The length of a rectangular rug is 4 less than twice its width. The perimeter of the rug is 40 feet. What is the area of the rug?
1) 96 sq ft
2) 56 sq ft
3) 104 sq ft
4) 86 sq ft

The required function y = 7 cos (2π * 0.1 * x) and period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

he cosine function can be used to model periodic motion, and its general form is:

y = A cos (Bx + C) + D

where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

In this case, we know that a 14 in. wave occurs every 10 s, so we can use this information to find the frequency, which is the reciprocal of the period. The period is the time it takes for one complete cycle of the wave, which in this case is 10 s.

Therefore, the frequency is:

\(f = \frac{1}{T}=\frac{1}{10} = 0.1 Hz\)

We can also see that the amplitude of the wave is 7 inches, since the wave has a height of 14 inches from its highest point to its lowest point.

Now we can write the function that models the height of the particle in inches y as it moves in seconds x:

y = 7 cos (2π * 0.1 * x)

Here, the frequency is expressed in radians per second (2π * 0.1 = 0.2π), since the cosine function takes radians as its argument. The phase shift and vertical shift are both zero in this case, since the wave starts at its highest point and has no vertical shift.

Therefore, the period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

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Answer:

Graph 1:   x > 2, -x < -2

Graph 2:   -x > -2, x<2

Graph 3:   x ≥ 2, -x ≤ -2

Step-by-step explanation:

#1

Hence inequality is x>2

#2

#3

Solid sphere means <= or >=

Here the inequality is

Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.

The answer to this problem: 2

Bethany worked a total of 44 hours, which means that she worked 40 normal hours and 4 extra hours.

Let x be the amount earned per 1 normal working hour since she earns a half more for each extra hour we can express the money earned above her 40 normal hours as 1.5 times x ( x+0.5*x = 1.5x), then we can express the gross pay like this:

gross pay = earnings per normal hour * normal hours + earnings per extra hour * extra hours

gross pay = x * normal hours + 1.5x * extra hours

As mentioned, she worked 40 normal hours and 4 extra hours, then we get:

gross pay = x*40 + 1.5x*4

gross pay = 40x + 1.5*4x

gross pay = 40x + 6x

gross pay = 46x

From the given information, we know that the gross pay equals $575, then we get:

575 = 46x

46x/46 = 575/46

x = 575/46

x=12.5

The amount earned with extra hours is 1.5x, then we get:

Extra hour earning = 1.5*12.5=18.75

Then, Bethany earned $18.75 for each extra hour

Answer:-16

Step-by-step explanation:

add all the temperature together =-112

then you divide by the number of temperatures given which is 7 which gives you -16

Answer:

-16 degrees C.

Step-by-step explanation:

When they say mean, they mean the average. You add the numbers together and divide them on how many numbers there are.

Answer and Step-by-step explanation:

We are given the perimeter equation: P = 2w + 2l, where w is width and l is length.

We want to find l. We do this by getting all of the variables to one side of the equation and have l by itself on the other side of the equation.

We start off by subtracting 2w from both sides of the equation.

P - 2w = 2w + 2l - 2w

P - 2w = 2l

Now we divide both sides of the equation by 2.

\(\frac{P-2w}{2} = \frac{2l}{2}\)

   \(\frac{P-2w}{2} = l\)

To simplify it further, we can write the equation as such:

\(l = \frac{1}{2}P - w\)

Have a good day!

The length of unknown side x is 58.

The correct answer is option D.

To find the unknown side length, x, in a right triangle with the base measuring 42 and the perpendicular measuring 40, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let x be the hypotenuse. Applying the Pythagorean theorem, we have:

\(x^2 = 42^2 + 40^2\)

Simplifying:

\(x^2\) = 1764 + 1600

\(x^2\)= 3364

Taking the square root of both sides to solve for x:

x = \(\sqrt{3364}\)

Simplifying the square root:

x = (\(\sqrt{4 * 841)}\)

Since 841 is a perfect square (\(29^2\)), we can further simplify:

x = 2 * 29

x = 58

Therefore, the unknown side length, x, is equal to 58.

From the options provided the correct option is D.

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The work required to pump the oil out through a hole to the top of the tank is approximately 6,476,160π/3 foot-pounds.

We can find the work required to pump the oil out of the tank by using the formula:

W = ∫[V1, V2]ρgh dV

Where

First, we need to find the density of the oil. We are told that the oil weighs 50 pounds per cubic foot, so:

ρ = 50 lb/ft^3

Next, we need to find the height of the oil column being pumped. The tank is half full, so the height of the oil column is:

h = r - (r/2) = r/2 = 8/2 = 4 feet

Now, we need to find the volume of oil being pumped. Since the tank is half full, the volume of oil is:

V = (1/2)(4/3)πr^3 = (1/2)(4/3)π(8)^3 = 1,024π/3 cubic feet

Finally, we can integrate the work formula to find the total work required:

W = ∫[V1, V2]ρgh dV

W = ∫[0, 1,024π/3] (50 lb/ft^3)(32.2 ft/s^2)(4 ft) dV

W = (6,476,160π/3) ft-lb

Therefore, the work required to pump the oil out through a hole to the top of the tank is approximately 6,476,160π/3 foot-pounds.

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Answer:

the son age is 13band Evans age is 52 years old at present day

Dan is 12 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the Age of Dan is x years

Mr. Evans Age = 4x

If Mr. Evans was 46 years old 2 years ago

The, Present age of Mr. Evans = 48 years

So, Dan's Age = 48/4

                        = 12 years.

Hence, Dan is 12 years old.

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Answer: Angle 1 corresponds with Angle 7.

Answer: To factor the expression -14 - (-8) completely using the distributive law, we need to simplify it first.

Remember that when we subtract a negative number, it is equivalent to adding the positive number. Therefore, -(-8) is the same as +8.

So the expression becomes:

-14 + 8

To factor it further using the distributive law, we can rewrite the addition as multiplication by distributing the -14 to both terms:

(-14) + (8) = -14 * 1 + (-14) * 8

This can be simplified as:

-14 + 8 = -14 * 1 + (-14) * 8 = -14 + (-112)

Finally, we can add the two negative numbers to get the result:

-14 + (-112) = -126

Therefore, the expression -14 - (-8) factors completely as -126.

The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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Answer:

Wouldn't it be 27 dollars?

Step-by-step explanation:

Answer:

Opportunity cost is the forgone benefit that would have been derived from an option not chosen. ... Considering the value of opportunity costs can guide individuals and organizations to more profitable decision-making.

Step-by-step explanation:

Answer:

Opportunity cost is the comparison of one economic choice to the next best choice.

The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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Answer:

\(f(x) = \frac{1}{2}x + 5\)

Step-by-step explanation:

So you can generally express a linear function use the slope-intercept form as such: \(y=mx+b\) where m=slope, and b=y-intercept.

The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule: \(f(x) = mx+5\)

The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula: \(m=\frac{y_2-y_1}{x_2-x_1}\) and this can be found using any two points, since the slope is constant.

We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run

\(\frac{6-5}{2-0} = \frac{1}{2}\)

So plugging this into the slope-intercept form you get the function

\(f(x) = \frac{1}{2}x + 5\)

Answer:

10 010 10 10 10 10 101 01 mo1

Step-by-step explanation:

If the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

In this question, we have been that the top 2% of athletes will go pro.

We are required to find the Z-Score that is required to be the top 2%.

Because only 2% of the top is pro then it will be a two tailed test.

The required percentage will be 2/2=1%

The value which we will require to catch up from table = 0.01

Z value = 0.0438

Therefore, if the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

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The True statements are:

Each element of X is given exactly one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

For D (x) = 2 x:

- x is the independent variable,

- D ( 6 ) = 2 · 6 = 12.

10 = 2 · 5,     12 = 2 · 9,     - 4 = 2 · ( - 2 ).

True statements are:

A ) D ( x ) is a function.

D ) D ( x ) is a direct variation.

E ) D ( x ) is a rule for the set of points ( 5, 10), ( 6, 12 ) and ( -2, - 4 ).

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Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

Answer:

Kindly check explanation

Step-by-step explanation:

regression to fit

x1 0 1 1 2 2 3 3 4 4

x2 0 1 2 1 2 1 2 1 2

y 15.1 17.9 12.7 25.6 20.5 35.1 29.7 45.4 40.2

Using technology ;

The multiple linear regression fit for the data is :

y = 9.025x1 - 5.704x2 + 14.461

Where 9.025 and - 5.704 are the slope values of x1 and x2 respectively.

14.461 = intercept.

The Correlation Coefficient, R from the output is 0.998 ; this depicts a strong positive relationship  between the independent variables and dependent variable.

Step-by-step explanation:

3x - 3y=3 which means 3x=3+4y

3x/3=3/3+4y/3 devide both sides by 3 to find c

x=1+4/3y we solve x instead of y

3(1+4/3y)-4y=3 replace x instead of y

Any value of y makes the equation True.

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer: 58 is the answer

hope this help and here my steps use a mark or a pin

and line it with the line if it's wrong sorry for the wrong

answer

Check the picture below.

Answer:

The cost of one share of the stock on Friday is $41.45

Step-by-step explanation:

The initial cost of one share of the stock on Monday is $41.45.

On Tuesday, the cost goes up by $0.58, so the cost becomes:

$41.45 + $0.58 = $42.03

On Wednesday, the cost goes down by $0.26, so the cost becomes:

$42.03 - $0.26 = $41.77

On Thursday, the cost also goes down by $0.26, so the cost becomes:

$41.77 - $0.26 = $41.51

Finally, on Friday, the cost goes down by $0.06.

So the expression to represent the cost of one share of the stock on Friday is:

$41.51 - $0.06

To evaluate this expression, we simply subtract $0.06 from $41.51:

$41.51 - $0.06 = $41.45

Therefore, the cost of one share of the stock on Friday is $41.45

Answer:

currency? . . . . . ........

Answer:

orange juice is better than Apple Juice

250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of alloy #11 and y represent the amount of alloy #15, hence:

(0.36x) + (y * 0.36) = 1(0.36)   (1)

Also:

0.28x + 0.64y = 1(0.55)    (2)

From both equations:

x = 0.25, y = 0.75

250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.

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The blank spaces in the statements area. S, R, and Q  are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

(a.) S, R, and Q are on a straight line. Therefore S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

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