Mrs. Jonah’s class of 18 students checked out a total of 351 books from the library last year. What was the ratio of books to students? Responses

The number is 90.

Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentage is %. Percentages are a measure of frequency.

When the number is decreased, the number becomes smaller. This means that the original number is larger than 81.

The equation that can be used to represent the information in the question is:

(1 - percentage decrease) initial number = 81

(1 - 0.1)x = 81

0.9x = 81

x = 81 / 0.9

x = 90

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Since their dot product is zero, then (6,-3) and (2,4) are normal to each other.

Step-by-step explanation:

Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.

These two vectors are also called orthogonal to each other.

Let u = (u₁, u₂) and  v = (v₁, v₂), then the dot product u . v is defined as:

u . v = u₁v₁ + u₂v₂

To check whether the vectors are normal to each other, let us check their dot product.

The given vectors are: (6,-3) and (2,4).

Let u = (6, -3) and  v = (2, 4), then,

u . v = 6 . 2 + (-3) . 4

        = 12 + (-12) = 0

Since u.v = 0, then (6,-3) and (2,4) are normal to each other.

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The value of x in the angles is 14.

When parallel lines are cut by a transversal, angle relationships are formed.

The angle relationships that are formed includes corresponding angles, alternate angles, vertical angle etc.

Therefore, the value of x can be found as follows;

m∠1 = m∠7 (vertical angles)

Therefore,

m∠7 = m∠15(corresponding angles)

Hence,

m∠1 = m∠15

m∠1 = 8x - 4

m∠15 = 6x + 24

Therefore,

8x - 4 = 6x + 24

8x - 6x = 24 + 4

2x = 28

divide both sides by 2

x = 28 / 2

x = 14

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Based on the given function on the number of pears on the pear tree, the true statement is that The number of pears on the tree increases by 2 each week.

A linear regression line takes the form:

y = mx + b

y = number of pears

m = change in the number of pears per week

x = number of weeks

b = number of pears at first week

When the function is converted to a linear regression form, it takes the form:

P(x) = 2(2+x)

P(x) = 4 + 2x

This shows that the change in the number of pears per week is 2. This means that the number of pears on the tree increases by 2 each week

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Solution of this polynomial equation is y = 12

In mathematics, simply polynomial or polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

2y+1=25

=> 2y +1 -1 = 25-1

=> 2y = 24

=> y = 12

Thus solution for given equation is y=12.

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Answer:

Step-by-step explanation:

When we apply the exponent rule: [tex](\sqrt[n]{x})^n = x[/tex]

[tex](\sqrt[3]{9})^2 * (\sqrt{20})^2 = 30(\sqrt[3]{9})^2[/tex]

[tex]= \mathrm{Decimal:\quad }\:129.80246\dots[/tex]

Answer:

Phase shift = [tex]\frac{3\pi }{5}[/tex]

Vertical shift = [tex]0[/tex]

Step-by-step explanation:

Shift Definition

[tex]\text{For\:}f\left(x\right)=A\cdot g\left(Bx-C\right)+D\text{,\:where\:}g\left(x\right)\text{\:is\:one\:of\:the\:basic\:trig\:functions,\:}[/tex] [tex]\frac{C}{B}\text{\:is\:phase\:shift}[/tex], [tex]D\text{\:is\:vertical\:shift}[/tex]

Here we have

[tex]\left(x\right)=4\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]

which can be written in the form [tex]g\left(Bx-C\right)=\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]

So comparing the two we get [tex]B=\frac{5}{4}, C=\frac{3\pi }{4},\:D=0[/tex]

Phase shift = [tex]\frac{C}{B} = \frac{\frac{3\pi }{4}}{\frac{5}{4}}[/tex] [tex]= \frac{3\pi }{5}[/tex]

Vertical shift [tex]D = 0[/tex]

The diameter of the given sphere is; 39.5 cm

The formula for Volume of Sphere is;

V = 4/3 πr³

where;

V is volume

r is radius

We are given; V = 32250 cm³

Thus;

4/3 πr³ = 32250

Make r the subject of the formula to get;

r = ∛((32250 * 3/4)/π)

r =  ∛7699.12

r = 19.75 cm

Now, radius * 2 = diameter

Thus; diameter = 2 * 19.75 = 39.5 cm

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The value of the ratio is CD = 24 cm

The given parameters are

SR : CD = 3 : 4

SR = 18 cm

Substitute SR = 18 cm in the ratio SR : CD = 3 : 4

So, we have

18 cm : CD = 3 : 4

Express the ratio as a fraction

So, we have

18 cm/CD = 3/4

This gives

CD = 18 cm * 4/3

Evaluate

CD = 24 cm

Hence, the value of the ratio is CD = 24 cm

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The common difference for the recursive equation [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 5  is 5.

It is a sequence where the difference between each consecutive term is the same.

We have,

The recursive equation:

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 5

and [tex]a_{1}[/tex] = -3

We can find the consecutive term using the recursive equation.

[tex]a_{2}[/tex] = [tex]a_{1}[/tex] + 5 = -3 + 5 = 2

[tex]a_{3} =a_{2}[/tex] + 5 = 2 + 5 = 7

The sequence we get is:

-3, 2, 7, 12,....

The common difference means the differences in between two consecutive terms.

2 - (-3) = 5

7 - 2 = 5

12 - 7 = 5

Thus the common difference is 5.

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Answer:

2

Step-by-step explanation:

(0,2) is the y-intercept

Answer:

75 flowers

Step-by-step explanation:

she needs to make 18 arrangements, so we divide 18 by 6 and get 3. 3 * 25 is 75 so the answer is 75.

Laura will arrange 18 flowers within 75 minutes of the time.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Laura can make six flower arrangements in 25 minutes if she makes 18 flower arrangements. The time will be calculated as,

Time = ( 25 x 18 ) / 6

Time = 25 x 3

Time = 75 minutes

Hence, it will take 75 minutes to arrange 18 flowers.

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Step-by-step explanation:

[tex] = - 8( - 6) - (25) \\ = 48 - 25 \\ = 23[/tex]

HOPE THIS HELPS!!

The value given expression of (x⁵ + 8)/(x + 1) is (x⁶ + 8x).

The given expression is-

(x⁵ + 8)/(x + 1)  .......equation 1

It is stated that;

x² + x = 1

Taking x common;

x(x + 1) = 1

Bring x on the other side.

(x + 1) = 1/x

Put the value of (x  + 1) in equation 1.

= (x⁵ + 8)/(x + 1)

= (x⁵ + 8)/[1/x]

Simplifying;

= (x⁵ + 8)x

Multiplying x on both values;

= x⁵x + 8x

= x⁶ + 8x

Thus, the value of the given expression is (x⁶ + 8x).

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The three undefined terms that form the basis for geometry are:

- Point

- Line

- Plane

The term undefined is often used to refer to an expression that is not assigned an interpretation or a value.

The main three undefined terms of geometry are:

- Point

In geometry, a point has no dimension.

A point is represented by a dot.

The point has no length, width, or thickness.

A dot can be very tiny or very large.

- Line

A line is a straight one-dimensional figure that has a length but does not have a thickness, and it extends endlessly in both directions.

A line is made of a set of points that is extended in opposite directions infinitely.

- Plane

A plane, in geometry, prolongs infinitely in two dimensions.

It has zero thickness, zero curvature, infinite width, and infinite length.

It is also known as a two-dimensional surface.

Thus,

The three undefined terms that form the basis for geometry are:

- Point

- Line

- Plane

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The solutions to the equations are:

A. b = ac² (dark green); b = 2

B. v = m - k (light blue); v = 5

C. p/q = r/s; q = 8

D. m = 3n/4 (red); m = 6

E. x = y(w + z) (light green); x = 10

F. d1 = 2m - d2 (dark blue); d1 = 7

G. s = 8r/9 (purple); s = 4

H. w = [tex]\sqrt{\frac{x - y}{v} }[/tex] (orange); w = 3

I. x = [tex]\frac{y - y_1 }{m} + x_1[/tex] (pink); x = 1

J. c = 5a - 7 (brown); c = 9

To solve for a variable in an equation, we need to isolate the variable to one side of the equation.

A. a = b/c²

a(c²) = b/c²(c²) [multiplication property of equality]

ac² = b

b = ac² (dark green)

Substitute a = 1/8 and c = 4 into the equation

b = (1/8)(4²)

b = (1/8)(16)

b = 2

B. m - v = k

m - v - m = k - m [subtraction property]

-v = k - m

v = -k + m

v = m - k (light blue)

Substitute k = -7 and m = -2 into the equation

v = -2 - (-7)

v = -2 + 7

v = 5

C. p/q = r/s

Cross multiply

qr = ps

qr/r = ps/r [division property]

q = ps/r (yellow)

Substitute k = -7 and m = -2 into the equation

q = (14)(-4)/-7

q = 8

D. 4m + 2n = 5n

4m + 2n -2n = 5n - 2n [subtraction property]

4m = 3n

4m/4 = 3n/4 [division property]

m = 3n/4 (red)

Substitute n = 8 into the equation

m = 3(8)/4

m = 6

E. w = x/y - z

w + z = x/y - z + z [addition property]

w + z = x/y

y(w + z) = x/y(y) [multiplication property]

y(w + z) = x

x = y(w + z) (light green)

Substitute w = -8, y = -5, and z = 6 into the equation

x = -5(-8 + 6)

x = -5(-2)

x = 10

F. m = 1/2(d1 + d2)

2m = d1 + d2 [multiplication property]

2m - d2 = d1 [subtraction property]

d1 = 2m - d2 (dark blue)

Substitute m = 10 and d2 = 13 into the equation

d1 = 2(10) - 13

d1 = 20 - 13

d1 = 7

G. 2r = 5s/2 - s/4

2r = (10s - s)/4

2r = 9s/4

2r(4) = 9s/4(4) [multiplication property]

8r = 9s

8r/9 = 9s/9 [division property]

8r/9 = s

s = 8r/9 (purple)

Substitute r = 9/2 into the equation

s = 8/9(9/2)

s = 4

H. vw² + y = x

vw² + y - y = x - y

vw² = x - y

vw²/v = (x - y)/v

w² = (x - y)/v

w = [tex]\sqrt{\frac{x - y}{v} }[/tex] (orange)

Substitute v = 5, x = 38, y = -7 into the equation

w = [tex]\sqrt{\frac{38 - (-7)}{5} }[/tex]

w = √9

w = 3

I. [tex]y - y_1 = m(x - x_1)[/tex]

[tex]\frac{y - y_1 }{m} = x - x_1\\\\\frac{y - y_1 }{m} + x_1 = x[/tex]

x = [tex]\frac{y - y_1 }{m} + x_1[/tex] (pink)

Substitute x1 = 9, y = 19, y1 = -5, and m = -3 into the equation

x = (19 - (-5))/-3 + 9

x = -8 + 9

x = 1

J. 2a + 3c = 17a - 21

2a - 17a = -3c - 21

-15a = -3c - 21

-15a + 21 = -3c

-15a/-3 + 21/-3 = -3c/-3

5a - 7 = c

c = 5a - 7 (brown)

Substitute a = 16/5 into the equation

c = 5(16/5) - 7

c = 16 - 7

c = 9

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The domain of f ( x ) = R , its range = y ≥ 4 and the domain of g ( x ) = R and its range = R as well .

Domain : The set of all the possible values of x is called domain of the function .

Range : The set of all the possible values of y is called the range of the function  .

Given : f ( x ) = [tex]x^{2}[/tex] + 4  , g ( x ) = 3 x - 1 .

To find : Domain and Range of functions .

f ( x ) = [tex]x^{2}[/tex] + 4

Domain = R ( real nos. )

Range = y ≥ 4 .

g ( x ) = 3 x - 1

Domain = R ( real nos. )

Range = R ( real nos. )

Therefore , the domain of f ( x ) = R , its range = y ≥ 4 and the domain of g ( x ) = R and its range = R as well .

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The solution for the radical equation √(x+3) = 4√x-2 is 7 / 3.

The phrase "algebraic expression" refers to any arrangement of terms that have undergone operations like addition, subtraction, multiplication, division, etc. (or variable expression).. Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.

Eliminate the radical on the both sides by squaring on both sides- 

Both sides must be raised to the second power.

√(x+3) ²=(4√x-2 )²

After squaring we get

x+3=16(x-2)

Solving the equation-

We get rearranged equation as :

x+3=16x-32

15x=35 x=35/15 which further reduces to 7/3 .

Check if the  solution is correct by putting it in original equation-

putting x=7/3 in the equation √(x+3) = 4√x-2 

we get √16/3=√16/3

Therefore, the solution for the radical equation √(x+3) = 4√x-2 is 7 / 3.

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Answer:

[tex]f' \left(\dfrac{\pi}{3}\right) =\dfrac{1}{2}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\sin x[/tex]

The differentiation of sin(x) is cos(x).

[tex]\implies f'(x)=\cos x[/tex]

Therefore:

[tex]\implies f' \left(\dfrac{\pi}{3}\right) = \cos \left(\dfrac{\pi}{3}\right)[/tex]

[tex]\implies f' \left(\dfrac{\pi}{3}\right) =\dfrac{1}{2}[/tex]

The area of a new circle that has line segment GX as its diameter is 121 pi cm² .

Suppose that,

The radius of the small circle (GH) = 10 cm.

The radius of the big circle (HX) = 12 cm.

We will add the line GH and HX to get the total length of line segment GX.

So, GX = GH + HX

            = 10 + 12

      GX = 22 cm.

So, the diameter of new circle will be equal to line segment GX as it is given in the question.

Then, the area of new circle  = π r²    ( r = radius)

 Radius = D/2 = 22/2      (D = Diameter)

           r = 11

Now,     Area = π × 11²

                     = 121π cm²

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(a) Grade = 2.86%

(b) Grade = 5.85%

Find the road grade to two decimal places:

Grade in terms of percentage = (rise/run) * 100%

(a) Grade = (40/1400) * 100% = 2.86%

(b) Grade = 5.85%

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Answer:

C. <3 and<4

Step-by-step explanation:

Complementary angles are angles whose two angles make the sum 90°.

Guess bestie slay you'll do great!

Answer:

3x^3 -8*x^2 + 8*x + 3

Step-by-step explanation:

The standard form for a plolynomial is:

a*x^n + b*x^(n-1) + c*x^(n - 2) ........

We have:

(x-1)(3x^2-5x-3)

this is equal to:

3*x^3 - 5*x^2 + 3*x - 3*x^2 +5*x + 3

where the thing that i did is distribute the multiplication

this is equal to:

3x^3 -8*x^2 + 8*x + 3

ln (e) = 1, by the properties of logarithm.

Now,

As seen by the definition of logarithms, [tex]log_b(a)=x[/tex]

In case of natural logarithm, b = e, i.e., [tex]log_e(a)=x[/tex] = ln (a) = x

In the given expression, a = e

Hence, ln (e) = x

By properties of logarithms, we get that: ln (e) = 1.

Hence, ln (e) = 1, by the properties of logarithm.

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The required value of sports imports of the United States in 2012 is $2,745,240,000,000.

.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

the total value of exports from the United States in 2012 = $2,210,585,000,000

Now it is also given that,

the total value of exports from the United States in 2012 = $837,965,000,000 more than half of the US imports

Therefore, we can write

the total value of exports from the United States in 2012 = $837,965,000,000 + imports/2

Putting the value of exports we get,

2,210,585,000,000 = 837,965,000,000 + imports/2

Taking alike terms together we get,

Imports/ 2 = 2,210,585,000,000 - 837,965,000,000

Solving we get,

Imports/ 2 = 1,372,620,000,000

Multiplying by 2 both the side by 2 we get,

Imports = 2,745,240,000,000

Thus, the value of imports of the United States in 2012 = $2,745,240,000,000

Thus, the required value of imports of the United States in 2012 is $2,745,240,000,000.

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The correct question is :

in 2012 the total value of exports from the United States was $2,210,585,000,000 that year exports were $837,965,000,000 more than half of the US imports. find the value of imports of the United States In 2012