Aubree invested $16,000 in an account paying an interest rate of 5.6% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $45,600?

Answer:

The answer to the question provided is possibly 2.

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: \: \: \: 3y + 77 = 2y + 79 \\ \frac{ - 2y \: \: \: \: \: \: = - 2y}{1y + 77 = 79} \\ \frac{ \: \: \: \: \: \: \: \: - 77 = - 77}{ \frac{1y}{1} = \frac{2}{1} } \\ \\ y = 2\)

Answer:

question 1: answer is 4

question 2: answer is 1

Step-by-step explanation:

Answer: i think its A

Step-by-step explanation: hope this helped

The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The perimeter of a rectangle is 40 cm. The length is 14 cm.

Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.

Fran says she can find the width using the equation 2x + 28 = 40.

now, we get,

1. Divide both sides by 2

 2(x+14) = 40

 x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

 2x + 28 = 40

 2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

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Answer:

i think it's the last one 1,-5

Step-by-step explanation:

9514 1404 393

Answer:

  (3, 4)

Step-by-step explanation:

The ordered pairs comprise a function because no x-value is repeated. If you want the list to be not-a-function, then one of the x-values must be repeated.

The x-values given in the original function list are -2, 3, 7, 9. The only one of these that is an x-value in an answer choice is 3, in the pair (3, 4).

Adding (3, 4) will make the relation not a function.

Answer:

The answer is 5%

Step-by-step explanation:

Hope this helps!!

Answer:

27 inches

Step-by-step explanation:

We can use The Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

21.6 ^2 + 16.2^2 = c^2

466.56+262.44 = c^2

729 = c^2

Taking the square root of each side

sqrt(729) = sqrt(c^2)

27  = c

Answer:

x = 75

Step-by-step explanation:

Step-by-step explanation:

According to the question,

g(X)=5x ------------------------(eq-i)

g(X)=15 -------------------------(eq-2)

By comparison the two following equation

\(5x=15\\\\x=\dfrac{15}{5}\\\\x=3\)

Angle values of trigonometric functions are in degrees or radians. If θ is an angle and sin θ = 0.5, then θ can be equal to 30° or 150°.If θ is an angle and cos θ = 1/2, then θ can be equal to 60° or 300°.

If θ is an angle and tan θ = √3, then θ can be equal to 60° or 240°. Now let's see which of the following is NOT equal to 60°:

A) sin⁻¹ √3/2. The function sin ⁻¹ returns the angle whose sine is equal to the given number. sin 60° = √3/2, hence sin⁻¹ √3/2 = 60°

B) cos⁻¹ 1/2. The function cos ⁻¹ returns the angle whose cosine is equal to the given number. cos 60° = 1/2, hence cos⁻¹ 1/2 = 60°C) tan⁻¹ √3.

The function tan ⁻¹ returns the angle whose tangent is equal to the given number. tan 60° = √3, hence tan⁻¹ √3 = 60°D) tan⁻¹² √3/3

Let's simplify the expression tan⁻¹² √3/3We know that tan 60° = √3, hence tan⁻¹ √3 = 60°. Thus the answer is D. tan⁻¹12 √3/3 is NOT equal to 60°.

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The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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Answer:

98

Step-by-step explanation:

Given: The ratio of dimes to quarters in a money bag is 12.2

Also, there are 8 quarters.

To find: Number of dimes

Solution:

Number of dimes : Number of quarters = 12.2

Number of dimes : 8 = 12.2

Therefore,

Number of dimes = 12.2 × 8 = 97.6 ≈ 98

If there are 40 bottles in the machine when is it to be serviced, 40 number will go in the second column.

Numbers are used to performing arithmetic calculations. Examples of numbers are natural numbers, whole numbers, rational and irrational numbers, etc. 0 is also a number that represents a null value.

A number has many other variations such as even and odd numbers, prime and composite numbers.

To determine the number that will go in the second column, we need to understand the context of the problem.

Assuming the second column refers to the number of bottles in the machine when it should be serviced, the answer

would be 40.

The machine should be serviced when there are 40 bottles in it.

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Question

A vending machine in an office building sells bottled beverages. The machine keeps track of all changes in the number of bottles from sales and from machine refills and maintenance. This record shows the changes for every 5-minute period over one hour.  The machine must be emptied to be serviced. If there are 40 bottles in the machine when it is to be serviced, what number will go in the second column in the table?

time number of bottles

8:00–8:04 -1

8:05–8:09 +12

8:10–8:14 -4

8:15–8:19 -1

8:20–8:24 -5

8:25–8:29 -12

8:30–8:34 -2

8:35–8:39 0

8:40–8:44 0

8:45–8:49 -6

8:50–8:54 +24

8:55–8:59 0

service

Answer:

HCF of 60 and 80 is 20.

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

We have to divide polynomial given as (x³ - 21x² + 147x - 343) by (x - 7) by synthetic division.

7 | 1     -21     147      -343

  ↓       7     -98        343

    1     -14      49          0

Therefore, quotient is (x² - 14x + 49) and the remainder will be 0.

Option (3) will be the answer.

Answer:  \(_{4}^{8}\textrm{C} \cdot _{3}^{5}\textrm{C}\) ways we can form a subcommittee.

How does combination is helpful in selection?

Explanation:

The selection of 4 men out of 8 men is given as: \(_{4}^{8}\textrm{C}\)

The selection of 3 women out of 5 women is given as: \(_{3}^{5}\textrm{C}\)

The number of ways by which subcommittee of 4 men and 3 women can be formed from a committee off 8 men and 5 women is given as:

\(_{4}^{8}\textrm{C} \cdot _{3}^{5}\textrm{C}\)

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The inverse of a conditional statement is when both the hypothesis and conclusion are negated.

What is hypothesis and conclusion?

A conditional statement's first clause, or "if," contains the hypothesis.

A conditional statement's second, or "then," component is the conclusion. A hypothesis produced the conclusion.

You can enroll in a reputable college if you earn good grades.

You will get into a good college if you get good grades, and the part that comes after the "if" is known as a hypothesis.

The part that comes after the "then" is known as a conclusion. An "If-then" or "conditional statement" is a series of hypotheses followed by a conclusion.

The opposite of a conditional statement is when the hypothesis and conclusion are both negated.

This is done by negating both the "If" part (p) and the "then" part (q).

The conditional statement is known as p q in geometry. The inverse is written as pq, where q stands for the negation of the statement or not.

Hence, the inverse of a conditional statement is when both the hypothesis and conclusion are negated.

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Answer: Inverse

Step-by-step explanation: Inverse Statements: The inverse of a conditional statement is found by negating the hypothesis and the conclusion. That means you will write the opposite for both parts of the conditional statement.

Example: statement: If two angles are vertical angles, then they are congruent.

Inverse: If two angles are not vertical angles, then they are not congruent. This is not valid.

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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The side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

The first such theorem is the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are equivalent to two sides and an included angle of another triangle.

Therefore, the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

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Answer:

x = \(\sqrt{116}\)  feet

Step-by-step explanation:

Pythagorean Theorem: \(a^2=b^2+c^2\)

where a = hypotenuse, and b and c are legs of the right triangle.

We plug in our variables into the equation and solve for x:

\(10^2=4^2+x^2\)

which would isolate to:

\(116=x^2\)

so x = \(\sqrt{116}\)

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\( \tt{sin(\Theta) = \cfrac{3}{8}} \)

\(\qquad \tt \rightarrow \: x = 6\:\: cm\)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad \tt \rightarrow \: \sin( Theta) = \cfrac{Opposite \:\: side}{Hypotenuse}\)

\(\qquad \tt \rightarrow \: \sin( \Theta) = \cfrac{3}{8} \)

since the Triangles are similar, ratio of their corresponding sides are equal :

\(\qquad \tt \rightarrow \: \sin( \Theta) = \cfrac{3}{8} = \dfrac{x}{16} \)

\(\qquad \tt \rightarrow \:x = 16 \sdot \cfrac{3}{8}\)

\(\qquad \tt \rightarrow \: x = 2 \sdot3\)

\(\qquad \tt \rightarrow \: x = 6 \: \: cm\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Since  the two right-angled triangles have the same angles, the values are; ai. sin θ= 3/8ii. sin θ= x/16b. x = 6cm

Using the sine trigonometric identity expressed as;

sin θ = opposite/hypotenuse

Then, we have that for the first triangle;

sin θ= 3/8

For the bigger triangle;

sin θ= x/16b.

Then, since we have that the sine identity is;

sin θ= x/16

But sin θ= 3/8

Divide the values and find the sine inverse in

θ= 0. 375θ = 22. 0 degrees

x = 0. 375 (16)

Multiply

x = 6 cm

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The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High  .

In the question ,

it is given that

the Summer is planning to build a small snow cone shed .

the distance from north junior high = 7/8 miles = 0.875 miles

the distance from South elementary = 0.680 miles

the distance from West Side elementary = 5/6 miles = 0.833 miles

From , above result we see that

the farthest from summer snow cone is north junior high which is 0.875 miles .

the nearest from summer snow cone is South Elementary which is 0.680 miles .

So , the order from closest to farthest is

South Elementary < West Side Elementary < North Junior High

Therefore , The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High  .

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Answer:

A

Step-by-step explanation:

Given

- 2x² + 5x - 3 ← factor out - 1 from each term

= - 1(2x² - 5x + 3) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 3 = 6 and sum = - 5

The factors are - 2 and - 3

Use these factors to split the x- term

2x² - 2x - 3x + 3 ( factor the first/second and third/fourth terms )

2x(x - 1) - 3(x - 1) ← factor out (x - 1) from each term

(2x - 3)(x - 1)

Then

- 2x² + 5x - 3 = - 1(2x - 3)(x - 1) → A

Answer:

1) 5/8

\(\frac{5}{8} rad = 35.809\textdegree\)  or (atau)   \(\frac{5}{8} \pi rad = 112.5\textdegree\)

2) a. 75°  b. 132°

\(75\textdegree = 1.308\) \(rad\)   or (atau)    \(75\textdegree = 0.41\overline{6}\) \(\pi\) \(rad\)

\(132\textdegree = 2.303\) \(rad\)  or (atau)    \(132\textdegree = 0.7\overline{3}\) \(\pi\) \(rad\)

The percent decrease in the travel time after getting a new job is 36%.

Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".

First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.

decrease in time = 48 - 30.72

decrease in time = 17.28

Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.

percent decrease = (17.28 / 48) x 100

percent decrease = 36%

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The solution of the given problem of Permutation and Combination is .There are38,760 different groups of 10 can be formed from the 18 volunteers.

A permutation is a way of arranging a set of objects or events in a specific order. The number of possible permutations of a set of n objects taken r at a time is given by the formula nPr = n!/(n-r)!, where n! (n factorial) is the product of all positive integers up to n.

A combination, on the other hand, is a way of selecting a subset of objects or events from a larger set, where the order of the elements does not matter. The number of possible combinations of a set of n objects taken r at a time is given by the formula nCr = n!/r!(n-r)!.

The number of different groups of 10 that can be formed from 18 volunteers can be calculated using the formula for combinations:

C(18, 10) = 18! / (10! * 8!)

where "C(18, 10)" represents the number of ways to choose 10 volunteers out of 18.

Simplifying the expression:

C(18, 10) = (18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10!) / (10! * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

The 10! in the numerator and denominator cancel out, leaving:

C(18, 10) = (18 * 17 * 16 * 15 * 14 * 13 * 12 * 11) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying further, we get:

C(18, 10) = 38,760

Therefore, there are 38,760 different groups of 10 that can be formed from 18 volunteers.

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Answer:

Pretty sure its B

Answer:

Answer: B

Step-by-step explanation:

Count the number of atoms of each element on each side. They must be equal.

Only B has equal numbers of atoms of each element on both sides of the equation.

B

left side: 1 C, 2 H, 1 O

right side: 1 C, 2 H, 1 O

We will use conversion factors

1 hour = 60 minutes

We need to make sure to put them so the units cancel

We also know that 1,61 km = 1 mi

1.81 km 60 min 1 mi

---------- * ----------- * ---------------

min 1 hr 1 . 61 km

67.45341615

Rounding to the nearest hundredth

67.48 miles/ hr