \\ \)

\(x + 2 = 18\)

Subtract sides 2

\(x + 2 - 2 = 18 - 2\)

\(x = 16\)

Done...

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The investment problem is modeled by an initial value problem (IVP) where the rate of change of the investment is determined by the initial investment, monthly deposits, and the interest rate.

a) The investment problem can be modeled by an initial value problem where the rate of change of the investment, y(t), is given by the initial investment, monthly deposits, and the interest rate. The IVP can be written as:

dy/dt = 0.09y + 200, y(0) = 500.

b) To solve the IVP, we can use an integrating factor to rewrite the equation in the form dy/dt + P(t)y = Q(t), where P(t) = 0.09 and Q(t) = 200. Solving this linear first-order differential equation, we obtain the solution for y(t).

c) To find the value of the investment after 2 years, we substitute t = 2 into the obtained solution for y(t) and calculate the corresponding value.

d) After 2 years, the monthly deposit increases to $300. To find the value of the investment a year later, we substitute t = 3 into the solution and calculate the value accordingly.

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Answer:

61. hope it helps ☺️

Step-by-step explanation:

12x3=36+25=61

The length of the arc in terms of pi is 3π units.

The length of the arc is calculated by applying the formula for the length of arc as shown below;

L = 2πr (θ/360)

where;

The length of the arc in terms of pi is calculated as follows;

L = 2π x 9 (60/360)

L = 3π units

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Answer:

5 ÷ 1/3

5 × 3/1

5 × 3

=15

Step-by-step explanation:

the answer is 15

Answer:

1/4

Step-by-step explanation:

5 plus 7 equals to 12

3 football games

3/12=1/4

The quantity of positive numbers smaller than or equal to \($10,000$\) is \($\fbox{958}$\).

We see that a number \($n$\) is \($p$\)-safe if and only if the leftovers from\($n\mod p$\) is greater than \($2$\) and less than \($p-2$\); thus, there are \($p-5$\) residues \($\mod p$\) that a \($p$\)-safe number can have. Therefore, a number \($n$\) satisfying the circumstances of the issue may \($2$\) different residues \($\mod 7$\), \($6$\) different residues \($\mod 11$\), and \($8$\) different residues \($\mod 13$\). According to the Chinese Remainder Theorem, for a number \($x$\) that is \($a$\) (mod b) \($c$\) (mod d) \($e$\) (mod f) has one solution if \($gcd(b,d,f)=1$\). For instance, in this instance, the number \($n$\) can be: \(3 (mod 7) 3 (mod 11) 7 (mod 13)\)so since \($gcd(7,11,13)=1$\), there is \(1\) solution for \(n\) for this case of residues of \($n$\). As a result, according to the Chinese Remainder Theorem, \($n$\) can have \($2\cdot 6 \cdot 8 = 96$\) different residues mod \($7 \cdot 11 \cdot 13 = 1001$\). Thus, there are \($960$\) values of \($n$\) satisfying the conditions in the range \($0 < n \le 10010$\). Nevertheless, we now have to eliminate all values bigger than \($10000$\) that satisfy the conditions. We can simply see by looking at residues that the only suitable values are \($10006$\) and \($10007$\), so there remain \($\fbox{958}$\) values satisfying the conditions of the problem.

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Therefore, √128 lies between 11 and 12 on a number line.

To determine the two numbers between which √128 lies on a number line, we can calculate the square roots of consecutive perfect squares that surround 128.

By calculating the square roots, we can find the two nearest whole numbers that √128 lies between.

Calculating the square roots of perfect squares near 128:

√121 = 11

√144 = 12

Since 128 is greater than 121 and less than 144, √128 lies between √121 and √144 on the number line.

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Answer:

Patricia's amount of money = $125

Armando's amount of money = $95

Step-by-step explanation:

Given:

Total amount of money = $220

Patricia have $30 more than Armando

Find:

Amount of money each have.

Computation:

Assume;

Patricia's amount of money = a

So,

Armando's amount of money = a - 30

So,

a + a - 30 = 220

2a - 30 = 220

2a = 250

a = 125

Patricia's amount of money = $125

Armando's amount of money = 125 - 30

Armando's amount of money = $95

The addition of the polynomial \(x^{3}+3xy-2xy^{2} +y^{3}\) with \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is  \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

What is a polynomial?

⇒ A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

⇒ In the addition of polynomials, the like terms are added while in subtraction, the like terms are subtracted.

Calculation;

We have been given two polynomial which we have to add   \(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\)

The sign after addition or subtraction will always be of the variable having more value.

\((x^{3}+3xy-2xy^{2} +y^{3} )+(2x^{3}-5x^{2} y-3xy^{2}-2y^{3})\)

On adding like terms with each other

⇒ \((x^{3} +2x^{3})+ 3xy-5x^{2} y-(2xy^{2}+3xy^{2})+(y^{3}-2x^{3})\)

⇒ \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\)

Hence the addition of the polynomial\(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

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Answer: -16.1

Step-by-step explanation: Multiply.

Answer:

Step-by-step explanation:

Answer:25,472

Step-by-step explanation:

Answer:

the awnser od easy ots 25,472

Answer:

y=4

Step-by-step explanation:

because this is an equilateral triangle, this means that all the size of the lengths is equal this means that,

2y+5 = 4y-3

(add 3 for both sides)

2y+8 = 4y

(subtract 2y for both sides)

8 = 2y

(divide by 2 for both sides)

4 = y

so,

y=4

It is to be noted that the height of the bread is 5 centimeters. The hint given is in the information about the surface area. See the explanation below.

In this case, the surface area of bread is the total sum of the area of the base and perimeter. The surface area of the bread is given below.

That is:

A = 2 x b + p x H,

Where b is the area of the base,  p is the perimeter of the base and h is the height.

Recall that it is stated that 50% of the surface area of the bread is the crust.

The implication is that the surface area of both sides of the base is equivalent to the surface area of its perimeter.

That is:

2 x b = p x h

We can compute the perimeter of the bread as:

P = 4 x length
p = 4 x 10
p = 40cm

The area of the base is:

b = 10 x 10
b = 100cm²

Substituting the values in the above formula,
2 x 100 = 40 x h
200 = 40h
h = 200/40

h= 5cm.

Hence the height of the bread is 5cm.

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Answer:

I forgot to change pi into 3.14

∠XBC is 55 degrees because it is corresponding to ∠AXY..

The angle ∠BXC is 70 degrees

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, same interior angles, vertically opposite angles etc.

Therefore, XY and BD are parallel lines.

XB = XC

ΔXBC is an isosceles triangle.

Therefore, ∠XBC is 55 degrees because it is a corresponding angle to ∠AXY.

Let's find ∠BXC.

Therefore, the base angles of an isosceles triangle are congruent.

Hence,

∠XBC = ∠BCX = 55 degrees

Therefore,

55 + 55 + ∠BXC = 180

110 + ∠BXC = 180

∠BXC = 180 - 110

∠BXC = 70 degrees

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Step-by-step explanation:

When k = 10

Then

k + 26

= 10 + 26

= 36

Hope it will help :)

Answer:

36

Step-by-step explanation:

k = 10

k + 26 =

10 + 26 =

36

The computation of (TR)546 - (TR)540 will give a value of 3261.

TR(546)  =  546(546 + 1)/2  =  273 * 547

TR (540)  =  540(540 + 1)/2  =  270 * 541

273 * 547  = (270 + 3)(541 + 6)

= 270*541  + 270*6  + 541 *3  +  18

= 270*541  + 1620  + 1623  +  18

= 270*541  + 3261

TR(546) -TR (540)   = 270*541  + 3261  - 270 * 541

= 3261  

TR(546) -TR (540)   = 3261  

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The probability of  rolling a fair die once and getting a number greater than 2 is 0.7.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let  a fair dice is roll once.

The total numbers on dice are 6

The total numbers greater than 2 on dice are  4 which are 3, 4, 5, and 6.

So,

P(getting number greater than 2) = 4/6 = 0.7

Hence, the probability of  rolling a fair die once and getting a number greater than 2 is 0.7.

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Answer:

2

Step-by-step explanation:

Answer:

none bc theres no 6 in the list

Step-by-step explanation:

hope this helps :D

Answer:

x = 12

A = 144

Step-by-step explanation:

Angles A and B are the same so we can set them equal to each other

We can create the following equation

\(10x + 24 = 6x + 72\)

Reduce

4x = 48

x = 12

We the plug x into 10x + 24 in order to calculate angle A.

144

Answer:

32 cartons

Step-by-step explanation:

Total sets needed

48 + 43 + 46 + 50 = 187

Cartons needed

187 / 6 = 31 1/6

need 32 cartons

Answer:

32 cartons

Step-by-step explanation:

add up all of the students = 187

divide by 6 = 187/6 = 31.16

round = 32 cartons

Answer:

3x5x2=30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

You are multiplying all 3 terms. Multiply straight across:

(3 * 5) * 2

(15) * 2

30

30 is your answer.

~

Autumn's physiological response, characterized by her increased heart rate, sweaty hands, and flushed cheeks, indicates that her sympathetic nervous system has been activated.

Autumn's physiological response, such as an increased heart rate, sweaty hands, and flushed cheeks, is a typical manifestation of the fight-or-flight response, which is controlled by the sympathetic nervous system. In this situation, Autumn's body is reacting to a perceived threat or a stressful stimulus, which in this case is the presence of the boy she has a crush on.

When the sympathetic nervous system is activated, it triggers the release of stress hormones like adrenaline, which leads to various physiological changes in the body. These changes include increased heart rate, dilation of blood vessels, increased blood flow to the muscles, and sweating, all of which prepare the body for action in response to a perceived threat. This response is part of the body's automatic reaction to stressful or arousing situations and helps to mobilize the body's resources to deal with the perceived threat or challenge.

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Answer:

5x=90 x=90/5=18. So, the answer is 18.

Answer:

Step-by-step explanation:

given

5x = 90

x = 18

Answer:

7.8 cm

Step-by-step explanation:

Let's find the volume of the water bottle first. The radius is 5.5/2 = 2.75 cm

V = πr²h = 3.14 * 2.75² * 20 = 474.925 cm³

If we call the minimum side length of the cube as x we can write:

x³ = 474.925 because the volume of the cube is x * x * x = x³

x ≈ 8 cm