Tom took 1/2hours to clean the den. Then he took 2 1/8 hours to clean the bedroom. How much total time did Tom take to clean the two rooms?

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Answer:

To find the median marks, we need to arrange the marks in ascending order and find the middle value.

0-20: 42 students

21-30: 38 students

31-40: 120 students

41-50: 84 students

51-60: 48 students

61-70: 36 students

71-80: 32 students

Since there are a total of 450 students, the median will be the value at the 225th position if we arrange the marks in ascending order. The value at the 225th position will be the lower value of the interval that the 225th student falls in.

The students in the intervals 0-20, 21-30, and 31-40 account for 42+38+120 = 200 students, which means that the 25th student falls in the 41-50 interval. Therefore, the median marks are 41.5.

To find the percentage of failures, we need to count the number of students who scored below 35 marks and divide it by the total number of students, and multiply the result by 100 to express it as a percentage. The number of students who scored below 35 marks is 42+38 = 80. The percentage of failures is 80/450 * 100 = 17.78%.

Answer: -2x + 3y > 7

Step-by-step explanation:

x coordinate is -2

y coordinate is 3

> is the left side

Besides that answer is the only one that makes sense if you only look at the x and y coordinate

Answer:

I'm going sit on a computer with me to work and get some milk for a bacon for the blue cup next time I'm in level 12 with all my heart broken bones so I'm going sit on it all the night and get back on it all night so I'm going sit on my couch with the milk to make it can't be gk for a bit

4q² + 8q +4 = (4q+4)(q+1) = 4(q+1)²

Given, 4q² + 8q +4

Factorization of the given equation takes place as follows:

the equation is a function of q

or f(q) = 4q² + 8q +4

we can write 8q = 4q + 4q

f(q) = 4q² + 4q+ 4q +4

now we can take (q+1) as common

f(q) = 4q(q+1) + 4(q+1)

or f(q) = (4q+4)(q+1) = 4(q+1)²

4q² + 8q +4 = (4q+4)(q+1) = 4(q+1)²

Therefore, the factors of 4q² + 8q +4 are (4q+4)(q+1) or 4(q+1)².

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Answer: 4 (q + 1)²



Step-by-step explanation:

I did the attached solution through middle term breaking meothod, but you could apply the whole square formula as well and get the same answer. i.e (a + b)² = a² + 2ab + b²

hope that helps...

An answer which classifies the function using finite differences is: B. the function is linear with a constant first difference of 3.

Based on the data points in the table, we have the following input and output values;

x                 f(x)

-16            -13.5

-12            -10.5

-8              -7.5

-4              -4.5

0                -1.5

Next, we would determine the slope of this function for data points 1 and 3 as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-7.5 - (-13.5))/(-8 - (-16))

Slope, m = 3/4

For data points 1 and 5, the slope is given by;

Slope, m = (-1.5 - (-13.5))/(0 - (-16))

Slope, m = 3/4

For the common difference, we have:

Common difference = -10.5 - (-13.5) = 3

Common difference = -7.5 - (-13.5) = 3

Common difference = -4.5 - (-7.5) = 3

Common difference = -1.5 - (-4.5) = 3

Therefore, this function is linear because the slope is constant and the common difference is constant between successive data points.

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Complete Question:

Consider the table that includes the input and output values of a function.

-16    -13.5

-12    -10.5

-8      -7.5

-4      -4.5

0       -1.5

Which answer classifies the function using finite differences?

The function is linear with a constant first difference of –3.

The function is linear with a constant first difference of 3.

The function is quadratic with a constant second difference of –3.

The function is quadratic with a constant second difference of 3.

Answer: Yes

Step-by-step explanation:

Alyssa worked 1 hour walking dogs and 13 hours clearing tables. This solution satisfies all of the given conditions.

The first inequality represents the condition that Alyssa must work at most 3 hours walking dogs:

a ≤ 3

The second inequality represents the condition that Alyssa can work a maximum of 15 total hours:

a + y ≤ 15

The third inequality represents the condition that Alyssa must earn at least $130 in a given week:

8a + 10y ≥ 130

We can graph these inequalities on the same coordinate plane to find the region of possible solutions. The solution to the system of inequalities is the region of the plane that satisfies all of the inequalities.

The red line represents the first inequality, a ≤ 3. The blue line represents the second inequality, a + y ≤ 15. The green line represents the third inequality, 8a + 10y ≥ 130.

The region of the plane that satisfies all three inequalities is the area above the red line and below the green line, and to the left of the blue line. This region is shaded in the graph above.

Thus, one possible solution is point (1,13), which is the intersection of the red and blue lines. This corresponds to Alyssa working 1-hour walking dogs and 13 hours clearing tables. This solution satisfies all of the given conditions.

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The area of the shape Illustrated will be 202 square inches.

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

We can break this shape down into two rectangles, one with the dimensions of 13in by 4in and the other by 15in and 10in. Now we can find the area of both shapes by multiplying the sides together so the 13in by 4in shape has the area of 52 square inches and the 15in by 10in shape has the area of 150 square inches.

Now, add the two areas together and the total area of the whole shape:

= 150 + 52

= 202 square inches

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The total cost of the dinner is given by the equation A = $ 259.457

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of the dinner be represented as A

Now , the equation will be

The restaurant bill is = $ 235.87

The percentage of tip for the waitress= 20 %

So , the amount of tip = restaurant bill x percentage of tip for the waitress

Substituting the values in the equation , we get

The amount of tip = 235.87 x ( 20/100 )

On simplifying the equation , we get

The amount of tip = $ 47.174

So , the restaurant bill including the tip = $ 235.87 + $ 47.174

The restaurant bill including the tip = $ 283.044

Now , you have a coupon for 10% off the price of food

So , Cost of dinner with the coupon discount = restaurant bill including the tip  - ( 10/100 )$ 235.87

On simplifying the equation , we get

Cost of dinner with the coupon discount = 283.044 - 23.587

Cost of dinner with the coupon discount = $ 259.457

So , the total cost of dinner A = $ 259.457

Therefore , the value of A is $ 259.457

Hence , the cost of dinner is $ 259.457

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Answer:

True.

Step-by-step explanation:

When two lines are crossed by a transversal, the interior angles between them will always add up to 180 degrees, which means they can never be parallel.

Answer:

[tex](a-b)^3 = (a-b)^(a-b)^2\\\\=(a-b)(a^2 - 2ab +b^2)\\\\= a(a^2 -2ab +b^2) -b(a^2 - 2ab +b^2)\\\\= a^3 -2a^2b -ab^2 -a^2b + 2ab^2 -b^3\\\\= a^3 - 3a^2b + 3ab^2 -b^3[/tex]

Step-by-step explanation:

I am not sure if you wanted it in exactly 4 steps, But this is the way to do it.

If in exactly 4 steps, omit the third step. Then we would get:

[tex](a-b)^3 = (a-b)^(a-b)^2\\\\=(a-b)(a^2 - 2ab +b^2)\\\\= a^3 -2a^2b -ab^2 -a^2b + 2ab^2 -b^3\\\\= a^3 - 3a^2b + 3ab^2 -b^3[/tex]

Hope that helps ya

Using the concept of proportion and substitution with the total money to be divided given, The answer is Carl gets $480, Stacy gets $720, and Peter gets $240.

Proportion refers to the relationship between two or more quantities or values, often represented as a ratio or fraction. It can also refer to the relative size or scale of something in relation to something else. In mathematics, a proportion is an equation that states that two ratios are equal. For example, "the ratio of apples to oranges is 2:3" can be written as the proportion "2/3 = x/y," where x and y represent the number of apples and oranges. In statistics, a proportion is a measure of the frequency with which an event occurs, often expressed as a decimal or percentage.

The substitution method is a technique used to solve systems of equations, which are sets of two or more equations containing multiple variables. The basic idea behind the substitution method is to solve for one variable in terms of the others in one equation, and then substitute that expression into the other equations. This can be done by isolating one variable by adding or subtracting other variables from both sides of the equation, and then using the resulting equation to express that variable as a function of the others. Once one variable is expressed in this way, it can be substituted into the other equations, allowing us to solve for the other variables.

S = 3P (Stacy gets three times as much as Peter)

P = C/2 (Peter gets half the amount that Carl gets)

C + S + P = 1200

We can substitute the first equation into the second one to get:

S = 3(C/2)

Now we can substitute the second equation into the first one to get:

C + 3(C/2) + C/2 = 1200

We can simplify this equation by multiplying out the 3(C/2) term and combining like terms to get:

5C/2 = 1200

Now we can solve for C by multiplying both sides by 2/5:

C = 480

Now that we know C = $480, we can use the earlier equations to find S and P:

S = 3P = 3(480/2) = $720

P = C/2 = 480/2 = $240

So Carl gets $480, Stacy gets $720, and Peter gets $240.

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Answer:

Each person would have to get 8.3 oz of the drink.

Step-by-step explanation:

100/12=8.3

(Sorry if I misunderstood your question)

The density of the wood weighing 19.5061 grams is approximately 19.313 g/cm².

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given the data in the question

First, we determine the volume of the wood which is the change in the volume of volume in the cylinder.

Volume of the wood = Final volume of water - Initial volume water

Volume of the wood = 9.76cm³ - 8.75cm³

Volume of the wood = 1.01 cm³

Now, we determine the density of the wood.

p = m / v

p = 19.5061g / 1.01 cm³

p = 19.313 g/cm²

Therefore, the density of the wood is 19.313 g/cm².

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The domain of the function y=√x+6-7 is x>= -6.

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

The set of inputs that a function will accept is known as the domain of the function in mathematics. It can also be written as dom (f) or dom f, where f stands for the function.

To put it more exactly, the domain of f is X given a function f: X - Y. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.

Given data :

The given function is a radical function.

Note that a radical function is only defined for values that will make the radicand greater than or equal to zero.

Hence, the radicand of the given function must be greater than or equal to zero or:

x+6>=0

x + 6 - 6  0 - 6

x>= -6

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Width is 50 on each side and length.

Find the dimensions of the field if the length ?

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Answer:

1) 7 pizzas

2) 20 people

Step-by-step explanation:

8 people for 2 pizzas is

4 people for 1 pizza

[tex]\frac{1}{4}[/tex] = [tex]\frac{x}{28}[/tex]

4 x 7 = 28

1 x 7 = 7

She will need to order 7 pizzas for 28 people.

1 pizza is needed for 4 people

5 pizzas will allow 20 people (5 x 4)

Answer:

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

The x-intercepts are the roots of the function and according to the graph the roots are:

Hence the function is:

Answer:

D)  f(x) = (x - 1)(x - 2)(x - 3)

Step-by-step explanation:

From inspection of the given graph, the points at which the curve intersects the x-axis are:

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

According to the factor theorem, as f(x) = 0 when x = 1, x = 2 and x = 3 then (x - 1) and (x - 2) and (x - 3) are factors of the polynomial.

Therefore, the equation of the function is:

The surface area of the given cuboid excluding the bases is; 28 square units

The formula for surface area of a cuboid is;

SA = 2lw + 2lh + 2hw.

We are given;

Length; l = 2 in

Width; w = 1.5 in

Height; h = 4 in

Now, since we are to exclude the bases, it means that;

SA = 2(lh + hw)

= 2((2 * 4) + (4*1.5))

= 2 * 14

= 28 square units

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The  company´s revenue function can be written as 0.36x ² + 815.04x + 11,340.

It was recorded that the demand d for a company's product at cost x is predicted by the function d(x)=0.36x + 810.

We also told that  price p that the company can charge for the product is given by p(x) = x+14.

The Revenue can be computed as [ price × quantity]

where p(x) = x+14

And d(x) = 0.36x + 810

Then if we inpued to the formula , we have

=[ (x + 14) * (0.36x + 810)]

then if we open the bracket we have:

0.36x² + 810x + 5.04x + 11,340

Then we can make some simplification as:

= 0.36x ² + 815.04x + 11,340

Therefore, the Company's revenue  wilol be  0.36x ² + 815.04x + 11,340

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Answer:

x = -1

Step-by-step explanation:

There are lots of places to make mistakes.  I think that I did it correctly.

The required interest rate in order for Emma to end up with $7,200 is given as follows:

6.5%.

The balance of an account, using continuous compounding, after t years, is presented by the equation given as follows:

[tex]A(t) = A(0)e^{rt}[/tex]

In which the parameters are given as follows:

The values of the parameters in the context of this problem are given as follows:

A(t) = 7200, A(0) = 3300, t = 12.

Hence the interest rate can be obtained solving the exponential equation as follows:

7200 = 3300e^(12r)

e^(12r) = 7200/3300

e^(12r) = 2.181818

ln(e^(12r)) = ln(2.181818).

(as exponential and ln are inverse operations)

12r = ln(2.181818).

r = ln(2.181818)/12

r = 0.065.

As a percentage, the interest rate is given as follows:

6.5%.

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In the similar quadrilaterals shown, the value of x is 18.3.

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

Given two quadrilaterals whose all four angles are the same. In this condition ratio of their side are equal

Thus,

22 / 18 = x / 15

x = 18.33

Therefore, the value of the x in the given similar quadrilaterals is 18.3.

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Answer:

-2\x^2-1

Step-by-step explanation:

The solution of |2x - 1|= 5  are x=-2 and x=3.

Two or more expressions with an Equal sign is called as Equation.

The given equation is |2x - 1| = 5

2x-1=+5

Add 1 on both sides

2x=6

Divide both sides by 2

x=3

Now take 2x-1=-5

Add 1 on both sides

2x=-4

x=-2

The solution of |2x - 1|= 5  are x=-2 and x=3.

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1.To find the total distance Julia has traveled, you can use the Pythagorean theorem. The distance she traveled in the x-direction (west) is 10 km and the distance in the y-direction (south) is 15 km. The total distance traveled is the square root of (10^2 + 15^2) = 17.67 km.

2.In a right angle triangle, the side opposite the 90 angle is the hypotenuse. The side opposite the 250 angle is the side that is opposite to the angle and not the hypotenuse. Using the sine function of trigonometry, the opposite side can be calculated as: opposite = 15 cm * sin 250 = 12.08 cm. Rounded to nearest centimeter, the length of the side opposite the 250 angle is 12 cm.

3.The ladder forms a right triangle with the house and the ground. To find the length of the ladder, you can use the Pythagorean theorem. The ladder's length is the square root of (12^2 + 12^2) = 16.97m. Rounded to the nearest whole number, the ladder is approximately 17 meters long.

4.To find the length of the line Mark drew, you can use the Pythagorean theorem. The length of the line is the square root of (20^2 + 25^2) = 29.89 ft.

5.To find the length of the diagonal of the screen, you can use the Pythagorean theorem. The diagonal length is the square root of (13^2 + 12^2) = 16.97cm. Rounded to the nearest whole number, the size of the screen is 17 cm.

6.To find the length of the ramp, you can use the tangent function of trigonometry. The length of the ramp is: 15m / tan 550 = 18.24m. Rounded to nearest whole number, the length of the ramp is 18m.

7.To find the height of the building you can use the Pythagorean theorem. The height of the building is the square root of (185^2 - 90^2) = 129.49m. Rounded to nearest whole number, the height of the building is 129m.

8.To find the length of the ramp, you can use the tangent function of trigonometry. The length of the ramp is: 10m / tan 320 = 16.6m. Rounded to nearest whole number, the length of the ramp is 17m.

9.To find the distance from point B to C, you can use the information given. The distance from point A to point B is 15 feet, and the distance from point A to point C is 10 feet. If you subtract the distance from A to B from the distance from A to C, you get 10 - 15 = -5 feet. This distance is not possible as it is negative, therefore the answer is not valid.

10.To find the height on the building where the mini-stick touched, you can use the tangent function of trigonometry. The height is 9 inches * tan 430 = 16.24 inches. Rounded to nearest whole number, the height on the building where the mini-stick touched is 16 inches.

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The ratio of the base areas and ratios of volume are respectively; 1/9 and 1/27

A) Base area of the cone has the formula;

A_b = 3V/h

where;

V is volume

h is the vertical height

Since the ratio of both heights is 5:15 = 1:3, then;

Ratio of base areas = 1²/3² = 1/9

B) Formula for the volume of a cone is;

V = ¹/₃πr²h

Thus;

Va = ¹/₃π(r²)5

Va = ⁵/₃π(r²)

Vb = ¹/₃π(R²)15

Thus;

Va/Vb = ⁵/₃π(r²)/¹/₃π(R²)15

Earlier, we saw that;

r²/R² = 1/9. Thus;

Va/Vb = (1/3) x (1/9)

Va/Vb = 1/27

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Answer:

25 cups

Step-by-step explanation:

6 1/8 quarts is equal to 25 cups.

[tex]6\frac{1}{8}[/tex] quarts is equal to 49/2 cups.

Given that we have [tex]6\frac{1}{8}[/tex] quarts, we can multiply this value by 4 to obtain the equivalent amount in cups:

[tex]6\frac{1}{8}[/tex] quarts × 4 cups per quart

= (6 + 1/8)× 4 cups

First, let's convert the mixed number [tex]6\frac{1}{8}[/tex] to an improper fraction:

[tex]6\frac{1}{8}[/tex] = (6 × 8 + 1) / 8

= 49/8

Now, (49/8) × 4 cups

= (49 × 4) / 8 cups

= 196/8 cups

Divide both the numerator and denominator by their greatest common divisor, which is 4:

(196/8) ÷ 4/4 = 49/2

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Answer:

10.12

Step-by-step explanation:

100%+6.5%=106.5%

106.5% divided by 100=1.065

155.75 multiplied by 1.065=165.87375..

165.87375-155.75=10.12375

which equals 10.12