Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo

Kevin has $768 invested in the 11% account and $1218 invested in the 14% account.

Let x be the amount invested in the 11% account

y be the amount invested in the 14% account.

The equation for the two different interest rate is determined as;

y = x + $450

0.11x + 0.14y = $255

Solve the two equation simultaneously;

0.11x + 0.14(x + $450) = $255

0.11x + 0.14x + $63 = $255

0.25x = $192

x = $768

Then we can use the first equation to find y;

y = x + $450

y = $768 + $450

y = $1218

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Answer:

f(x)=(x+3)(x+2)(x-3)(x-4)

Step-by-step explanation:

Answer: f(x)=(x+3)(x+2)(x-3)(x-4)

Step-by-step explanation:

Answer:

24 cm²

Step-by-step explanation:

area of square base = 2 X 2 = 4cm²

area of a triangle = 0.5 X width X vertical height

area of one slanted side = 0.5 X 2 X 5 = 5

there are 4 sides to square pyramid. so area of 4 slanted sides = 4 (5)

= 20cm²

total surface area = 4 slanted sides + base

                             = (20 + 4)cm²

                             = 24cm²

Each year, your bank account would accumulate $30 in interest.

A bank account is a financial account provided by a bank or financial institution that allows individuals or businesses to deposit money, make withdrawals, and perform various financial transactions. Bank accounts offer a secure and convenient way to manage and store your money.

To calculate the amount of money that would accumulate in your bank account each year from a $600 tax refund invested at 5% simple interest, we can use the formula:

Interest = Principal * Rate

where:

Principal = $600 (initial investment)

Rate = 5% (0.05 in decimal form)

Interest = $600 * 0.05

Interest = $30

Therefore, each year, your bank account would accumulate $30 in interest.

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Answer:

30.48cm

Step-by-step explanation:

The best way to perform conversion is by the multiplication of fractions to keep track of units. You'll see in the equation below that inches cancels out. Leaving you with cm in 1 ft.

[tex]\frac{2.54 cm}{1in}* \frac{12 in}{1ft} = \frac{30.48cm}{1ft}[/tex]

Answer:

30.48 centimeters

Step-by-step explanation:

To answer this question, keep in mind 1 foot = 12 inches. If 2.54 cm = 1 in., and you are trying to find how many centimeters there are in 12 inches (1 ft), you need to multiply (2.54)(12)=30.48

Step-by-step explanation:

Not yet sure how to do this other than graphically....

.88893 ~ = x

The solution x = 3 and y = 9 means that the point of intersection of the two lines

Other solutions are italicized below

The statement in the question is given as

Solution to a system of linear equation is x = 3 and y = 9

The intersection of the points can be described as

From the origin, move 3 units right and 9 units up

The meaning of the solution is that

The point of intersection of the two lines

Can you have more than one solution to a system of linear equations?

The answer to this is No.

This is because, the lines are straights and they can only intersect once or none at all

Can you have exactyly one solution to a system of linear equations?

The answer to this is also No.

This is because, the lines are straights and they can only intersect once or none at all

Can you have no solution to a system of linear equations?

The answer to this is Yes.

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The frequency, f, on a piano is equivalent to the pitch or tone of a specific note produced by a vibrating string or air column.

On a piano, the frequency of a particular note can be determined using the formula:

[tex]f = 2^{(n/12) }\times f0[/tex]

In this formula, f represents the frequency of the note, n is the number of half-steps from a reference note, and f0 is the frequency of the reference note.

To understand the equivalences to f, let's break down the formula components:

[tex]2^{(n/12)[/tex]: This part of the formula calculates the factor by which the frequency of the note changes based on the number of half-steps away from the reference note. It uses the exponential function with a base of 2 and raises it to the power of n/12. This term accounts for the logarithmic nature of musical pitch and determines the frequency ratio between two adjacent notes on a piano.

f0: This term represents the frequency of the reference note, which serves as a starting point for the calculation. The reference note is typically A4 (the A above middle C) and has a standard frequency of 440 Hz. However, different tuning systems or historical contexts may use alternative reference frequencies.

Combining these elements, the formula calculates the frequency of a note based on its position relative to the reference note, taking into account the logarithmic nature of musical pitch.

Therefore, "f" in the given formula is equivalent to the frequency of the note being considered on the piano. By plugging in the appropriate values for "n" (the number of half-steps from the reference note) and "f0" (the frequency of the reference note), we can determine the specific frequency of any note on the piano.

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There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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Answer:

754 cm²

Step-by-step explanation:

The total surface area of a cylinder
= Lateral Surface Area + Top surface area + Bottom Surface Area

Top and Bottom surfaces are both circles

Given radius r and height h

Lateral surface area = 2πrh

Top surface area = Bottom surface area = πr²

Top + Bottom surface area = πr²  + πr²   = 2πr²

With r = 6 and h = 14 cm

Total surface area
= 2πrh + 2πr²
= 2πr(h + r)

= 2π · 6(14 + 6)

= 12π (20)

= 240 π

≈ 754 cm²

The new coordinates of the triangle after enlargement by a scalar factor of -3 with center (3,3) are: (3, 0), (-3, -3), and (3, -3).

To enlarge a triangle by a scalar factor of -3 with center (3,3), we need to use the following formula to find the new coordinates:

(x', y') = (-3(x-3) + 3, -3(y-3) + 3)

where (x, y) are the original coordinates, and (x', y') are the new coordinates after the enlargement.

For the point (3, 4):

(x', y') = (-3(3-3) + 3, -3(4-3) + 3)

= (3, 0)

So the new coordinates for this point are (3, 0).

For the point (5, 5):

(x', y') = (-3(5-3) + 3, -3(5-3) + 3)

= (-3, -3)

So the new coordinates for this point are (-3, -3).

For the point (3, 5):

(x', y') = (-3(3-3) + 3, -3(5-3) + 3)

= (3, -3)

So the new coordinates for this point are (3, -3).

Therefore, the new coordinates of the triangle after enlargement by a scalar factor of -3 with center (3,3) are: (3, 0), (-3, -3), and (3, -3).

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Hello!

--------------------------------------------------------------------------------------------------------

(a) y = 36° and x = 36°

DAB = 90°

so y = 90° - 54° = 36°

---------------------------------

AB // DC

so x and y are alternate-internal

so x = y = 36°

--------------------------------------------------------------------------------------------------------

(b) y = 73° and x = 68°

SPQ = 90°

so yPQ = 90° - 51° = 39°

the sum of the angles of the triangle PQR = 180°

so y = 180° - (39° + 68°) = 73°

---------------------------------

PSy = 90°

the sum of the angles of the triangle PSy = 180°

so PyS = 180° - (51° + 90°) = 39°

SyxR is a flat angle = 180°

so x = 180° - (39° + 73°) = 68°

--------------------------------------------------------------------------------------------------------

(c) y = 36° and x = 54°

The center of the triangle is K.

So the triangles NKO, MKP, MNK, POK are isosceles

NKO = MKP and MNK = POK

MKP and NKO are opposed

so MKP = NKO = 72°

K is a full angle = 360°

so MKN and PKO = 360° - (72° + 72°) = 216°

so MKN = PKO = 216°/2 = 108°

PMN = y so because MKN is isoscel.

so we know x + y = 90° because PMN = 90°

and so we know PON = OPM = y

and so we know KNO = KON = x

the sum of the angles of the triangle KNO = 180°

so KNO and KON = 180° - 72° = 108°

so x = 108°/2 = 54°

---------------------------------

the sum of the angles of the triangle MKN = 180°

so KMN and KNM = 180° - 108° = 72°

so y = 72°/2 = 36°

--------------------------------------------------------------------------------------------------------

Answer:

[tex]y = - \frac{8}{5}x + 8[/tex]

Answer:

y = - [tex]\frac{5}{3}[/tex] x + 8

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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 3) and (x₂, y₂ ) = (6, - 2) ← 2 points on the line

m = [tex]\frac{-2-3}{6-3}[/tex] = [tex]\frac{-5}{3}[/tex] = - [tex]\frac{5}{3}[/tex]

the line crosses the y- axis at (0, 8 ) ⇒ c = 8

y = - [tex]\frac{5}{3}[/tex] x + 8 ← equation of line

These two expressions can be used to represent the total amount you will have to pay, taking into account the cost of a cookie and the sales tax of 5.5%.

To calculate the total amount you will have to pay, considering the cost of a cookie (represented by "c") and the sales tax of 5.5%, you can use the following expressions:

Expression for the sales tax amount:

The sales tax amount can be calculated by multiplying the cost of the cookie (c) by the sales tax rate of 5.5% (or 0.055). The expression would be:

Sales Tax = c × 0.055

Expression for the total amount to be paid:

To calculate the total amount you will have to pay, including the cost of the cookie and the sales tax, you need to add the cost of the cookie to the sales tax amount. The expression would be:

Total Amount = c + (c × 0.055)

Therefore, these two expressions can be used to represent the total amount you will have to pay, taking into account the cost of a cookie and the sales tax of 5.5%.

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The two expressions representing the total amount to pay after sales tax of [tex]5.5\%[/tex]:

[tex]\[ \text{Sales tax amount} = 0.055c \][/tex]

[tex]\[ \text{Total amount with tax} = 1.055c \][/tex]

To represent the total amount you will have to pay when buying a cookie, including the sales tax of [tex]5.5\%[/tex], we can start with the cost of the cookie, represented by the variable [tex]\(c\)[/tex]. The two expressions required are as follows:

1. Expression for the total amount with tax added:

The first expression represents the total amount you need to pay, which includes the cost of the cookie plus the sales tax. The sales tax of [tex]5.5\%[/tex] can be calculated by multiplying the cost of the cookie [tex](\(c\))[/tex] by [tex]0.055[/tex] (since [tex]5.5\%[/tex] is equivalent to [tex]0.055[/tex] as a decimal). Therefore, the expression becomes:

[tex]\[ \text{Total amount with tax} = c + 0.055c \][/tex]

Simplifying this expression, we can combine the two terms involving [tex]\(c\)[/tex]:

[tex]\[ \text{Total amount with tax} = 1.055c \][/tex]

2. Expression for the sales tax amount:

The second expression represents only the sales tax amount that needs to be added to the cost of the cookie. It can be calculated by multiplying the cost of the cookie [tex](\(c\))[/tex] by [tex]0.055[/tex]. Thus, the expression is:

[tex]\[ \text{Sales tax amount} = 0.055c \][/tex]

These two expressions represent the total amount you will have to pay when purchasing a cookie, accounting for the [tex]5.5\%[/tex] sales tax.

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Answer:

7.28 units

Step-by-step explanation:

To find the distance between two points, we use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates given, we can plug in the values:

d = √((-5 - 2)^2 + (5 - 7)^2)

d = √((-7)^2 + (-2)^2)

d = √(49 + 4)

d = √53

Therefore, the distance between (2,7) and (-5,5) is approximately 7.28 units (rounded to two decimal places).

Mahdi's score is,

⇒ 0.5

We have to given that;

3 times Mahdi’s score is one and a half.

Now, Let Mahdi's score = x

Hence, We can formulate;

⇒ 3x = 1 1/2

⇒ 3x = 3/2

⇒ x = 1/2

⇒ x = 0.5

Thus, Mahdi's score is,

⇒ 0.5

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The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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Hello!

5/9 x 4

= 4x5/9

= 20/9

= 2,2222miles

Answer: No

Step-by-step explanation:

The definition of a function includes that each input must have one and only one output

The first graph has the input 5 giving two different outputs so it is not a function

The second graph has the input 7 giving two different outputs so it is not a function

Answer:

2.61 miles

Step-by-step explanation:

A unit can be used for measurement and is commonly found in mathematics to describe length, size, etc.

If we know that 1 mile = 5280 feet, then we can divide the elevation in feet by the number of feet per mile.

The elevation of the Grand Teton in miles would be:

Therefore, the elevation of the Grand Teton is approximately 2.61 miles above sea level when rounded to two decimal places.

Answer:

2.61

Step-by-step explanation:

Randy's error is in the first step of the division, where he subtracts 4x² instead of adding it. The correct subtraction should be: x³ + 2x² + 5x - 3

Randy made an error in the step where he subtracted (2x² - 2x + 1) from (2x² - 3x³ - 3x² + 7x - 3).

Instead of getting -x³ + 4x² + 6x - 4 as the result, he got 2x⁴ - 4x³ + 2x². This error occurred because he forgot to change the sign of all the terms in (x² - 2x + 1) when subtracting it from the polynomial.

It should be (3x³ - 2x² + 7x - 3) divided by (x² - 2x + 1).

Let me proceed with this corrected version of the question.

Randy divides (3x³ - 2x² + 7x - 3) by (x² - 2x + 1) as,
2x² + x + 3
____________
x² - 2x + 1) 3x³ - 2x² + 7x - 3
2x³ - 4x² + 2x
_____________
x³ - 2x² + 5x
x³ - 2x² + x
____________
-3x² + 4x - 3
-3x² + 6x - 3
___________
[tex]-2x^2[/tex] + x - 3

3x³ - 2x² + 7x - 3
-(2x³ - 4x² + 2x)
______________
x³ + 2x² + 5x - 3

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Randy made an error while dividing (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). He mistakenly subtracted intermediate results from zero instead of the original polynomial, leading to an incorrect division.

Randy made an error in his division of the polynomial (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). Let's go through the division process step by step to identify the mistake:

Randy correctly started by dividing 2x⁴ by x², which gives him 2x² as the first term of the quotient.

He then multiplied (x² - 2x + 1) by 2x², which resulted in 2x⁴ - 4x³ + 2x². So far, so good.

Randy should have subtracted this result from the original polynomial (2x⁴ - 3x³ - 3x² + 7x - 3), but he mistakenly subtracted it from 0. The correct step should have been to subtract 2x⁴ - 4x³ + 2x² from (2x⁴ - 3x³ - 3x² + 7x - 3).

Here's the corrected division:

(2x⁴ - 3x³ - 3x² + 7x - 3) - (2x⁴ - 4x³ + 2x²) = -3x³ - 5x² + 7x - 3

Now, Randy should have continued the division by bringing down the next term, which is -3x², and repeated the process. However, he incorrectly moved to the next step without subtracting -3x³ - 5x² + 7x - 3 from (x² - 2x + 1).

So, Randy's error is that he failed to properly subtract the intermediate result from the original polynomial, causing the division process to go awry.

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The value of the functions, f(x) at the specified x-values are;

26. A. -1

27. C. 8

28. B. 1/2

29. A. -176

A function is a rule or definition that maps the elements of a set of input variables unto a set of output variables, such that each input maps to exactly one of the elements in the set of the output variables.

26. The function is; f(x) = 3·x² + 2·x - 1

Therefore; f(0) = 3 × 0² + 2 × 0 - 1 = -1

The correct option is therefore;

A. -1

27. The function is; g(x) = (1/2)·x³ + 2·x

Therefore; g(2) = (1/2) × 2³ + 2 × 2 = 8

The correct option is therefore;

C. 8

28. The function is; f(x) = (√(9 - x))/4

Therefore; f(5) = (√(9 - 5))/4 = 1/2

f(5) = 1/2

The correct option is therefore;

B. 1/2

29. The function is; f(x) = (11·(x - 24))/2

Therefore; f(-8) = (11 × ((-8) - 24))/2 = -176

The correct option is therefore;

A. -176

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Answer:

the cheeseburgers were purchased by micky

[tex]\underline{ \textbf{Hello !}}[/tex]

[tex]\sf{average = \frac{5+15+30+25+40}{5} =\frac{115}{5} = 23}\\\\{\boxed{\textbf{The~ average~ is~equal~to~23}}[/tex]

Answer:

The diagonals of a rectangle are congruent, so the other diagonal is also 15 feet.

Step-by-step explanation:

Answer:

f(x) is 579.

Step-by-step explanation:

The equation y=9x^6+x^4-2x^2-5 represents a function where y depends on the value of x. To find the f(x) of this function, we simply replace y with f(x), which gives us:

f(x) = 9x^6 + x^4 - 2x^2 - 5

This means that if you plug in a specific value of x, the function will output a corresponding value of f(x). For example, if you plug in x=2, you would get:

f(2) = 9(2)^6 + (2)^4 - 2(2)^2 - 5

f(2) = 9(64) + 16 - 8 - 5

f(2) = 576 + 3

f(2) = 579

So when x is 2, f(x) is 579.

The values of the underlined digits in the given numbers are as follows:

1. 8 , 2. 0 , 3. 1 , 4. 3 , 5. 8

To determine the value of the underlined digit in each of the given numbers, let's examine each number separately:

1. 34.98:

The underlined digit is the 8 in the tenths place. It represents 8/10 or 0.8.

2. 67.04:

The underlined digit is the 0 in the hundredths place. It represents 0/100 or 0.

3. 5.614:

The underlined digit is the 1 in the thousandths place. It represents 1/1000 or 0.001.

4. 400.563:

The underlined digit is the 3 in the tenths place. It represents 3/10 or 0.3.

5. 0.782:

The underlined digit is the 8 in the hundredths place. It represents 8/100 or 0.08.

Therefore, the values of the underlined digits in the given numbers are as follows:

1. 8

2. 0

3. 1

4. 3

5. 8

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a) The probability that the test comes back negative for all six people is  95.8%,

b)  The probability that the test comes back positive for at least one of the six people is 4.2%.

(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.

Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:

P(negative for all 6) = (0.993)^6 ≈ 0.958

Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.

(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.

The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.

The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:

P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042

Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.

In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.

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Answer:

number 1 : the amount of foil i need to line my crock pot