It costs $5820 to get new windows for a certain house. Each of the 28 windows costs the same amount.
Determine an estimate for the cost of each window. Justify your reasoning.
What is the cost of each window, rounded to the nearest dollar? Show your work. Leave the remainder undivided.

a. The expression to represent the total distance is 5 × 3 + 3.

b. The total distance Gabriella travelled is 18 metres.

Gabriella swims downward 5 meters per second for 3 seconds. She then swims up 5 meters toward the surface of the water.

Therefore, the expression that represent the distance Gabriella travels can be represented as follows:

distance = speed × time

distance = 5 × 3

Therefore,

total distance = 5 × 3 + 3

Therefore, the total distance of Gabriela is 5(3) + 3 = 15 + 3 = 18 metres.

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The number of ways in which a panel of 3 women and 4 men can be formed is 1960 ways.

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant.

a. The number of ways In which a panel of 3 women and 4 men can be formed Is:

[tex]$$\begin{aligned}& 8 C_3 * 7 C_4 \\& \frac{8 !}{(8-3) ! 3 !} * \frac{7 !}{(7-4) ! 4 !} \\& 56 * 35 \\& 1960\end{aligned}$$[/tex]

The number of ways In which a panel of 3 women and 4 men can be formed Is 1960 ways.

b. The number of ways In which a panel with at least 2 women can be formed Is:

[tex]$$\begin{aligned}& 8 C_2 * 7 C_5+8 C_3 * 7 C_4+8 C_4 * 7 C_3+8 C_5 * 7 C_2+8 C_6 * 7 C_1+8 C_7 * 7 C_0 \\& 28 * 21+56 * 35+70 * 35+56 * 21+28 * 7+8 * 1 \\& 588+1960+2450+1176+196+8 \\& 6378 \text { ways }\end{aligned}$$[/tex]

The number of ways In which a panel with at least 2 women can be formed is 6378 ways.

c. The ways in which Miss A refuses If Mr. B is a member can be calculated by reducing one woman and one man from the Inltal members:

[tex]$$7 C_3 * 6 C_4$$[/tex]

420

The panel formed when Miss A refuses can be calculated as:

1960 - 420

1540 ways.

Hence the panel if Miss A refuses on the panel if Mr. B is a member can be formed in 1540 ways.

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The coefficient of y in the expression -2x² * y² * z is 0

From the question, we have the following parameters that can be used in our computation:

An algebraic expression

The algebraic expression is given as

- 2x ^ 2 * y ^ 2 * z

Express the exponents as proper subscripts

So, we have the following representation

-2x² * y² * z

There is no term in the expression with the variable y

Instead, the term has a y² as its variable

This means that the coefficient of y is 0

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Answer:

p = 9/55

Step-by-step explanation:

2/3p + 3p = 3/5.

2/3p + 9/3p = 3/5

11/3p = 3/5

Divided both sides by 11/3

p = 9/55

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The rate of change that Daniel runs depends on number of tracks, so the rate of change is 8/5 = 1.6 miles per practice.

You should be aware that rate of change is the same thing as slope.  In slope as y increases, x also increases. vice versa.

Daniel runs depends on the number of track practices he attends.

The rate of change (ROC) is the speed at which a variable changes over a specific period of time. ROC is often used when speaking about momentum, and it can generally be expressed as a ratio between a change in one variable relative to a corresponding change in another; graphically, the rate of change is represented by the slope of a line. The ROC is often illustrated by the Greek letter delta (Δ).Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.

The formula for rate of change is:

R = (D2 - D1)/T

Rate of change = change in y/ change in x

= 10-2/5-0

=8/5

=1.6

In conclusion the ratio of Daniels run is 1.6

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Answer:

-10x+18y=4 is an equation in the slope-intercept form, where y is the dependent variable, x is the independent variable, -10 is the coefficient of x, 18 is the coefficient of y and 4 is the constant.

This is a Linear equation and it represent a straight line in a two-dimensional coordinate system. The slope of the line is -10/18 or -5/9 and the y-intercept is 4/18 or 2/9.

It is important to note that the equation represents all the points that are on that line, where x and y are coordinates of those points, and for each value of x, there is a corresponding value of y that makes the equation true.

1.  The average rate of change for P between 1992 and 2000 is  -1.025.

2.  For values of t = 1996 and t = 1992, the function has a negative average rate of change, and value of rate of change will be -2.4.

3.   For values of t = 2000 and t = 1996, the function has a positive average rate of change, and value of rate of change will be 0.35.

Rate is a mathematical term which we use, When two quantities are compared and expressed as a ratio and both have different units.

1.   we need to calculate the average rate of change in 1992 & 2000

    percentage of voters in 2000 = 34.5

    percentage of voters in  1996 =  33.1

    percentage of voters in 1992  = 42.7

it is known that,

Rate of change = change in percentage/change in years

Rate of change in between 1992 &1996 is,

R₁=   (33.1 - 42.7)/(1996-1992)

R₁=    -2.4  

Rate of change in between 1996 & 2000 is,

R₂=   (34.5-33.1)/(2000-1996)

R₂=    0.35

Average rate of change = (R₁ + R₂)/2

Average rate of change = (-2.4 + 0.35)/2

Average rate of change =  -1.025

2. One of the pair of values of t  for which rate of change will be negative are 1996 & 1992,

R=   (33.1 - 42.7)/(1996-1992)

R=   -2.4  

3. One of the pair of values of t  for which rate of change will be positive are 1996 & 2000,

R=   (34.5-33.1)/(2000-1996)

R=   0.35

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Answer: B. 12cm^2.

Step-by-step explanation:

To find the area of the shape, you need to count the number of squares inside it and then multiply that number by the area of a single square. If each grey square is 1cm by 1cm, then the area of a single square is 1cm x 1cm = 1cm^2. If you count the squares inside the shape, you will see that there are 12 squares. Therefore, the total area of the shape is 12cm^2. The correct answer is therefore B. 12cm^2.

Answer:

7/60

Step-by-step explanation:

solution

(x*y) + z

(1/3*-2/5) + 1/4

-2/15 + 1/4

LCM 60

-8 + 15/60

7/60

Answer:

7/60

Step-by-step explanation:

Looking at the numbers:

x = 1/3

y = -2/5

z = 1/4

We can simply add them into the equation:
(x × y) + z

(1/3 × -2/5) + 1/4 =?

1/3 × -2/5 ≅ -0.1333333 or [tex]\frac{-1333333}{10000000}[/tex]

-0.1333333 + 1/4 = 0.1166667 or [tex]\frac{7}{60}[/tex]

Answer:

∛x

Step-by-step explanation:

Replace x with y and then solve

[tex]y=x^3\\x=y^3\\\sqrt[3]{x} = y[/tex]

Answer:

25

Step-by-step explanation:

25

The diagonals of a square bisect the vertical angles​

(i) In an ABCD diagram,

AB=AB ( common line) 

BC=AD ( opposite sides of a square) 

ABC=BAD (90 degrees)

ΔABC≅ΔBAD( By SAS property) 

AC=BD ( by CPCT) 

In an OAD and an OCB,

AD=CB ( opposing sides of a square) 

∠OAD=∠OCB ( transversal AC ) 

∠ODA=∠OBC ( transversal BD ) 

ΔOAD≅ΔOCB (ASA property) 

OA=OC ----(i)

Furthermore, OB=OD ----(ii)

AC and BD divide each other at I and (ii).

Currently in an OBA and ODA,

(From (ii)) OB=OD

BA=DA

OA=OA ( common line )

(by CPCT) AOB=AOD---(iii)

∠AOB+∠AOD=180° (linear pair)

2∠AOB=180°

∠AOB=∠AOD=90°

∴ AC and BD bisect each other at vertical angles.

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The number of batches of cookies required for your dad to bake is 6.33 batches.

Number of people at the party = 38

Number of cookies each would have = 4

Total number of cookies needed = Number of people at the party × Number of cookies each would have

= 152 cookies

Number of cookies baked per batch = 24

Equate the number of batches to the number of cookies baked.

Let x = number of batches required

1 : 24 = x : 152

1/24 = x / 152

cross product

1 × 152 = 24 × x

152 = 24x

divide both sides by 24

x = 152 / 24

x = 6.33 batches

Therefore, your dad should bake 6.33 batches of cookies for everyone at the party.

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The local linear approximation of f(x) 2In(x) at x = 2 is y = x - 2 + log (4).

As per the given data, the function f(x) is given by:

f(x)=2 log (x) at x = 2

Here we have to determine the linear approximation of f(x).

A linear approximation is a mathematical phrase that describes using a linear function to approximate a general function.

We know the linear form of the function is

y = f(a) + f'(a) ( x - a )

Here, a = 2

Therefore y = f(2) + f'(2) (x - 2) . . . (1)

Now, f(2) = 2 log (2)

= log [tex](2)^2[/tex]

= log (4)

Again, f'(x) =[tex]\frac{d}{d x}[f(x)][/tex]

[tex]=\frac{d}{d x}(2 \log (x)) \\[/tex]

f'(x) = [tex]2 \cdot \frac{1}{x}=\frac{2}{x} \\[/tex]

Therefore f'(2) = [tex]\frac{2}{2}[/tex] = 1

Plug in the values of f(2) and f'(2) in equation (1) we get,

y = log (4) + 1(x - 2)

y = x - 2 + log (4) (which is the linear approximation of f(x))

Therefore option (b) is correct

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You can form two different types of quadrilaterals from the given sticks of 8cm,8cm,5cm,5cm.

A quadrilateral is a polygon with four sides and four angles. Quadrilaterals are two-dimensional shapes, meaning they exist on a flat surface and have length and width, but no depth. Some examples of quadrilaterals include rectangles, squares, parallelograms, and trapezoids.

You can form two different types of quadrilaterals using four sticks of 8cm, 8cm, 5cm, and 5cm in length such as a rectangle of the two 8cm sticks as the length and the two 5cm sticks as the width to create a rectangle, and you can also form a parallelogram by using the two 8cm sticks as the length, and the other two 5cm sticks as the width.

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Your question seems incomplete, but I assume the complete question was:

"How many types of quadrilaterals can be formed using these sticks of 8cm, 8cm, 5cm, 5cm?"

Answer:

a^4

Step-by-step explanation:

a^7 / a^3 = a^(7-3) = a^4

Answer:

ML = 10

Step-by-step explanation:

Given:
LN = ML + 2
JL = 15
LK = 18

We use AAA Similarity Criterion: If two triangles are equiangular, then they are similar. By equiangular, it means that the measurements of the corresponding angles of the two triangles are equal. It is also called the Angle Angle Similarity Theorem.

If lines MN and JK are parallel, then ∠LMN=∠LJK and ∠LNM=∠LKJ and hence ΔMLN∼ΔJLK. Based on the proportionality of the sides, we compose an equation and solve it:

LK/JL = LN/ML
18/15 = LN/ML
6/5 = LN/ML

Since LN = ML + 2, the equation can be written:

6/5 = (ML + 2)/ML
6/5 = 1 + 2/ML
1/5 = 2/ML
ML/5=2
ML=10

The system of inequality of the situation is y = 2x and x + y ≥ 45 and the possible number of candy bars Sierra sold are 15, 16 and 17

From the question, we have the following parameters that can be used in our computation:

Represent Sierra with x and Breanna with x

Based on the readings from the question, we have the following inequalities

y = 2x

x + y ≥ 45

Substitute y = 2x in x + y ≥ 45

So, we have

x + 2x ≥ 45

Evaluate

3x ≥ 45

Divide by 3

x ≥ 15

This means that the number of candy bars Sierra sold are at least 15

The possible numbers are 15, 16 and 17

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x=3 is the solution of equation 2x-3=3 which represent the line parallel to y axis such that x coordinate is always 3

In mathematics, an axis is a line that is used to take or indicate measurements. The coordinate plane's x and y axes are two of its most important axes. The x-axis is represented by a horizontal number line, and the y-axis by a vertical number line. The perpendicular intersection of these two axes yields the coordinate plane. The x-axis and y-axis are also known as the ordinate and abscissa, respectively.

in the question we have:

⇒ 2x - 3 = 3

⇒ 2x = 6

⇒ x = 3

which represent a line parallel to y axis where x is always equal to 3 .To plot graph take any y such that point is (3, y) .

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Answer:

Step-by-step explanation:

The equation 45x + 55x = 350 could be used to solve the following problem:

Two vehicles start from the same point traveling in the same direction. One vehicle travels 55 miles per hour (mph) and the other 45 mph. When will the two vehicles be 350 miles apart?

Answer:

9

Step-by-step explanation:

Answer:

Use PEMDAS, answer is 9

Step-by-step explanation:

The middle term of a quadratic trinomial is positive, then the sum of the factors for the middle term must be negative.

In a quadratic trinomial in the form  [tex]ax^2 + bx + c[/tex], the middle term is represented by bx. When the middle term is positive, it means that b (the coefficient of x) is positive. To factor the quadratic trinomial, to find two numbers that multiply to b and add up to the coefficient of the middle term.

Since b is positive, the two factors must have the same sign (both positive or both negative) to add up to a positive value. However, the middle term itself is positive, indicating that the two factors add up to a positive value.

Hence, both factors must be negative so that their sum is positive.

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A: The composite function that represents the number of U.S. dollars equivalent to x British pounds is 1.54x

B: An item that costs 15 British pounds is equivalent to 23.10 U.S. dollars.

What is the composite function?

A composite function is a function that is formed by the composition of two or more functions. It is a new function that is made by plugging the output of one function into another function. The notation for a composite function is f(g(x)) or f(g), where f and g are the two functions being composed.

a. To write a composite function that represents the number of U.S. dollars equivalent to x British pounds, we want to substitute the output of f(x) into g(y). So, we want to find g(f(x))

g(f(x)) = g(9.09x) = 0.17(9.09x) = 1.54x

So, the composite function that represents the number of U.S. dollars equivalent to x British pounds is 1.54x

b. To find the value in U.S. dollars of an item that costs 15 British pounds, we substitute x = 15 into the composite function:

1.54(15) = 23.10

So, an item that costs 15 British pounds is equivalent to 23.10 U.S. dollars.

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The solution to the equation 3 x 2 − 12 d − 2 is 1/3.

Solving the equation for d because the value of d would be the required solution to this equation:

Now

 3 x 2 − 12 d − 2  = 0

  6     -  12 d   - 2  =  0

Sitting the constant terms to the right side of the equation while keeping the term with d to the left-hand side of the equation:

Now

   -12d   =  -6 + 2

     -12d =  -4

     d = -4/-12

       d=  1/3

After solving the given equation for d, the solution of the equation is determined to be 1/3.

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The amount of Drew's 2022 child tax credit is $2,000.

Gross income less adjustments to income is known as adjusted gross income (AGI). Your salary, dividends, capital gains, company revenue, retirement payouts, and other sources of income are all included in your gross income.

On the other hand, one may receive money from the Child Tax Credit (CTC) during tax time to assist with such expenses. On their tax return, eligible parents and caretakers can claim a credit of up to $2,000 for each kid under the age of 17 (i.e., 16 years old or younger) at the end of the tax year for which you claim the credit.

Since Peppa is already 17 and that leaves Sage as the only child for him to qualify, he amount of Drew's 2022 child tax credit is $2,000.

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Using the diameter given, the volume of the sphere is 14137.17cm³

The volume of a sphere is a measurement of how much space it takes up. It is calculated using the following formula and represents the volume of the sphere:

v = 4/3 * π * r³

Where: r is the radius of the sphere, which is the distance from the sphere's center to its surface, and π is a mathematical constant roughly equal to 3.14.

The formula is based on the observation that a sphere's volume is two thirds that of a cylinder with the same radius and height.

The volume of a sphere is directly proportional to the cube of the radius, which is a crucial point to remember.

In the problem, the diameter given is 30cm, we can calculate the radius from this.

radius = diameter / 2

radius = 30 / 2

radius = 15cm

We can plug in the values to calculate the volume of this sphere;

v = 4/3πr³

v = 4/3(3.14)(15)³

v = 14137.17cm³

The volume is 14137.17cm³

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Answer:

Varies, see below

Step-by-step explanation:

We need to find the number of math problems per minute. To do that, we divide 40/32 to find that she completes 1.25 problems per minute.

Or, on the flippity flop, we can find the number of minutes per math problem. So we would do 32/40 to get  0.8 minutes per math problem.

Choose the one according to your needs.

There are 30 students in the Maths class, 30 students in the English class and 40 students in the history class using Gauss-Jordan elimination to solve the system of equations.

We shall derive and solve the system of equations as follows:

homework questions corrected per week;

10x + 20y + 30z = 2100...(1)

number of homework papers corrected per week;

x + y + z = 100...(2)

x = number of students in the math class

y = number of students in the English class

z = number of students in the history class.

since the maths and English classes have the same number of students then x = y and: equations (1) and (2) becomes;

10x + 20x + 30z = 2100

30x + 30z = 2100

30(x + z) = 2100 {divide through by 30}

x + z = 70...(3)

x + x + z = 100

2x + z = 100...(4)

Subtract equation (3) from (4) to eliminate z

2x + z - x - z = 100 - 70

x = 30

Now we will substitute this value of x back into the equation (4) such that;

2(30) + z = 100

60 + z = 100

z = 100 - 30 {subtract 60 from both sides}

z = 40

So there are 30 students in the Maths class, 30 students in the English class and 40 students in the history class using Gauss-Jordan elimination to solve the system of equations.

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