1. A wife works three days then a day off while his husband works five days then a day off. If the couple has a day-off together today, how many days after will they have another day off together?
2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth. If a man weighs 180 pound on the surface of the earth, what would his weight be at an altitude 1000 miles? Assume the radius of the earth to be 4000 miles
3. Two turtles A and B start at the same time move towards each other at a distance of 150 m. The rate of turtle A is 10 m/s while that B is 20 m/s. A fly flies from one turtle to another at the same time that the turtles start to move toward its each other. The rate of the fly is constant at 100 m/s. determine the total distance traveled by the fly until the two turtles met?

Answer:

The student factored the numerator and denominator incorrectly. Instead of factoring to (x+1)(x+2)/(x+4)(x+2), they factored to (x+1)(x+2)/(x+4)(x+2) = (x+1)/x+4.

Factoring polynomials can be a difficult skill to master, and mistakes in factoring can lead to errors in simplifying rational expressions. Additionally, students may rush through factoring or not double-check their work, leading to careless errors.

Students can avoid mistakes like this by practicing factoring polynomials regularly and double-checking their work. It can also be helpful to write out each step clearly and show all work, so mistakes can be caught more easily.

My advice would be to practice factoring polynomials regularly, and double-check your work when simplifying rational expressions. Also, it is important to take your time and show all work, so mistakes can be caught more easily.

The expression can be expanded as a sum of three logarithms:

[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

What is the logarithms?

Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.

Using the properties of logarithms, we can expand the expression as follows:

[tex]log4(xy^5 Z^4) = log4(x) + log4(y^5) + log4(Z^4)[/tex]

Now, we can simplify each logarithm using the property that log[tex](a^b[/tex]) = b log(a):

[tex]log4(x) + log4(y^5) + log4(Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

Hence, the expression can be expanded as a sum of three logarithms:

[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

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The pool is 0.5 centimeters long in the drawing.

The ratio of 1 centimeter to 4 meters means that for every 4 meters in real life, Alice drew 1 centimeter in her drawing.

To find out how long the pool is in the drawing, we need to divide the actual length of the pool by the scale factor.

The scale factor is 4 meters : 1 centimeter, which is the same as 1 meter : 0.25 centimeters.

So to find the length of the pool in the drawing, we need to divide the actual length of the pool by 4 to get the length in meters, and then multiply by 0.25 to convert to centimeters:

Length in drawing = (32 meters / 4) x 0.25 = 2 x 0.25 = 0.5 centimeters

Therefore, the pool is 0.5 centimeters long in the drawing.

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Mrs Sheperd was going  7.5 miles per hour

Let us assume that d represents the distance covered by Mrs Shepard, 't' represents the time required and 's' represents the speed of her bike.

Here, d = 5.25 miles

t = 0.7 hours

We know that the formula of speed is speed = distance/time

Using this formula we calculate the speed (s) of Mrs Shepard's bike.

speed = distance/time

⇒ s = d/t

⇒ s = 5.25/0.7

⇒s = 7.5 miles per hour

This means that the speed (s) of Mrs Shepard's bike was 7.5 miles per hour

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Answer:

please your question is incomplete

Step-by-step explanation:

if....... of a number

Answer:

a = 13.3

Step-by-step explanation:

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

15^2 = a^2 + b^2

a^2 = 15^2 - 7^2 = 225 - 49 = 176

a = √176 = 13.26 = 13.3

The standard form for the circle x² - 10x + y² + 14y - 7 = 0 is (x - 5)² + (y + 7)² = 81. The correct answer is D.

To find the standard form of the given circle, we must complete the square by rearranging the equation and adding constants to both sides of the equation to create perfect squares. Here are the steps:

1. Rearrange the equation so that the x and y terms are together:
x² - 10x + y² + 14y = 7

2. Complete the square for the x terms by adding (10/2)² = 25 to both sides of the equation:
x² - 10x + 25 + y² + 14y = 7 + 25

3. Complete the square for the y terms by adding (14/2)² = 49 to both sides of the equation:
x² - 10x + 25 + y² + 14y + 49 = 7 + 25 + 49

4. Simplify the equation by factoring the perfect squares:
(x² - 10x + 25) + (y² + 14y + 49) = 7 + 25 + 49

(x - 5)² + (y + 7)² = 81

So, the standard form for this circle is (x - 5)² + (y + 7)² = 81, which is option D.

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Answer:

5°

Step-by-step explanation:

because: -5°+5°=0° I think

Answer:

5 degrees

Step-by-step explanation:

-5+5=0

Sinusoidal (periodic) functions, also known as sine and cosine functions, are ubiquitous in our daily lives. They are used to model a wide range of phenomena in fields such as engineering, physics, and mathematics.

One of the most common applications of sinusoidal functions is in the field of electronics, where they are used to model alternating current (AC) circuits.

Sinusoidal functions are also used in signal processing, audio and image compression, and speech recognition. In addition, they are used in the design of various mechanical and electrical systems, such as engines, turbines, and power generators.

Sinusoidal functions also play an important role in wave motion, such as ocean waves and sound waves. They are used to model the behavior of waves and to predict their properties, such as wavelength and frequency.

Furthermore, sinusoidal functions are used in the field of optics to model the behavior of light waves. They are used to describe the properties of light waves, such as amplitude, frequency, and phase.

In conclusion, sinusoidal functions have a wide range of applications in various fields, from electronics and signal processing to mechanics and optics. Their versatility and accuracy make them an essential tool for modeling and predicting real-world phenomena.

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The expression of one hundred twenty rupees and five paise in rupees is equals to the rupees 120.05.

We have, 120 rupees and 5 paise and we will express as rupees using decimals.

We have been given 5 paise. As we see 120 rupees so it's remain as it but we have to change 5 paise in rupees. Using the conversation factor, as we know that 100 paise = rupee 1

=> 1 paisa = Rs. 1/100

so, here conversation factor is = 1/100

The required value is obtained by multiplying the observed values by conversion factor. Therefore,

5 paise = Rs. (5×1/100)

= 5/100

= Rs. 0.05

Therefore, in decimals 5 paise = Rs. 0.05. Now, 120 rupees 5 paise = Rs. 120 + Rs. 0.05 = Rs. 120.05

Hence, required value is Rs. 120.05.

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Complete question:

Express in form of rupees

120 rupees 5 paise = — rupees.

The equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

equation of a line using point-slope form is-

y - y1 = m(x - x1)

Points: (17,-12) and  slope -3.

Put the values:

y - (-12) = -3(x - 17)

y + 12 = -3x + 51

y = -3x + 51 - 12

y = -3x + 39

Thus, the equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

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Answer:

0.38

Step-by-step explanation:

The graph and the table show the high temperatures in a city over a 10-day period. here are the right answer:

a. 60, b. 2, 4, and 6 days

c. Yes, the high temperature is a function of the day.

The following group is shows a the high temperatures in a city for 10 -days. Where height temperature is on day 9, lowest temparature in day 7. Here the high temperature is a function of the day.            

Here we have

The graph and the table show the high temperatures in a city for 10-days    

From the table,

The high temperature on Day 7 = 60      

The high temperature 61 degrees on 2, 4, and 6 days

Since the graph shows the change in temperature as well as the change in the number of days the high temperature is a function of the day  

Therefore,

The answer are

a. 60, b. 2, 4, and 6 days

c. Yes, the high temperature is a function of the day.

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The range οf P-values wοuld be 0.01 < P-value < 0.02

In statistics, a test statistic is a numerical value that is calculated frοm a sample οf data and is used tο determine whether οr nοt tο reject a null hypοthesis in a hypοthesis test.

The chοice οf test statistic depends οn the specific hypοthesis test being perfοrmed and the nature οf the data being analyzed. Fοr example, in a t-test fοr the mean οf a nοrmally distributed pοpulatiοn, the test statistic is the t-value, which is calculated as the difference between the sample mean and the hypοthesized pοpulatiοn mean divided by the standard errοr οf the mean.

Using Table A-3 with n = 38 and a left-tailed test statistic t = 2.714, we find the cοrrespοnding P-value tο be between 0.01 and 0.02. Therefοre, the range οf values fοr the P-value is:

0.01 < P-value < 0.02

Sο the cοrrect respοnse is:

0.01 < P-value < 0.02

Hence, the range οf P-values wοuld be 0.01 < P-value < 0.02

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Complete Question:

The equations y-6=x² and y=2x²+5-3x³ are non linear. Therefore, options D and F are the correct answers.

A linear function is a function that represents a straight line on the coordinate plane. The standard form of a linear function is y = mx + b.

Here, 'm' is the slope of the line, 'b' is the y-intercept of the line, 'x' is the independent variable and 'y' (or f(x)) is the dependent variable.

A) y=x

Here, degree of the equation is 1, so the equation is linear.

B) 2y=12x

Here, degree of the equation is 1, so the equation is linear.

C) y=8+x

Here, degree of the equation is 1, so the equation is linear.

D) y-6=x²

Here, degree of the equation is 2, so the equation is quadratic.

E) y=13-5x

Here, degree of the equation is 1, so the equation is linear.

F) y=2x²+5-3x³

Here, degree of the equation is 3, so the equation is cubic.

Therefore, options D and F are the correct answers.

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In quadrilateral EFGH, sides FG and EH are congruent because they each have a length of 7.07. Sides EF and GH are not congruent. The area of quadrilateral EFGH is closest to 41 square units.

For the width, we would determine the distance between the vertices F (-1, 4) and G(4, -1)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance FG = √[(4 - (-1))² + (-1 - 4)²]

Distance FG = √[5² + (-5)²]

Distance FG = √50

Distance FG = 7.07 units.

Distance EH = √[(1 - (-4))² + (-4 - 1)²]

Distance EH = √[5² + (-5)²]

Distance EH = √50

Distance FG = 7.07 units.

For the length, we would determine the distance between the vertices E (-4, 1) and F (-1, 4)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance EF = √[(-1 - (-4))² + (4 - 1)²]

Distance EF = √[3² + (3)²]

Distance EF = √9

Distance EF = 3 units.

Distance HG = √[(4 - 1)² + (1 - (-4))²]

Distance HG = √[3² + (5)²]

Distance HG = √34 units.

Mathematically, the area of a rectangle can be calculated by using this formula:

Area of rectangle = length × width

Area of rectangle = √34 × 7.07

Area of rectangle = 41.22 square units.

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The length of the diagonal of this square is 11 and option 4 is the correct answer.

A diagonal line is a line segment that joins two of a shape's vertices when there isn't already an edge between them. It doesn't go directly above, below, or across. The diagonals are always in the form of a straight line. In other terms, a diagonal is a line that passes through the vertex of a polygon or polyhedron and links its opposing corners.

Given that, x is the length of the diagonal of the square.

Also, x² = 132

The value of x is:

x = √132

x = 11.48

Hence, the length of the diagonal of this square is 11 and option 4 is the correct answer.

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In order to outline the yard and the garden allotment with bricks and Using Pythagorean theorem, Mariah will need to buy about 69.4  yards³ of brick.

what is pythagoras theorem ?

According to the Pythagorean Theorem, the square of the length of the hypotenuse in a right triangle equals the total of the squares of the lengths of the other two sides. The hypotenuse is the side that faces the right angle. In mathematics, it can be expressed as:

c² = a² + b²

where the lengths of the other two sides (the legs) of the right - angled triangle are a and b, and c is the length of the hypotenuse. Pythagoras, an ancient Greek mathematician, is attributed with discovering and proving this theorem, so it bears his name. Geometry, algebra, and other fields of mathematics and science all make extensive use of the Pythagorean Theorem.

given

The Pythagorean formula can be used to determine side C.

C² = A² + B²

C²= 30² + 50²

C² = 900 + 2500

C² = 3400

C ≈ 58.3

As a result, the triangle-shaped yard's circumference is:

30 + 50 + 58.3 ≈ 138.3 feet

We require information regarding the measurements of the rectangular garden plot. Let's assume it is 20 feet long and 15 feet wide.

Thus, the vegetable plot's perimeter is as follows:

2(20 + 15) = 70 feet

The perimeters must now be converted from feet to yards (since we are calculating square yards).

circumference of a triangular yard: 46.1 yards x 138.3 feet

Garden plot boundaries measured as 70 feet by 23.3 yards.

In order to calculate the overall number of bricks required, we add the two perimeters:

46.1 plus 23.3 equals 69.4 square yards.

In order to outline the yard and the garden allotment with bricks, Mariah will need to buy about 69.4  yards³ of brick.

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Answer:

962.084375 meters² or 306.25π

Step-by-step explanation:

A diameter is a line that goes straight through the center of the circle. Since it goes through the center, it creates 2 radii. This splits the diameter into 2 separate parts, and since the diameter is 25 meters, that means that the radius will be 25/2 = 17.5 meters.

The formula for the area of a circle is pi • r²

Since we know the radius (17.5), we can solve this expression:

pi • 17.5²

pi • 306.25

If we use 3.1415 for pi, we get962.084375 meters²

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The given permutations can be expressed as the product of the following cyclic permutations: (1 4 5 10)(2 6)(3 9 7 8).

The given permutations can be expressed as products of cyclic permutations as follows:

S10 = ([1,2,3,4,5,6,7,8,9,10],[4,6,9,5,10,2,8,3,7,1])

= (1 4 5 10)(2 6)(3 9 7 8)(7 8 3 9)

= (1 4)(4 5)(5 10)(2 6)(3 9)(9 7)(7 8)(8 3)

= (1 4 5 10)(2 6)(3 9 7 8)

Therefore, the given permutations can be expressed as the product of the following cyclic permutations: (1 4 5 10)(2 6)(3 9 7 8).

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Answer:

the answer is 88 square inches

Step-by-step explanation:

[tex]2(6 \times 4) + 2(4 \times 2) + 2(6 \times 2) = 88[/tex]

Answer: m=2

Step-by-step explanation: First convert the equation to slope-intercept form; y=mx+b. This new equation would be 3y=6x-12. Because y must be singular, each side must be divided by 3, to isolate the variable y. After doing this, the equation is y=2x-4. In terms of y=mx+b, m is attached to x, making the slope of this equation 2.

Answer:

y - 7 =  3/5 (x - 1)

Answer:

   ∠e = 32°

   ∠d = 69°

   ∠f = 79°

Step-by-step explanation:

       Angle e and 32° are vertical angles, so this means that ∠e = 32° because vertical angles are congruent.

       Next, a straight line is equal to 180°, and angle e is equal to 32°, so we can write the following equation to solve for angle f:

69° + e + f = 180° ➜ 69° + 32° + f = 180° ➜ 101° + f = 180° ➜ f = 79°

       Lastly, angle d and 69° are also vertical angles, so this means that ∠d = 69° because vertical angles are congruent.

Answer:

Step-by-step explanation:

it's -4.89279003

Option D is correct, the total purchase price is $111.65.

percentage, a relative value indicating hundredth parts of any quantity.

Lets find the price of each item

Inflatable shark: $12.99

8 gallons of chlorine at $1.99 each: 8 x $1.99 = $15.92

2 gallons of algaecide at $7.99 each: 2 x $7.99 = $15.98

1 thermometer for $12.99: $12.99

2 sets of fins at $22.99 each: 2 x $22.99 = $45.98

Now add the costs of all the items:

$12.99 + $15.92 + $15.98 + $12.99 + $45.98 = $103.86

we multiply the total cost by the tax rate to find the sales tax.

$103.86 x 0.075 = $7.79

Finally, we add the sales tax to the total cost to get the final purchase price:

$103.86 + $7.79 = $111.65

Therefore, the total purchase price is $111.65.Option D is correct.

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Therefore, approximately 408 packages of paper can be put on the shelf.

Area is a measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units such as square meters, square inches, or square feet. The area of a shape can be found by multiplying the length of the shape by its width. The concept of area is used in many areas of mathematics and in a wide range of real-world applications, including architecture, engineering, physics, and geography. The ability to calculate the area of a shape is an important skill in many fields and is a fundamental concept in geometry.

Here,

To solve this problem, we need to find the number of packages of paper that can fit on the warehouse shelf by dividing the total shelf area by the area of each package.

First, we need to convert the height of the shelf from feet and inches to inches:

1 foot = 12 inches

1' 5" = 1 * 12 + 5 = 17 inches

Next, we need to convert the length of the shelf from yards to inches:

1 yard = 36 inches

2 yards = 2 * 36 = 72 inches

Now we can find the area of the warehouse shelf:

Area = length * height

Area = 72 inches * 17 inches

Area = 1224 square inches

The area of each package of paper is:

Area = height * width

Area = 2 inches * 1.5 inches

Area = 3 square inches

Now we can find the number of packages of paper that can fit on the warehouse shelf:

Number of packages = Shelf area / Package area

Number of packages = 1224 square inches / 3 square inches

Number of packages ≈ 408

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Answer:

Step-by-step explanation:

1. Figure out which terms are alike. I have separated the like terms using parenthesis for clarification, however, this is not necessary when solving by yourself.

(3y + 4y) + (8 + 2)

2. Combine both sets of like terms however the signs dictate. In this case, add all the signs.

3y + 4y = 7y  

(solve as if there was no constant so if 3 + 4 = 7 then 3y + 4y = 7y)

8 + 2 = 10

3. Put it all together

Final answer: 7y + 10

Note: Understanding how to combine and simplify like terms will be very helpful when you eventually will have to solve for y. When solving an equation you will always want to start by combing and simplifying like terms first.