In the first ten months of the year, people took out 427,113 books from the Brookton Library. The librarian would like to set a new record and have 500,000 books go out in one year. If 38,264 books are taken out in November, how many must go out in December to meet the librarian?s goal?

Answer:

s = 1.5

Step-by-step explanation:

10 + 2.375 = 12.375 = 8.85

12.375/8.25 = 8.25s/8.25

s = 1.5

Answer:

To shrink the height it has to be shrunk by:

27 / x = 12

x = 2.25 times

The width would be 45 / 2.25 =

20 centimeters.

Step-by-step explanation:

Answer:

7.2 cm wide

Step-by-step explanation:

Set it up as a proportion.. (45/27) = (12/x)

Cross multiply and solve for x.

Consecutive numbers: 1, 2, 3, 4, 5.

As we can see it's the latest plus 1

So,

x, x + 1, x + 1 + 1, x + 1 + 1 + 1

x, x + 1, x + 2, x + 3 and so on

So it's x + 1.

For this case we have that by definition, a consecutive number is obtained by adding a unit to the previous one.

Example:

n, n + 1, n + 2, n + 3 ...

So:

If "x" is the first number of Ameekah, its second number to form a series of consecutive integers must be:

x + 1, that is, add "1" to the previous number.

Answer:

x + 1

Option B

Answer:

2500

Step-by-step explanation:

Let the first square number be [tex]x^2[/tex] then the next square number is [tex](x+1)^2[/tex].

The difference between these two consecutive numbers is 99.

This implies that:

[tex](x+1)^2-x^2=99[/tex]

We expand to get:

[tex]x^2+2x+1-x^2=99[/tex]

Simplify:

[tex]2x=99-1[/tex]

[tex]2x=98[/tex]

Divide both sides by 2

[tex]x=49[/tex]

Therefore the value of the larger perfect number is

[tex](49+1)^2=50^2=2500[/tex].

2880

Step-by-step explanation:

Final answer:

To find out how many minutes are in 222 days, multiply the number of days (222) by the number of hours in a day (24) and then by the number of minutes in an hour (60). The result is 319,680 minutes.

Explanation:

The student is asking how many minutes are in 222 days. We begin the conversion using the provided information:

There are 24 hours in 1 day

There are 60 minutes in 1 hour

Now, we just need to multiply the number of days by the number of hours in a day, and then by the number of minutes in an hour, to get our answer.

222 days × 24 hours/day × 60 minutes/hour = 319,680 minutes

There are 319,680 minutes in 222 days.

Answer:

Domain is all real numbers; Range is all numbers less than or equal to 0

Step-by-step explanation:

Domain covers x values, range covers y values.  The domain of an x^2 parabola, which is what this is, has a domain of all real numbers.  Meaning that while the branches of the function keep going up and up and up or down and down and down, the values of x will never stop growing.

The range here is indicative of the lowest y value to the highest that the function covers.  In this case, since the parabola is upside down, we have the highest to the lowest.  The highest that the function goes up the y axis is right at the origin, where y = 0.  Then it drops down into forever.  So the range is all values of y less than or equal to 0

The Domain of [tex]f(x)[/tex] is all the real numbers, and

The Range of [tex]f(x)[/tex] is  [tex]y\le0[/tex] or [tex]f(x)\le0[/tex]

The diagram shows the graph of the quadratic function

[tex]f(x)=-x^2[/tex]

The domain of [tex]f(x)[/tex] is all the real numbers, since the function has defined values for all real values of [tex]x[/tex].

The range of [tex]f(x)[/tex] is the set of values that [tex]f(x)[/tex] can assume. The square function has a range

[tex]\{y \text{ }|\text{ }y=x^2\text{ and }y\ge0\}[/tex] or the half-open interval [tex][0,\infty)[/tex].

This means that the negative of the square function will have the range

[tex]\{y \text{ }|\text{ }y=-x^2\text{ and }y\le0\}[/tex] or the half-open interval [tex](-\infty,0][/tex].

So, the domain of [tex]f(x)[/tex] is the open interval [tex](-\infty,\infty)[/tex] (all the real numbers), and the range of [tex]f(x)[/tex] is the half-open interval [tex](-\infty,0][/tex] (or, [tex]y\le0[/tex])

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Answer:  [tex]\bold{D)\quad h^{-1}(x)=\dfrac{1}{6}(x-1)}[/tex]

Step-by-step explanation:

Inverse is when you swap the x's and y's and then solve for y

y = 6x + 1

x = 6y + 1          swapped the x's and y's

x - 1 = 6y           subtracted 1 from both sides

[tex]\dfrac{1}{6}[/tex] (x - 1) = y         divided both sides by 6

Answer:

This is the alternate exterior angle theorem

Step-by-step explanation:

This is because angle 2 and angle 7 are in the outer part of each side of opposite lines

Answer:

[tex](n+6)(5u+x)[/tex]

Step-by-step explanation:

The given expression is;

[tex]5u(n+6)+x(n+6)[/tex]

The greatest common factor is (n+6).

Let us factor the GCF to obtain:

[tex](n+6)(5u+x)[/tex]

Therefore the completely factored form of

[tex]5u(n+6)+x(n+6)[/tex]

is

[tex](n+6)(5u+x)[/tex]

Answer:

A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36

Step-by-step explanation:

We have two sides of the triangle and we have an angle.

A = 32 °, a = 19, b = 14

We use the sine theorem to find the angle B.

We know that according to the sine theorem it is true that:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

[tex]\frac{sin(32\°)}{19}=\frac{sin(B)}{14}[/tex]

[tex]sin(B)=14*\frac{sin(32\°)}{19}\\\\B=Arcsin(14*\frac{sin(32\°)}{19})\\\\B=22.98\°[/tex]

We know that the sum of the internal angles of a triangle is always equal to 180.

So:

[tex]C=180-32-22.98\\\\C=125.02\°[/tex]

Finally we find the c side

[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}[/tex]

[tex]\frac{sin(32\°)}{19}=\frac{sin(125.02)}{c}[/tex]

[tex]0.02789=\frac{sin(125.02)}{c}[/tex]

[tex]c=\frac{sin(125.02)}{0.02789}\\\\c=29.36[/tex]

Answer:

1

8

Step-by-step explanation:

What do we know:

John and George raked 7/8 of the yard.

John raked 3/4 of 7/8

What we need to know is:

How much did George rake?

How? Subtract the fractions given.

7 - 3

8 4

To do this we must make the denominator (bottom) number the same. How? Find the least common denominator for 8 and 4. Basically what is the lowest number that both 8 and 4 can be divided.

Answer is 8

8 divided by 8 is 1

4 divided by 8 is 2

so

7 - 3 ×2 6

8 4 ×2 = 8

7 _ 6 = 1

8 8 8 is how much George raked.

Answer:

The angle of elevation is [tex]40.36\°[/tex]

Step-by-step explanation:

Let

[tex]\theta[/tex] ----> the angle of elevation

we know that

The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle

we have that

[tex]tan(\theta)=\frac{85}{100}[/tex]

[tex]\theta=arctan(\frac{85}{100})=40.36\°[/tex]

D is the correct answer

the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.

To subtract (5x + 3) from (9x - 7), we need to distribute the negative sign to all the terms in (5x + 3) and then perform the subtraction term by term.

(9x - 7) - (5x + 3)

= 9x - 7 - 5x - 3

Now, combine like terms:

= (9x - 5x) + (-7 - 3)

= 4x - 10

So, the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.

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Answer:

$4501.51

Step-by-step explanation:

Because you're compounding annually, which is only once per year, you can use a simple formula:

[tex]A(t)=P(1+r)^{t}[/tex]

Filling in our info gives us

[tex]A(t)=3100(1+.055)^7[/tex]

Do the adding inside the parenthesis and then raise 1.055 to the 7th power to get

A(t)= 3100(1.454679161)

A(t)= $4509.51

ANSWER

[tex]165.6 \degree[/tex]

EXPLANATION

The measure of arc AC corresponds to 22% + 24%=46%

The complete angle of the circle is 360°.

Therefore the measure of arc AC is

[tex] = \frac{46}{100} \times 360[/tex]

This simplifies to

[tex]165.6 \degree[/tex]

The correct answer is A.

Answer:

True

Step-by-step explanation:

The incentre is equally distant from the triangles 3 sides and like centroids is always inside the circle.

Answer:

48 people

Step-by-step explanation:

1. 4/50 = x/600  do 4x600 and 50 times x

2.50x=2400

3. divide both sides by 50 to get a result of x=48.

Answer:

400 units³

Step-by-step explanation:

The volume (V) of the square pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × height (h)

where h is the perpendicular height.

Consider the right triangle formed by a segment from the vertex to the midpoint of the base and the slant height ( the hypotenuse )

Using Pythagoras' identity on the right triangle

h² + 5² = 13²

h² + 25 = 169 ( subtract 25 from both sides )

h² = 144 ( take the square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12

Area of square base = 10² = 100, hence

V = [tex]\frac{1}{3}[/tex] × 100 × 12 = 4 × 100 = 400

f(-1) means the x value is -1 and you need to find what the Y value is.

Find -1 in the set of parenthesis and see what the Y value is.

When x = -1, y = 3

The answer would be 3.

Answer:

The measure of arc BC is 44°

Step-by-step explanation:

we know that

m arc AD+m arc DC+m arc BC+m arc AB=360° ----> by complete circle

substitute the given values and solve for m arc BC

98°+120°+m arc BC+98°=360°

m arc BC+316°=360°

m arc BC=360°-316°=44°

Answer:

Step-by-step explanation:

Answer:

y=1/1 x+6

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

the slope from one point to another is rise up one and go the the right one, therefore the slope of the line is 1/1.

The y-intercept is 6 which is shown on the graph

To find the angle of depression, we can use trigonometry. The elevation of the North Rim and the campground, along with the line of sight distance, can be used to calculate the angle using the tangent function.

To find the angle of depression of the man's line of sight to the campground, we can use trigonometry. The angle of depression is the angle between the line of sight and a horizontal line. In this case, the elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The line of sight distance to the campground is 3044 ft.

We can use the tangent function to find the angle of depression. Tangent(theta) = opposite/adjacent. The opposite side is the difference in elevation between the North Rim and the campground (5389 ft - 2405 ft) and the adjacent side is the line of sight distance (3044 ft). So, tangent(theta) = (5389 ft - 2405 ft) / 3044 ft.

Using a scientific calculator, we can find the value of theta by taking the inverse tangent (or arctan) of the ratio: theta = arctan((5389 ft - 2405 ft) / 3044 ft). The answer is approximately 57.38 degrees.

Using law of sines:

Sin(angle) = opposite leg (height) / hypotenuse ( length of ladder)

Sin(70) = 25/x

x = 25 * sin(70)

x = 26.6 feet

Answer:

a) Acute

Step-by-step explanation:

   To clasify the triangle as Acute, Right, or Obtuse, we use the converse of the pythagorean theorem and see if c^2 is greater, less than, or equal to b^2+a^2.

So 16^2 ? 11^2 + 12^2

Since 11^2 +12^2 = 265 and 16^2 is 256, c^2 is less than b^2+a^2. So the triangle is acute.

Answer:

  a)  Acute

Step-by-step explanation:

If 11 and 12 were the legs of a right triangle, the length of the hypotenuse would be ...

  √(11² +12²) = √(121 +144) = √265 ≈ 16.3

The actual length of the longest side is shorter, so the opposite (largest) angle measure will be less than 90°. The triangle is acute.

Answer:

2) First option

3) Second option

Step-by-step explanation:

5² = 625

13 × 8 × 5 = 520

For this case we must find an expression equivalent to:

[tex]216 ^ {\frac {1} {3}[/tex]

So, we can rewrite the 216:

[tex]216 = 6 * 6 * 6 = 6 ^ 3[/tex]

Rewriting the expression:

[tex](6 ^ 3) ^ {\frac {1} {3}=[/tex]

By definition of power properties we have:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So:

[tex]6 ^ {\frac {3} {3}} =\\6 ^ 1 =\\6[/tex]

Answer:

[tex]216 ^ {\frac {1} {3}}= 6[/tex]

The equivalent expression of [tex]216^{1/3}[/tex] is determined as 6.

Simplification refers to the process of reducing an expression, equation, or fraction into its simplest or most concise form.

The equivalent expression is determined by converting the exponents into roots as follows.

The given expression;

[tex]216^{1/3}[/tex]

This expression is simplified as follows;

     [tex]216^{1/3}[/tex] = ∛ 216

The final expression becomes;

6³ = 216

So 6 is the answer

Thus, the equivalent expression of [tex]216^{1/3}[/tex] is determined as 6.

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Answer:

The first answer is the one you want

Step-by-step explanation:

The rate of change is the slope.  Here it is represented by the dollar value/number of tickets sold.  This will give you the 1:1 ratio, meaning it will give you the number of dollars generated by the sale of 1 ticket.  That's what rate of change is.

Use the slope formula and 2 points on the table.  I chose the points (225, 250) and (200, 0):

[tex]\frac{0-250}{200-225} =\frac{-250}{-25} =10[/tex]

That translates to $10 per ticket.

Answer:

arc NO has measure 48

Step-by-step explanation:

We assume all measures are in consistent units (degrees or something similar). The two inscribed angles intercept the same arc, so are congruent:

9x -3 = 4x +12

5x = 15 . . . . . . . add 3-4x

x = 3 . . . . . . . . . divide by 5

The measure of the inscribed angle is then ...

4x +12 = 4(3) +12 = 24

That is half the measure of the arc, so the measure of arc NO is ...

arc NO = 2·24 = 48

Answer:

48°

Step-by-step explanation:

I'm actually just assuming that you mean arc NO.  Proceeding with that...

Angle NMO is an inscribed angle which intercepts arc NO.  Angle NPO is also an inscribed angle that intercepts arc NO.  Because they both intercept the same arc, both inscribed angles have the same measure.  Therefore,

9x - 3 = 4x + 12

Solving for x:

5x = 15

x = 3.  Plug 3 in for x in either one of the equations to get that angles NMO and NPO measure

9(3) - 3 = 24°

The rule is that inscribed angles measure HALF of the arcs they intercept, so the measure of arc NO is 48°

Answer:

6th bounce: 40%

Starting amount: 100%

Decay rate: 10%

Equation: 100% - 10% - 10% - 10% - 10% - 10% - 10% =

Step-by-step explanation:

100% - 10% - 10% - 10% - 10% - 10% - 10% = 40%. 40% is the answer.

Using an exponential function, it is found that on the 6th bounce, the ball bounces up 5.31 ft.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem:

Then, the height after the nth bounce is given by:

[tex]A[n] = 10(0.9)^n[/tex]

After the 6th bounce, we have that:

[tex]A[6] = 10(0.9)^6 = 5.31[/tex]

On the 6th bounce, the ball bounces up 5.31 ft.

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1. False. [tex]f'(c)=0[/tex] does not necessarily mean that [tex]f(c)[/tex] is a maximum or minimum. It could just as easily be a saddle point. For example, consider the function [tex]f(x)=x^3[/tex] with [tex]f'(x)=3x^2=0[/tex] when [tex]x=0[/tex], yet [tex]f(x)<0[/tex] for [tex]x<0[/tex] and [tex]f(x)>0[/tex] for [tex]x>0[/tex].

2. True. If [tex]f'(x)=0[/tex] for all [tex]x[/tex] in [tex](a,b)[/tex], then [tex]f[/tex] must be constant on that interval.

3. False. In order for the MVT to apply, [tex]f[/tex] must be continuous on the closed interval. But [tex]\dfrac1{x^2}[/tex] does not exist at [tex]x=0[/tex].

The first statement about f'(c)=0 implying a local maximum or minimum is true. The second statement that if f'(x)=0 on an interval implies the function is constant is also true. Lastly, the Mean Value Theorem cannot be applied to f(x) = 1/x² on the interval [-1, 1] because the function is not continuous at x=0.

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