Each of John’s notebook is 3/4 inches wide. If he has 36 inches of space remaining on his bookshelf, how many notebooks will fit? Write your answer in simplest form.

Slope of line SP: -1

Slope of line FJ: -1

Point-Slope Form of Line FJ: \(y=-x-6\)

What to type inside the orange box? You must type "-x-6".

Concept. A parallel line to line SP. A parallel line is a line that has the same slope as another line, therefore, the line parallel to SP has the same slope of SP.

Let's solve!

1. Find the slope of line SP.

Line SP's expression is: \(y=-x-14\).

The slope of a linear function is always given by the coefficient of x when the equation is solved for y. Hence, the slope of line SP is -1, because x is being multiplied by -1.

2. Form the equation for line FJ.

Use the formula for finding linear equations: \(y-y_{1} =m(x-x_{1} )\), where m is the slope of the line, \(x_{1}\) is the x value of a point where the line passes, and \(y_{1}\) is the y value of a point where the line passes. \(x_1\) and \(y_1\) must be taken from a single point where the function passes.

Let's take the formula and find the equation for line FJ:

a. Substitute in the formula.

\(y-(0) =(-1)(x-(-6) )\)

b. Simplify.

\(y-(0) =(-1)(x-(-6) )\\ \\y=(-1)(x+6)\\ \\y=-x-6\)

3. Express your answers.

Slope of line SP: -1

Slope of line FJ: -1

Point-Slope Form of Line FJ: \(y=-x-6\)

The equation of the transformed function is (c) g(x) = 4(1/3x)²

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

f(x) = x²

g(x) = horizontally shrunk of f(x) by a factor 1/3 and vertical stretch by a factor of 4

The above equations implies that, we have the transformation to be:

Mathematically, this can be represented as

g(x) = 4f(1/3x)

Substitute the known values in the above equation, so, we have the following representation

g(x) = 4(1/3x)²

Hence, the transformed function is g(x) = 4(1/3x)²

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Answer:

119/139

Step-by-step explanation:

First, find the total amount of candies:
42 + 45 + 20 + 32 = 139

Then, add up all the candies that are not yellow:
42 + 45 + 32 = 119

Divide the not yellow candies by the total:
119/139

Answer:

A) 12 inches by 20 inches

Step-by-step explanation:

Dilation of a scale factor means to increase by a factor of 4.
That basically mean multiply the object by 4.

Therefore 3 inches x 4 = 12 inches

And 5 inches x 4 = 20

Answer:

Students that failed: 105

Step-by-step explanation:

Students that passed: 4x

Students that didn’t pass: x

4x + x = 535

5x = 535

x = 535/5

x = 105

Answer:

? = 9.2

Step-by-step explanation:

The angle between a tangent and radius at the point of contact is 90°

Then the triangle shown is right with legs ? , 6.9 and hypotenuse = (6.9 + 4.2) = 11.5

Using Pythagoras' identity in the right triangle

?² + 6.9² = 11.5²

?² + 47.61 = 132.25 ( subtract 47.61 from both sides )

?² = 84.64 ( take the square root of both sides )

? = \(\sqrt{84.64}\) = 9.2

Answer:

Solution given:

BC=BD=6.9 units

AD=4.6units

Now

AB=4.6+6.9=11.5units.

we have

<C=90°[the line from the tangent is perpendicular to the radius of circle]

we know that ∆ABC is a right angled triangle.

hypotenuse [h]=AB=11.5units

base[b]=BC=6.9 units

perpendicular [p]=x units

By using Pythagoras law

h²=p² +b²

11.5²=x²+6.9²

x²=11.5²-6.9²

x²=84.64

x=\( \sqrt{86.64} \)=9.2

Sothe segment length indicated is 9.2 units.

Answer:

Step-by-step explanation:

three squares with known area 25, 144,169...

1) area of the square =25

Side ×side=25

Side^2=25

Side=√25

Side =5.

Answer is 5.

2) area of the square =144

Side ×side=144

Side^2=144

Side=√144

Side =12

Answer is 12.

3)area of the square =169

Side ×side=169

Side^2=169

Side=√169

Side =13

Answer is 13.

Answer:

c. Random

Step-by-step explanation:

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

There are various types of sampling used by researchers and these are;

1. Systematic sampling.

2. Convenience sampling.

3. Stratified sampling.

4. Cluster sampling.

5. Random sampling.

Random sampling can be defined as a type of sampling in which the researcher select a sample of the population in order to determine an outcome.

Thus, the type of sampling used is random sampling.

Answer: what unit is this?

Step-by-step explanation:yeah I’ll need the unit to solve this question

Answer:

f(-3)=-198

Step-by-step explanation:

Function: f(x) = -212-3x + 5

x=-3

First substitute -3 for x:

f(-3)=-212-3(-3)+5

Next multiply -3 by -3:

-3*-3=9

f(-3)=-212+9+5

-212+9=-203

f(-3)=-203+5

-203+5=-198

f(-3)=-198

I hope this helped you.

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Chris' gross pay for the week after selling computer equipment worth $17,000 is $2,600.

The gross pay is the addition of the base pay and the sales commission.

The sales commission is graduated and computed as follows:

Chris' base pay = $300

Sales Commissions:

First $5,000 = 10%

Above $5,000 = 15%

Last week's sales = $17,000

10% Commission = $500 ($5,000 x 10%)

15% Commission = $1,800 ($17,000 - $5,000 x 15%)

Total Commission = $2,300

Gross pay = Base Pay + Commission

= $2,600 ($300 + $2,300)

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The fractional part of the hobbies were stamp collections represented as: 1/3

Given:

there were 8 stamp collections at the hobby fair.

If there were 24 hobbies in all.

We are asked to determine fractional part of the hobbies = ?

⇒ Fractional part = number of stamps/total number of hobbies in fair.

⇒ 8/24

⇒ 1/3

hence the fractional part = 1/3

therefore, we get the answer as 1/3

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The group of measures which would lead to the provided conclusion is the range is 7, the mean of the data is 12, the median is 12 and the mode is 11.

Given that, the data is around 12. If another measurement were taken, it would probably be around 12.

We need to find which group of measures would lead to this conclusion.

The mean of the data is the average value of the given data. The mean of the data is the ratio of the sum of all the values of data to the total number of values of data.

The median of the data is the middle value of the data set when it arrange in ascending or descending order. The data is around 12 which suggests that the median is 12.

Median=12

The mode of a data set is the value, which occurs most times for that data set. The value which has the highest frequency in the given set of data is known as the mode of that data set.

Mean and mode is around the median. For this case, the mean of the data is 12 and the mode is 11.

Mode=11

Mean=12

Thus, the group of measures which would lead to the provided conclusion is the range is 7, the mean of the data is 12, the median is 12 and the mode is 11.

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The fraction which is closest to 1/2 is, 3/8. So option B is correct

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

A fraction number 1/2

In decimal form = 0.5

Closest fraction number = ?

Most closest number is that number from which we subtract the given number and the magnitude of result we get is very less,

Lets take, A fraction 1/6

In decimal form it can written as,  0.167

Difference 1 =  0.5 - 0.167

                  =   0.333

Similarly, For numbers 3/8, 3/4, -1/2

Difference 2 =  0.5 - 0.375  = 0.125

Difference 3 =  0.5 - 0.75  = -0.25

Difference 4 =  0.5 - (-0.5)  =  1.0

It can be seen that,

Magnitude of difference in case of 3/8 is very less

Hence, the closest number is 3/8

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Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer:

5

Step-by-step explanation:

Turn 3 1/3 into an improper fraction.

Multiply the denominator by the whole number.

9

Add the numerator.

10/3

Now we flip 2/3 to be 3/2

Multiply 10/3 by 3/2

30/6

Simplify.

5

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Answer:

5

Step-by-step explanation:

Answer:

Vectors \(p_{1} = 2+5\cdot x + 3\cdot x^{2}\), \(p_{2} = 4+11\cdot x +6\cdot x^{2}\) and \(p_{3} = 1+2\cdot x +x^{2}\) are linearly independent.

Step-by-step explanation:

From Linear Algebra, we must remember that a set of vectors is linearly independent if and only if coefficients of its linear combinations are all zeroes. That is:

\(\Sigma\limits_{i=1}^{n} \alpha_{i}\cdot p_{i}= 0\), where \(\alpha_{i} = 0\). (Eq. 1)

Where:

\(p_{i}\) - i-th Polynomial of the set of vectors, dimensionless.

\(\alpha_{i}\) - i-th coefficient associated with the i-ith polynomial of the set of vectors, dimensionless.

Let \(p_{1} = 2+5\cdot x + 3\cdot x^{2}\), \(p_{2} = 4+11\cdot x +6\cdot x^{2}\) and \(p_{3} = 1+2\cdot x +x^{2}\) elements of the set of vectors, whose linear combination is:

\(\alpha_{1}\cdot p_{1}+\alpha_{2}\cdot p_{2}+\alpha_{3}\cdot p_{3}= 0\)

\(\alpha_{1}\cdot (2+5\cdot x+3\cdot x^{2})+\alpha_{2}\cdot (4+11\cdot x +6\cdot x^{2})+\alpha_{3}\cdot (1+2\cdot x+x^{2}) = 0\)

\((2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3})+(5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3})\cdot x+(3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3})\cdot x^{2} = 0\)

Values of coefficient are contained in the following homogeneous system of linear equations:

\(2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3} = 0\) (Eq. 2)

\(5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3} = 0\) (Eq. 3)

\(3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3} = 0\) (Eq. 4)

The solution of this system is:

\(\alpha_{1} = 0\), \(\alpha_{2} = 0\), \(\alpha_{3} = 0\)

Which means that given set of vectors are linearly independent.

Answer:

  a)  V = (8 -4/3π)r³

  b)  2048(2 -π/3) cm³ ≈ 1951.34 cm³

Step-by-step explanation:

When a sphere is placed in a box the empty space volume is the difference between the box volume and the sphere volume. Here, the box is a cube with the same outside dimensions as the sphere.

__

The side length of the cube is 2r, where r is the radius of the sphere. So, the volume of the cube is ...

  V = s³ = (2r)³ = 8r³

The volume of the sphere is given by the formula ...

  V = 4/3πr³

The volume of the empty space is the difference of these:

  V = (8r³) -(4/3πr³)

  V = (8 -4/3π)r³ . . . . . . . formula for the empty volume

__

For r=8 cm, the empty volume is ...

  V = (8 -4/3π)(8 cm)³ = 4(2 -π/3)(512 cm³)

  V = 2048(2 -π/3) cm³ ≈ 1951.34 cm³ . . . . empty volume

Answer:

8:15

Step-by-step explanation:

The solution to the given addition problem is 150.6 ft^9.

Converting everything to the same unit is the simplest solution to this problem.

The conversions are:

1 cubic yard = (27 cubic feet)

1 cubic inch = (0.000578704 cubic feet)

The addition can be performed as,

(6 cu yd × 9 cu ft × 134 cu in) + (1 cu yd × 12 cu ft × 200 cu in)

=  [6(27 cu ft) × 9 cu ft × 134(0.000578704 cu ft)] + [1(27 cu ft) × 12 cu ft × 200(0.000578704 cu ft)]

= 150.6 ft^9

The result of the addition is 150.6 ft^9.

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Answer:

the answer is C

Step-by-step explanation:

Answer:

probability is one for the position of the fourth vertex

it's co ordinates will be (2,2)

Answer:

I believe it's C... Not sure though...

To find the solution to the system of equations represented by the two lines based on the given tables of ordered pairs, you can follow these steps:

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The single shift worked by Reem such that he earned $320 is 16 hours long.

Total earned = $320

First 8 hours (earning per hour) = $16

Additional hours = $24 per hour

Let the total number of hours worked = m

The Number of hours after 8 hours = m - 8

Representing the scenario with an equation :

(16 × 8) + (24 × (m - 8)) = 320

128 + 24m - 192 = 320

-64 + 24m = 320

24m = 320 + 64

24m = 384

Divide through by 24

m = 384 / 24

m = 16

Hence, the length of the shift is 16 hours.

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Answer:

4 cups of lemonade

Step-by-step explanation:

lemonade: tea   : total

1/2                1 1/2     1/2 + 1 1/2 = 2

We need a total of 16

16/2 = 8

Multiply each number by 8

lemonade: tea   : total

1/2 *8               1 1/2 *8     2*8

4                   12      16

4 cups of lemonade

Answer:

That's my slovings for your question

Answer:

16.24

Step-by-step explanation:

of means multiply

28% * 58

Change to decimal form

.28 * 58

16.24

Answer:

\(\Large \boxed{\mathrm{16.24}}\)

Step-by-step explanation:

\(28\% \times 58\)

\(\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}\)

\(\displaystyle \frac{28}{100} \times 58\)

\(\sf Multiply.\)

\(\displaystyle \frac{1624}{100} =16.24\)