$800 is deposited in an account that pays 9% annual interest compounded annually. Find the balance after four years

Answer:

22, 17, and 44.

Step-by-step explanation:

So what you do is you will have three equations that we will put together.

1. x. The first number is x because they don't give us anything about it.

2. x-5. It says that the second number is 5 less than the first number.

3. 2x. It says that the third number is 2 times the first number.

x+x-5+2x=83.

4x-5=83.

4x=88.

x=22.

That is the first number. To find the second and third, you will plug 22 into the x.

2. 22-5=17.

3. 2(22)=44.

22, 17, 44 are your answers.

Final answer:

By setting up equations based on the information provided, we solved for x as the first number and then used it to determine the other two numbers. The three numbers are 22, 17, and 44.

Explanation:

The sum of three numbers is 83. This is the first equation we'll use to solve the problem. Let's denote the first number as x. According to the question, the second number is 5 less than the first, which gives us the second equation y = x - 5. For the third number, it is given as 2 times the first, hence the third equation is z = 2x.

Now, we'll combine all three equations to express the sum:

x + (x - 5) + 2x = 83

Simplifying, we combine like terms:

4x - 5 = 83

Adding 5 to both sides gives us:

4x = 88

Dividing by 4, we find the first number:

x = 22

Now we'll use x to find the other two numbers:

y = 22 - 5 = 17

z = 2 × 22 = 44

Therefore, the three numbers are 22, 17, and 44.

The solution is

x = 27 and y = 43

See the image

The answer is :

(x+5)(x+3)

Answer:

[tex]7\frac{5}{7}\ laps[/tex]

Step-by-step explanation:

we know that

To find out how many laps they ran, divide the total distance by the distance of one lap

step 1

Convert the total distance from mixed number to an improper fraction

[tex]6\frac{3}{4}\ mi=\frac{6*4+3}{4}=\frac{27}{4}\ mi[/tex]

step 2

Find the number of laps

[tex]\frac{(27/4)}{(7/8)}=\frac{54}{7}\ laps[/tex]

step 3

Convert the number of laps to mixed number

[tex]\frac{54}{7}=\frac{49}{7}+\frac{5}{7}=7\frac{5}{7}\ laps[/tex]

A rectangle is a quadrilateral with four 90-degree angles. The opposite sides are equal, with two sides being the length (10 inches) and the other two being the width (7 inches).

Ty, when painting a rectangle, it's important to understand its attributes. A rectangle is a quadrilateral, meaning it has four sides. Two of these sides will be 10 inches long, and the other two will be 7 inches high - these are referred to as the 'length' and 'width'. Additionally, all interior angles of a rectangle are 90 degrees, which is a right angle. So when you are painting, make sure each corner forms a 90-degree angle. Also, the opposite sides of a rectangle are always equal. If any of these attributes are not followed, the figure will not be a rectangle.

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He could be thinking of any number between 3.1451 and 3.1459

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Option 2 -  [tex]-6x^3+x^2-\sqrt5[/tex]

Step-by-step explanation:

To find : Which algebraic expression is a polynomial?

Solution :

Polynomial is defined is the expression consisting of several terms with variable and constant.

Polynomial is always positive not a negative exponential.

Option 1 - [tex]4x^2-3x+\frac{2}{x}[/tex]

This is not a polynomial because it has a negative exponent.

Option 2 - [tex]-6x^3+x^2-\sqrt5[/tex]

This is a polynomial by definition.

Option 3 - [tex]8x^2+\sqrt x[/tex]

This is not a polynomial as  [tex]\sqrt x[/tex] is not considerable.

Option 4 - [tex]-2x^4+\frac{3}{2x}[/tex]

This is not a polynomial because it has a negative exponent.

Therefore, Option 2 is correct.

Answer:

Option C is correct

[tex]3x^3-4x^2-10[/tex]

Step-by-step explanation:

Like terms are those terms which have same variable to the same power.

Find the difference of the following:

[tex](3x^3-2x^2+4)-(2x^2+14)[/tex]

Remove the parenthesis we get;

[tex]3x^3-2x^2+4-2x^2-14[/tex]

Combine like terms;

[tex]3x^3-4x^2-10[/tex]

Therefore, the difference of [tex](3x^3-2x^2+4)-(2x^2+14)[/tex] is, [tex]3x^3-4x^2-10[/tex]

Answer its 5

Step-by-step explanation:

look it up theirs others with this question :)

Answer:

D. 5

Step-by-step explanation:

got it right n the test

Answer:

Diameter = 50 cm

Step-by-step explanation:

We are given that the area of a home bakes pizza is [tex] 6 2 5 \pi cm ^ 2[/tex].

Here, we are assuming that the pizza is circular and we know that the area of a circle is given by: [tex]\pi r^2[/tex]

So equating the given value to find the value of the diameter.

[tex]\pi r^2[/tex] [tex]=625\pi[/tex]

[tex]r^2=625[/tex]

[tex]r=\sqrt{625}[/tex]

[tex]r=25[/tex]

If the radius is 25 cm, then  diameter = 25 × 2 = 50 cm

Answer:

The diameter of the pizza= 50 cm

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where r is the radius of circle

It is given that, area of pizza is 625π cm²

A pizza is like a circle.

Find the radius of pizza

Area = πr²= 625π cm²

r² = 625π/π = 625

r = √625 = ±25

radius r = 25cm

To find the diameter of pizza

Diameter = 2r  = 2 * 25 = 50 cm

Answer:

Step-by-step explanation:

2x = 27

10% × 23.8 =

(10 ÷ 100) × 23.8 =

(10 × 23.8) ÷ 100 =

238 ÷ 100 =

2.38

Proof

2.38 ÷ 23.8 =

0.1 =

0.1 × 100/100 =

0.1 × 100% =

(0.1 × 100)% =

10%

Answer:

238

Step-by-step explanation:

Question: Find 10% of 238.  

Answer: 10% of 238 is 23.8.

Explanation

STEP 1: 1% of 238 = 238100=2.38

STEP 2: 10% of 238 = 10⋅2.38=23.8

Explanation 2:

STEP 1: Write 10% as a decimal number: 10%=10100=0.1

STEP 2: Multiply 0.1 by 238: 0.1⋅238=23.8

Result

Question: The number 238 is 10% of what number?

Answer: The number 238 is 10% of 2380.

Explanation

STEP 1: Write 10% as a decimal number:

10=10100=0.1

STEP 2: Divide 238 by 0.1:

2380.1=2380

When she adds to the original four sections by coloring three more, it represents the total colored sections.

Answer:

A. 4/8+3/8

E. 1/8+1/8+1/8+1/8+1/8+1/8+1/8

Step-by-step explanation:

Select the two correct answers:

A. 4/8+3/8

B. 4+3

C. 8/4+8/3

D. 1/8+3

E. 1/8+1/8+1/8+1/8+1/8+1/8+1/8

Answer:

A and B

Step-by-step explanation:

Parallel lines are lines which have the same slope. Perpendicular lines have negative reciprocal slopes.

For the options:

A. Both equations have 7/5 as the slope. They are parallel.

B. The slopes are 1 and -1. These are perpendicular.

C. The slopes are 9/2 and are parallel.

D. The slopes are 7/3 and -3/7. They are perpendicular.

The solution is A and B.

Answer:

20 quarts of milk used

Step-by-step explanation:

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷since there are 4 quarts in a gallon, you have 20 quarts.

There are four quarts in a gallon, so you times 4 and 5. The result you get is 20 quarts.  

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

Answer:

9/10

Step-by-step explanation:

convert 3/5 to 6/10

6/10+3/10=9/10

The value of fraction will be;

⇒ 9/10

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ 3/5 + 3/10

Now,

Since, The fraction is,

⇒ 3/5 + 3/10

Solve as;

⇒ 3/5 + 3/10

⇒ 6/10 + 3/10

⇒ (6 + 3) / 10

⇒ 9 / 10

Thus, The value of fraction = 9/10

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Mean (μ) ≈ 53.84, Standard deviation (σ) ≈ 16.51.

To solve this problem, we can use the properties of the normal distribution and the given information about the percentage of students scoring certain marks.

Let's denote the mean as μ and the standard deviation as σ. We know that in a normal distribution:

1. 10% of the students score more than 75 marks.

2. 20% of the students score less than 40 marks.

To find the values of μ and σ, we'll utilize the standard normal distribution table (Z-table), which provides the cumulative probabilities for a standard normal distribution (mean = 0, standard deviation = 1). Then we'll apply the z-score formula to convert these values to the corresponding marks in our distribution.

Let [tex]\( Z_{75} \)[/tex] be the z-score corresponding to 75 marks, and [tex]\( Z_{40} \)[/tex]  be the z-score corresponding to 40 marks.

From the standard normal distribution table:

1. The z-score corresponding to the 90th percentile (10% above) is approximately [tex]\( Z_{75} = 1.28 \)[/tex] .

2. The z-score corresponding to the 20th percentile (20% below) is approximately [tex]\( Z_{40} = -0.84 \)[/tex].

The z-score formula is:

[tex]\[ Z = \frac{{X - \mu}}{\sigma} \][/tex]

where:

- [tex]\( X \)[/tex] is the raw score (marks)

- [tex]\( \mu \)[/tex] is the mean

- [tex]\( \sigma \)[/tex] is the standard deviation

Using the z-score formula, we can write two equations based on the given percentiles:

1. For 75 marks:

[tex]\[ 1.28 = \frac{{75 - \mu}}{\sigma} \][/tex]

2. For 40 marks:

[tex]\[ -0.84 = \frac{{40 - \mu}}{\sigma} \][/tex]

Now, we have two equations with two unknowns [tex](\( \mu \) and \( \sigma \))[/tex], we can solve them simultaneously to find the values of [tex]\( \mu \) and \( \sigma \)[/tex].

From equation 1:

[tex]\[ 1.28\sigma = 75 - \mu \][/tex]

[tex]\[ \mu = 75 - 1.28\sigma \][/tex]

From equation 2:

[tex]\[ -0.84\sigma = 40 - \mu \][/tex]

[tex]\[ \mu = 40 + 0.84\sigma \][/tex]

Now, equating the expressions for [tex]\( \mu \)[/tex] :

[tex]\[ 75 - 1.28\sigma = 40 + 0.84\sigma \][/tex]

Solving for [tex]\( \sigma \)[/tex] :

[tex]\[ 1.28\sigma + 0.84\sigma = 75 - 40 \][/tex]

[tex]\[ 2.12\sigma = 35 \][/tex]

[tex]\[ \sigma[/tex] ≈ [tex]\frac{35}{2.12}[/tex]

[tex]\[ \sigma[/tex] ≈ [tex]16.51[/tex]

Now that we have [tex]\( \sigma \)[/tex], we can find [tex]\( \mu \)[/tex] using one of the equations for [tex]\( \mu \)[/tex]:

[tex]\[ \mu = 75 - 1.28 \times 16.51 \][/tex]

[tex]\[ \mu[/tex] ≈ [tex]75 - 21.16[/tex]

[tex]\[ \mu \approx 53.84 \][/tex]

So, the values of [tex]\( \mu \) and \( \sigma \)[/tex] are approximately 53.84 and 16.51, respectively.

Answer:1.33

Step-by-step explanation:

Byron spent $1.38 more than Cassandra on other groceries, as we subtracted Cassandra's spending ($11.50) from Byron's ($12.88) to determine the difference.

The question asks us to determine how much more money Byron spent compared to Cassandra on their grocery shopping. To find this out, we need to compare the total amount of money each person spent. We have the cost of other groceries for each person, but the cost of yogurt is not given. To solve this problem, we just need to compare the cost of other groceries since that is the only information provided.

Byron spent $12.88 on other groceries.

Cassandra spent $11.50 on other groceries.

To find out how much more Byron spent, we subtract Cassandra's total from Byron's total:

$12.88 - $11.50 = $1.38

Therefore, Byron spent $1.38 more than Cassandra on other groceries.

Answer:

36

Step-by-step explanation:

x^2 + 12 x = 2

In order to complete the square we need to add ( b/2)^2 to each side where b is the coefficient of the x term

b=12

12/2 = 6

6^2 = 36

We need to add 36 to each side

Answer:

The answer is 17 1/6  you didnt notice the little line above the six you techniclly just convert the decimal to a fraction i had this on my lesson it tricked me to

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

So first of all I would convert the 20% to a decimal by dividing by 100 and you get 0.2

Then multiply 0.2 and 275 together and you get 55

If you are unsure on an answer, a way to quickcheck is setting the answer over your total

55

-------- =  0.2   ⇒  which equals 20%

275

Answer: 55

Step-by-step explanation:

First, find 10% of 275 (move the decimal place back once).

We now have 27.5.

Now, multiply 27.5 by 2 because we are finding 20%

So, 27.5 x 2= 55

The measure of Angle 1 is 35 degrees and the measure of Angle 2 is 55 degrees.

When two angles are complementary, their measures add up to 90 degrees. Let's define these two angles as follows: Angle 1 = x and Angle 2 = 2x - 15 (since it is 15 degrees less than twice the measure of Angle 1). You set up an equation based on the fact that the two angles add up to 90 degrees: x + 2x - 15 = 90. Solving this equation, you get 3x = 105, so x = 35. Thus, Angle 1 = 35° and Angle 2 = 2(35) - 15 = 55°.

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ANSWER

[tex]8 {cm}^{2} [/tex]

EXPLANATION

First let us determine the scale factor of the enlargement

[tex]k = \frac{image \: length}{corresponding \: object \: length} [/tex]

[tex]k = \frac{8}{1.6} [/tex]

[tex]k = 5[/tex]

This implies that that, the corresponding length of the smaller rectangle is

[tex]l = \frac{25}{5} = 5cm[/tex]

The area of the smaller rectangle is

[tex] = 5 \times 1.6 = 8 {cm}^{2} [/tex]

Answer:

x < 61

Step-by-step explanation:

Given

x + 12 < 73

Isolate x on the left side by subtracting 12 from both sides

x < 63 ← is the solution

Answer:

3 sin(41t) - 3 sin(t)

Step-by-step explanation:

The general formula to convert the product of the form cos(a)sin(b) into sum is:

cos(a) sin(b) = 0.5 [ sin(a+b) - sin (a-b) ]

The given product is:

6 cos(21t) sin(20t) = 6 [ cos(21t) sin(20t) ]

Comparing the given product with general product mentioned above, we get:

a = 21t and b = 20t

Using these values in the formula we get:

6 cos(21t) sin(20t) = 6 x 0.5 [ sin(21t+20t) - sin(21t-20t)]

= 3 [sin(41t) - sin(t)]

= 3 sin(41t) - 3 sin(t)

Therefore, second option gives the correct answer

Answer: C. The y-intercept means the concentration will remain 30% if no solution is added.  <-- on edgen2020

Explanation: The first person who answered is correct! I'm attaching a screenshot of my quiz with this- Good luck everyone! :)

Answer:

C. The y-intercept means the concentration will remain 30% if no solution is added.  

Step-by-step explanation:

edge2022

Answer:

It would roughly be 7 inches and 1/5 of an inch.

I hope this answer helped you! If you have any further questions or concerns, feel free to ask! :)

Step-by-step explanation:

Two creek crossings are separated by distance A = 7.2 inches on the map.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

The information is ,

Let's say the equation looks like this: A

Right now, A is valued at

The two stream crossings' separation is indicated on the map as A.

And on the chart, 3 inches equals 0.75 miles, therefore the distance between the two stream crossings is 1.8 miles.

hence, 3 / 0.75 inches Equals 1 mile.

In the map, 1 mile equals 4 inches after simplifying the calculation.

The two creek crossing's distance on the map is therefore equal to 1.8 x 4.

The two stream crossings will be separated by 7.2 inches on map A.

Hence, the distance on the map is 7.2 inches.

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Answer:

c

Step-by-step explanation:

The correct option is c. $336.36. The previous day's closing price of  stock was:c. $336.36.

To determine the closing price of stock the previous day, we need to use the information provided in the table. The table shows the net change (Chg) in the stock price and the current closing price (Close). The net change is the difference between the current closing price and the previous day's closing price.

From the table:

- Current closing price (Close): $342.64

- Net change (Chg): $6.28

Since the net change represents the increase in the stock price from the previous day to the current day, we can calculate the previous day's closing price by subtracting the net change from the current closing price.

[tex]\[\text{Previous day's closing price} = \text{Current closing price} - \text{Net change}\][/tex]

[tex]\[\text{Previous day's closing price} = 342.64 - 6.28 = 336.36\][/tex]

Therefore, the previous day's closing price of stock was:

c. $336.36

let's recall something about a right-triangle.

it has a 90° angle, and the longest side, the hypotenuse, from the pythagorean theorem, is c² = a² + b², or namely c = √( a² + b²).

so, let's take a peek at the two smaller sides, 60 and 11, can we get the longest side from it using the pythagorean theorem?

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=\stackrel{adjacent}{60}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ 61=\sqrt{60^2+11^2}\implies 61=\sqrt{3600+121} \\\\\\ 61=\sqrt{3721}\implies 61=61~~\stackrel{\textit{yeap, it is}}{\checkmark}[/tex]

The given lengths of 60ft, 61ft, and 11ft can form a right triangle. This has been confirmed by applying the Pythagorean theorem, which gives equal results for both sides of the equation.

In the field of Mathematics, the formation of a right triangle with given side lengths can be verified using the Pythagorean theorem. The theorem states: If a triangle is a right triangle, then the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, as represented by this formula: a² + b² = c².

Applying this theorem to your question, we can use the three lengths you've provided: 60ft, 61ft, and 11ft. Let's assign the longest length (considered as the hypotenuse in a right triangle) as 'c', which is 61ft in this case. The other sides 'a' and 'b' would be 60ft and 11ft.

Here's how the theorem fits: 60² + 11² = 61².

Calculating the squares gives us 3600 + 121 = 3721 for the left-hand side, and 3721 for the right-hand side as well. Since the results are equal, the given lengths can indeed form a right triangle according to the Pythagorean theorem.

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