A window in the room has an actual width of 2. 5 feet. What is the width of the window in the blueprint? (same scale 3 in:5 ft)

Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

Given,

In the question:

Why are the tops of mountains round and the soil often rough, rocky, and thin in many places in the Northeast?

Now, According to the question:

The correct answer is:

Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

Other question is

4 + 2

By addition:

4 + 2 = 6

Hence, Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

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Answer:

Step-by-step explanation:

The midrange of the data set shown is 85 is true about the box-and-whisker plot below. The middle is the number in question. The least and greatest values should be added together, divided by two, or, in other words, the mean of the least and biggest values should be determined.

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The number of minutes after Cayaln puts the trays in the oven will he first remove the scones, muffins, and cookie at the same time is 300 minutes

Find the least common multiple of 25, 12 and 10 minutes

The least common multiple of of 25, 12 and 10 minutes is 300 minutes.

Therefore, the number of minutes Cayal removes the scones, muffins, and cookie at the same time is 300 minutes

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The three domains are the Archaea, the Bacteria, and the Eukary.

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a)4

so it's seven factorial divided by 7-5 factorial

Eplaination of algebraic rules with equation of line is describe below

Algebraic rules are maths expression of two variable that can be written in the form of equation.

Now we will understand by the equation of line given in the question,

we have Y = mx + c

where y is the intercept on y-axis, m is the slope of line, x is intercept on x-axis, and c is the point where line cuts y-axis.

This equation represent the line which follows algebraic rules.

Graph of equation:

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The Probability of an odd number = 0.5.

What is Probability?

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using probability, we can calculate everything from the possibility of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. The formula for computing probabilities in equiprobable sample spaces, the probability of the complementary event, etc., as well as the likelihood of two occurrences coming together, are essential to understand in order to properly appreciate this field of mathematics.

In the given question, we have:

The odd numbers on the given spin are 1,3,5,7 and 9;

So, The number of odd numbers is 6;

That is, n(odd) = 6;

and,

Total number of Spin = 12;

So, The probability of an odd number = [tex]\frac{odd number}{total number}[/tex]

The probability of an odd number = [tex]\frac{6}{12}[/tex]

Hence, The Probability of an odd number = 0.5.

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Check the picture below.

so the rocket will hit the ground when y = 0, so hmmm, there's no simple factoring that'd give us integers, so we'll plug the quadratic into the quadratic formula

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+240}x\stackrel{\stackrel{c}{\downarrow }}{+115} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (240) \pm \sqrt { (240)^2 -4(-16)(115)}}{2(-16)} \implies x = \cfrac{ -240 \pm \sqrt { 57600 +7360}}{ -32 }[/tex]

[tex]x= \cfrac{ -240 \pm \sqrt { 64960 }}{ -32 }\implies x=\cfrac{ -240 \pm 8\sqrt { 1015 }}{ -32 }\implies x=\cfrac{ 240 \mp 8\sqrt { 1015 }}{ 32 } \\\\\\ x=\cfrac{ 30 \mp \sqrt { 1015 }}{ 4 }\implies x\approx \begin{cases} -0.46\\\\ 15.46 ~~ \textit{\large \checkmark} \end{cases}[/tex]

now, let's notice, "x" cannot be negative, so the negative value is tossed.

Answer:

Note: A percentage is always a number over 100.      (34% = [tex]\frac{34}{100}[/tex])

Cost of meal = 100%

Cost of tip = 34%

Total = 134%

134% = [tex]\frac{134}{100}[/tex]

To find the total and the tip, you must multiply it by [tex]\frac{134}{100}[/tex]

Answer:

Bill times the 0.34 percent equals the price of the tip. After you find what the tip is, you add the base price (the bill price) to the tip and you get the total number paid. However, another way you can solve (in one step) this is by adding 1.00 to the percent you are multiplying by which in this case we add 0.34 by 1.00 and this gives us 1.34. Suppose we set the bill to 4 dollars and use the normal way (2-step equation) by doing 3(0.34) which is 1.02 and 1.02 + 3 = 4.02 as our final answer / final bill. However, when we do our one-step equation, we can write this as 3x(1.34) and this is equal to 4.02.

1st Step

Bill(0.34) = tip

tip + bill = total

2nd Step (one-step equation)

Note: we are going to set the bill in this equation as $4

4(1.34) = total; Total = 4.02 ← We added 1.00 to the tip percentage in decimal form.

Answer:

The answer is 80

Answer:

x=2/11 + (1/11) (√15) or 2/11 - (1/11) (√15)

Step-by-step explanation:

Plug it into the quadratic formula

The values of x are 9/11 and -5/11.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To use the quadratic formula to solve 11x² - 4x = 1.

We first need to rewrite the equation in the form ax² + bx + c = 0.

So,

11x² - 4x - 1 = 0

Now,

We can use the quadratic formula, which states that the solutions for the equation ax² + bx + c = 0.

x = (-b ± √(b² - 4ac)) / 2a

Now,

In our case,

a = 11, b = -4, and c = -1.

Substituting these values into the formula, we get:

x = (-(-4) ± √((-4)² - 4(11)(-1))) / 2(11)

x = (4 ± √(196)) / 22

x = (4 ± 14) / 22

So,

The solutions for the equation 11x² - 4x = 1

x = (4 + 14) / 22 = 9/11

x = (4 - 14) / 22 = -5/11

Therefore,

The values of x are 9/11 and -5/11.

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The number of the given statement will be inequality -2 < x <  4.

We have been given the statement "the sum of five times a number and three is between -7 and 23".

Let the number would be x

As per the given statement, we can represent this algebraic form with inequality as:

⇒ -7 < 5x + 3 < 23

Subtract 3 on both sides of the above inequality

⇒ -7 - 3 < 5x  < 23 - 3

⇒ -10 < 5x <  20

Divided by 5 into both sides of the above inequality

⇒ -2 < x <  4

Thus, the number of the given statement will be inequality -2 < x <  4.

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The question seems to be incomplete the correct question would be

Find the number if the sum of five times a number and three is between -7 and 23.

Compatible numbers are close in value to the real numbers, which simplifies problem-solving and estimation of the solution. 1,7,10/32 has a quotient (integer division) of 53 and a remainder ("leftover") of 14. The dividend is 1,7,10, while the divisor is 32.

Compatible numbers are those that divide equally into each other and are near to the numbers they are replacing. The outcome of a division is the quotient. 55,304 is not too far away from 56,000. 800 splits equally into 56,000 and is reasonably near to 875.

Our minds can occasionally spin when we are asked to find the total (in addition), difference (in subtraction), product (in multiplication), or quotient (in division). By rounding each number to the closest ten, twenty, fifty, or hundred, we employ suitable numbers to make the problem simpler to figure out mentally.

Numbers that are simple to mentally add, subtract, multiply, or divide are said to be compatible. To estimate a calculation, substitute compatible numbers for the actual numbers. Since it is simple to mentally calculate the sum of 800, the numbers 500 and 300 can be added together.

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There is a change of 1/2 for Adam to get strictly more heads than Ben.

The likelihood that Ben will get more heads than Adam is equal to the likelihood that Ben will get more tails than Adam. (by symmetry)

If Ben and Adam each have n+1 (101) coins, then Ben will receive more heads or even more tails than B, but never both.

Considering (1) and (2), we find that there is a 50% chance that Adam will get more heads than Ben.

Thus, there is a change of 1/2 for Adam to get strictly more heads than Ben.

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Two similar triangles have,

The ratio of two sides of one triangle  = Ratio of two sides of the other triangle

The distance between Alanton and Bishop is 14 miles.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

Alanton:

16 miles from Oakley.

8 miles from Crawford.

28 miles from Fayeville

We can have two similar triangles as shown below.

Two similar triangles have,

The ratio of two sides of one triangle  = Ratio of two sides of the other triangle

AB / AC = DE/ DF

8 / 16 = x / 28

1/2 = x/28

x = 28/2

x = 14

Thus,

The distance between Alanton and Bishop is 14 miles.

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The probability of getting at least one question right is 96.875%.

The question states that at least one guess should be right. This ultimately means that all guesses cannot be wrong, which is the only possibility being excluded here.

Probability for wrong guess =12=0.5

Probability for all wrong guesses =0.5*0.5*0.5*0.5*0.5=0.03125 or 3.125%

There is only 3.125% chance of all wrong guesses. Rest of the possibilities are our favorable conditions, i.e. at least one correct guess.

Therefore,

Probability of at least one correct guess=1-0.03125=0.96875 or 96.875%

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To balanced hanger, adding a circle to the left and a square to the right. To both sides, add two triangles. The option 1, 2, and 5 are correct.

What is balanced hanger?

Adding two circles to the left side and a square to the right would adjust the hanger's balance in accordance with the lesson's emphasis on maintaining the equation in balance.

adding a circle to the left and a square to the right. To both sides, add two triangles.

Hence the option 1, 2, and 5 are correct.

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For all proportional relationships, the true statements are:

A, D, and E.

A proportional relationship between two variables x and y is written as:

y = k*x

Now let's analyze each of the given statements:

A) The origin is the point (0, 0).

If you evaluate the general equation in x = 0 you get:

y = k*0 = 0

So yes, this equation passes through the point (0, 0).

B) This is false, as we saw above.

C) The formula for the constant of proportionality is:

y = k*x

y/x = k

So we can see that k = rise/run

the statement is false.

D) Yes, this is true, a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept, particularly if the y-intercept is zero, then we have a proportional relation.

E) Yes, slope, unit rate, constant of proportionality, are all equivalent terms for a proportional relation.

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The size of angle x is 54 degrees.

Let O be the complete angle,

<O = 360

Angle between diagonals = 360/5 = 72 degrees.

All diagonals of regular pentagon are equal and their opposite angles are equal .

With angle center O it forms a triangle:

sum of angles = 180

x + x + 72 = 180

2x + 72 = 180

2x = 180 - 72

2x = 108

divide by 2 on both sides

2x/2 = 108/2

x = 108/2

x = 54 degrees.

Therefore the size of angle x is 54 degrees.

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The total interest that Magdalena's parents would have to pay to repay the loan is  $864.50

The interest that Magdalena's parents will pay per year is:

= Value of loan x Simple interest rate per year

= 2, 600 x 7%

= $182

To find the total interest paid, this amount should then be multiplied by the number of years it would take Magdalena's parents to repay the loan. 4 years and 9 months in years is:

= 4 + 9/12 months in a year

= 4 + 3 / 4

= 4 + 0.75

= 4.75 years

The total interest is:

= 4.75 x 182

= $864.50

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The graph of line 3x-y= -1 will be as follows.

What is a line?

A line is an endlessly long, straight object that, despite being drawn with a minimum width, is considered to have no particular width in mathematics.

Main Body:

slope = m = 3     point = (0,1)

The formula for one point form for a line is -

y-y₁ = m(x-x₁)

y- 1 = 3(x-0)

3x-y =-1

Now the graph for the line will be plotted by using the point given and the slope--

on Graph mark the point (0,1)

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He may keep 82 movies on each shelf, using up to 492 movies and leaving 3 movies to retain.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. Arithmetic operators carry out operations on numbers. Variables are assigned values using assignment operators. Logical operators compare two values and return either "true" or "false" depending on whether the comparison is true (or false).

Here,

Movies that movie store has=495 movies

Number of shelves=6

If the owner wanted to make sure each shelf had the same number of movies,

=495/6

=82.5

He can keep 82 movies in each shelf that will use up to 492 movies and 3 movies will be left to keep.

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The congruency can be proved using SAS rule.

What are congruent triangles?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles is slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of harmoniousness is’ ≅’.

Main Body:

In ΔPQR and ΔRST

PR = RT           ---(1)

as both the sides are congruent , the third sides of triangles is also equal.

QR = RS          ----(2)

∠PRQ = ∠SRT   ----(3)

Hence by side- angle -side

ΔPQR and ΔRST are congruent.

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The maximum area is 640,000.

Given fencing yards = 3200

let the length be x and the width be y

The parameter of the rectangle is given as;

2(L + B),that is

2(x + y) = 3200

x + y = 1600

y = 1600-x

let the area of the rectangle be A, then

A = x y

A = x(1600-x)

A = 1600x - x^2

finding the maximum derivative of A with respect of x

da/dx = 1600 - 2x

set da/dx to zero,

1600 - 2x = 0

1600 = 2x

x = 1600/2

x =800

substitute the value of x = 800 in to y

y = 1600 - 800

y = 800

The maximum area is 800 x 800

Therefore Maximum area = 640,000.

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The greatest number of bags Caesar can make is 16 bags. Each of these bags will have 5 boxes of pasta and 8 jars of sauce.

Find the greatest common factor of 32 and 48

The greatest common factor of 32 and 48 is 16

So, the greatest number of bags Caesar can make is 16 bags

Number of pasta in each bag = 32/16

= 5 boxes of pasta per bag

Number of sauce in each bag = 48/16

= 8 jars of sauce per bag

If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.

He could use 8 bags but this is not the greatest number he could use.

Therefore, Caesar can use the greatest common factor to determine the highest number of bags he could use.

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The greater factor of 432, if 12 is the greatest common factor between the two factors is 36

The Greatest Common Factor is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The factors of 432 are 36,12, 24 ,18,4,108

But the two factors of 432 that has a multiple of 12 is 12 and 36

12× 36 = 432

The factors of 12 = 1,2,3,4,6,12

The factors of 36 = 1,2,3,4,6,9,12,18,36

the common factors are ; 1,2,3,4,6 and 12

therefore the greatest common factor = 12

since the GCF between 12 and 36 is 12, the second number will be 36

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The value of function is positive so the function have maximum value at x=3.

In the given question we have to find the maximum or the minimum value of a function.

The given function is

f(x) = -3x^2+18x+3

To find the maximum or minimum value we firstly find the value of f'(x).

f'(x) = -6x+18

Now put f'(x)=0

-6x+18=0

Subtract 18 on both side we get

-6x=-18

Divide by -6 on both side we get

x = 3

Now finding the value of function at x=3

f(3)= -3*(3)^2+18*3+3

f(3)= -3*9+54+3

f(3)= -27+54+3

f(3)= 30

Since the value of function is positive so the function have maximum value at x=3.

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