You have a shelf that holds 25 1/2 pounds. What is the most number of 1 1/4 pound books that the shelf can hold?​

Answer: the coefficient is 5

Answer:   1/2 |x| = -3?

Step-by-step explanation:

Answer:

\(\displaystyle d = 8\sqrt{2}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Point (-4, -4)

Point (4, 4)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

49sin21 or 17.5

Step-by-step explanation:

sinθ=o/h

sin21=x/49

x=49sin21=17.56

Hope this helps; please vote brainliest.

The parent function is f(x) = 7x + 5.

So let's find the equation for each transformation:

a) The function f reflected about the y-axis and translated 3 units left.

A reflection about the y-axis can be calculated just changing the sign of the variable x:

Now, in order to translate 3 units left, we just need to add 3 units to the x-value:

b) The function f stretched vertically by a factor of 3 and translated up by 2 units.

In order to stretch up the function, we multiply the whole function by the factor:

Then, to translated 2 units up, we add 2 units of the function:

c) The function f translated 2 units down and 3 units right.

To do a translation of 2 units down, we subtract 2 units of the function, and to translate 3 units right, we subtract 3 units from the value of x:

d) The function f stretched vertically by a factor of 2 and translated down by 3 units.

In order to stretch up the function, we multiply the whole function by the factor:

Then, to translated 3 units down, we subtract 3 units of the function:

Answer:

To create a perfect-square binomial of the form (y - k)^2, we need to find the value of k such that:

the first term of the binomial is y^2 (which is already the case)

the second term of the binomial is -2ky (which corresponds to -36y in the given expression)

the third term of the binomial is k^2 (which corresponds to 81 in the given expression)

To find k, we can use the formula:

k = (1/2)*(-b/a)

where a is the coefficient of y^2, b is the coefficient of y, and we are looking for the value of k that makes the expression a perfect square.

In this case, a = 1 and b = -36, so:

k = (1/2)(-b/a) = (1/2)(-(-36)/1) = 18

Therefore, the missing number to create a perfect-square binomial is 18:

(y - 18)^2 = y^2 - 36y + 324

The value of b for which ∫b0cos(ex)dx is minimum is π/2e..

To find the value of b for which the definite integral ∫b0cos(ex)dx is a minimum, we can find the critical points (i.e. local extrema) of the integrand cos(ex) in the interval [0, 2].

Since cos(ex) is a periodic function with period 2π/e, it suffices to consider the interval [0, 2π/e]. In this interval, cos(ex) has its maximum value of 1 at x = 0, and its minimum value of -1 at x = π/2e and x = 3π/2e.

Since e is positive, the function cos(ex) is increasing on the interval [0, π/2e) and decreasing on the interval (π/2e, π/e].

Therefore, if b is in the interval [0, π/2e), the integral is minimized when b = 0. If b is in the interval [π/2e, π/e], the integral is minimized when b = π/2e.

Since the maximum value of b is 2, and 2 < π/e, it follows that the integral ∫b0cos(ex)dx is minimized when b = π/2e.

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Answer:

lily - 5

5+8= 13

James - 13

13+5= 18

18-75= 57

Michael - 57

A. True. A compound event may consist of two dependent events. Dependent events are those in which the outcome of the first event affects the outcome of the second event. For example, drawing a card from a deck and not replacing it before drawing a second card would be an example of dependent events.

Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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\(\\ \sf\longmapsto 256x^2y^2-x^2y^2+49y^2x^2\)

\(\\ \sf\longmapsto 256x^2y^2-x^2y^2+49x^2y^2\)

\(\\ \sf\longmapsto (256-1+49)x^2y^2\)

\(\\ \sf\longmapsto 304x^2y^2\)

Answer:

15 percent

Step-by-step explanation:

just look up 180 plus each percentage

Answer:

61 divided by 5 = 12.2

12.2= 12 1/5

each piece is 12 1/5 meters long

Step-by-step explanation:

Hope this Helps!!

-xX..0Liyah0..Xx

Answer:

Step-by-step explanation:

Domain means what x's are on this graph, or what x's can you put into this equation. Range means what y's are in this graph or what y's can you get out if this equation. For y=x you can literally put in any x and get out any y, so the domain and range are both all real numbers. I couldn't see the choices on your drop down and there's several ways to write "all real numbers" as an answer. The absolute value graph y=|x| is a V-shaped graph so again, you can put in any x, but you only get positive numbers out (and 0, if you input 0) so the range us just all the y's that are 0 and bigger. That is y>=0. Again, there are several ways to write that such as {y | y>=0} or [0, infinity symbol)

The equation of the line is y = -3x + 5.

To find the equation of a line that passes through two points and is perpendicular to the equator, we need to calculate the slope of the line that passes through the two points first.

The slope of the line passing through (1,10) and (1,10) is 0. This means that the line is perpendicular to the equator, whose slope is undefined.

Next, we need to calculate the y-intercept. If we assume that the line passes through the point (1,10), then the y-intercept is 10.

Finally, we can use the slope and the y-intercept to write the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 0 and the y-intercept is 10, so the equation of the line is y = 0x + 10, which simplifies to y = 10.

Since the slope of the line is 0, we can also write the equation of the line in the form y = -3x + b, where b is the y-intercept. In this case, the y-intercept is 10, so the equation of the line is y = -3x + 10, which simplifies to y = -3x + 5.

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Answer:

all i could do was simplify it

Step-by-step explanation:

Let x= the average for all three classes combined. So x=85.25.

When you add two or more numbers and divide the result by the number of numbers you added together, you obtain an average.

The arithmetic mean is determined by adding a collection of numbers, dividing by their count, and obtaining the result.

average  =  total points / number of students

total points = average*number of students

Let the total number of students in  each class = a , b  and x

The total number of points the first class amassed  was   80a

The total number of points amassed by the second class was  85b

The total number of points amassed by the third class = 89c

For the first two classes we have

[ 80a + 85b ] / [ a + b] = 83

80a + 85b = 83a + 83b  

subtract  80a, 83b from both sides    

3a = 2b

a = 2/3b

For the second two classes we have

[ 85b + 89c ]  / [ b + c ]  =  87  

[  85b + 89c ]  = 87 [b + c]

85b + 89c = 87b + 87c      

subtract  85b, 87c from both sides

2c = 2b  

b  = c

For the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80a + 85b  + 89c ] /  [ a + b + c ]   =[sub for  a and c ]  

[80 (2/3)b  + 85b  + 89b]  /  [ (2/3)b  + b  + b ]  

b [ 80 (2/3)  + 85  + 89 ]  / [  b [( 2/3) + 1 + 1] ]       [cancel the b's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

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Answer:

Andre scored 14 points

Step-by-step explanation:

We make an equation describing the problem:

x + 9 = 5 + 9

x = 14

We compare Noah and Andre by doing:

2x + 10

and x = 5

This means Diego scored 5 points.

Answer:

"The expression represents a cubic polynomial with 3 terms. The constant term is -10, the leading degree is 3, and the leading coefficient is (-1/6)"

Step-by-step explanation:

We have the expression:

\(-\frac{x^3}{6} - 10 + x\)

First, what does that expression represents?

As al the powers of x are positive numbers, we can see that this is a polynomial, and the largest power is 3, so this is a polynomial of degree 3, also called a cubic polynomial.

How many terms are there?

The terms are the things separated by + or - symbols, is easy to see that there are 3 terms.

What is the constant term?

The constant term is the term where the variable, x, does not appear, here the constant term is: -10

What is the leading coefficient?

The leading coefficient is the coefficient that multiplies the term with the largest power of x, in this case, we can rewrite:

\(-\frac{x^3}{6} -10 + x = (\frac{-1}{6})*x^3 - 10 + x\)

the leading coefficient is:

(-1/6)

There is a part of the statement that I can't read, i suppose that there says:

"leading degree"

this is just the largest power of x that appears in the polynomial, in this case, is 3.

Then the complete statement is:

"The expression represents a cubic polynomial with 3 terms. The constant term is -10, the leading degree is 3, and the leading coefficient is (-1/6)"

Answer:

yes it is

Step-by-step explanation:

decimals and fractions are rational numbers

Answer:

no

Step-by-step explanation:

as it cannot be expressed as an integer or a quotient of an integer.

Answer:

1/2 lb

Step-by-step explanation:

(1)1.75 + 3(3.75) - 4 = 23.5/4

23.5x/4 = 2.95

23.5x = 11.8

x = 0.5

Answer:

2lb

I don't know what to write here but this is the answer

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:

Isnt it where you write it in the easiest way to understand it? sorry if its wrong :/

Step-by-step explanation:

If you mean standard from in math  it is basically writing down a smaller number instead of a larger one. For example 10 x 10 x 10, you could just write 10*3.  

The number of time constants must elapse before a capacitor in a series rc will be 0.634rc.

Explanation:

Let us denote the equilibrium charge with qₐ

   In the given question

      for the duration we are to obtain the final charge on the capacitor should be 47% of  qₐ

                                 q= qₐ(1-e⁻t/rc)

Where q is the final charge = 47%   = 0.47qₐ

             RC is the time constant

substitute the values:

                                           0.47qₐ= qₐ(1-e⁻t/rc)

                                              e⁻t/rc=0.53

   Taking natural log of both sides

                                  ln(e⁻t/rc) = ln(0.53)

                                     -t/rc = -0.634

                                          t/rc =0.634

                                       t=0.634rc

So the time constant will be t=0.634timeconstants

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Answer:

k = 7

Step-by-step explanation:

Vertical shift down by 7units, f(x) - 7

g(x) = (0.5)x - 7

g(x) = (0.5)x - k

Comparing both equations, k = 7

Answer:

k = 7

Step-by-step explanation:

it would be 7 and not -7 because there is already a minus symbol which shows that k is being moved downwards 7 UNITS.

Answer:

2 + 3 = 5

5 - 2 = 3

3.4 + 7.1 = 10.5

10.5 - 3.4 = 7.1

7 + 8 = 15

15 - 7 = 8

9/5 + 3/2 = 33/10

33/10 - 3/2 = 9/5

The values of the given expression having exponent with negative fractional base i.e. \(-2^{(3/2)^2}\\\) is evaluated out to be 16/9.

First, we need to simplify the expression inside the parentheses using the rule that says "exponents with negative fractional base can be rewritten as a fraction with positive numerator."

\(-2^{(3/2)^2}\) = (-2)² × (2/3)²

Now, we can simplify the expression  further by solving the exponent of (-2)² and (2/3)²:

(-2)² × (2/3)² = 4 × 4/9 = 16/9

Therefore, the value of the given expression \(-2^{(3/2)^2}\\\)  is 16/9.

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The question is :

What is the value of the expression \(-2^{(3/2)^2}\) ?

A circle is drawn inside the square and touches all four sides of the square . The approximate area of circle is 15.7 units.

Given:

Leftmost point:      R(-8,-2)

Rightmost point:    S(-3,-2)

Lowest point:        T(-3,-7)

Highest point:        U(-8,-7)

Let us consider any point (x, y) inside the square such that its distance from origin ≤ its distance from any of the edges, say AD.

∴OP < PM

⇒ (x 2 +y 2 ) < 1 − x

⇒y 2 ≤ −2(x - 1/2)  ------------------------ (1)

Above represents all points within the parabola P₁. If we consider the edge BC, then OP< PN will imply

y² < 2(x + 1/2)

Similarly, if we consider the edges AB and CD, we will have

x² < −2(y− 1/2)

x² < 2(y + 1/2 )

Hence, S consists of the region bounded by four parabolas meeting the axes at (± 1/2,0) and (0,±1/2).

The point L is intersection of P₁ and  P₃

given by (1) and (3).

y²− x² = −2(x−y)

          =2(y−x)

⇒ y − x = 0

⇒ y = x

⇒x² +2x − 1 = 0

⇒(x+1)² = 2

⇒x = 2−1 as x is positive

∴L is (√2−1, √2−1)

∴ The total area =4  [ square of side ( √2−1)+2∫√1 − 2xdx ]

=  4 {(√2−1)² +2∫ √(1-2x) dx}

=  \(4(3-2\sqrt{2} ) [1+\frac{2}{3}\) \(\sqrt{(3-2\sqrt{2} )}\)]

=  \(4(3-2\sqrt{2} ) [1+\frac{2}{3} (\sqrt{2} -1)\)

= \(4(3-2\sqrt{2} ) [1+ 2\sqrt{2}]\)

= 4/3 [4√2-5]

= 16√2 -20/ 3 units.

= 15.7 units.

​Therefore, the approximate area of the circle is 15.7 units.

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