Books in the clearance section at Reading Central Bookmart cost $6.00 for paperbacks and $12.00 for hardbacks. Which inequality best describes the number of paperback books, p, and the number of hardback books, h, that can be purchased for $53.00 or less?
A.
12p + 6h > 53
B.
6p + 12h < 53
C.
12p + 6h < 53
D.
6p + 12h < 53

Answer:

17.7 degree

Step-by-step explanation:

We can begin by drawing a diagram:

```

C

/|

/ |

/α | 10.5 mi```

A------β------B

\ /

\ /

\/

8.8 mi

```

We can label angles β and α as shown, where β represents the angle from point C to point B and α```

A ------- 9.2 mi -------- B

```

Let's label some angles in the diagram:

- Angle A: the angle between the line from A to C and the line from A to B

- Angle B: the angle between the line from C to A and the line from C to B

- Angle α: the angle at the buoy C

We want to find the measure of angle α. To do that, we can use the law of cosines to find the length of the side opposite angle α:

```

c^2 = a^2 + b^2 - 2ab cos(C)

```

where a = 8.8, b = 10.5, and C = angle B. We can solve for cos(C):

```

cos(C) = (a^2 + b^2 - c^2) / 2ab

```

Since we know a, b, and c (8.8, 10.5, and 9.2 respectively), we can calculate cos(C):

```

cos(C) = (8.8^2 + 10.5^2 - 9.2^2) / (2 * 8.8 * 10.5) ≈ 0.701

```

Now we can find angle B using the inverse cosine function:

```

B = cos^-1(cos(C)) ≈ 45.4°

```

Finally, we can find angle α by subtracting angle A from angle B:

```

α = B - A ≈ 17.7°

```

So the measure of the turn that the ship has to make at the buoy is approximately 17.7 degrees.

In a circle with congruent line segments DE and FG, statements A is true, B is false, C and D are false, and E may or may not be true.

In the given circle ⊙C, DE and FG are two line segments that are congruent. The following statements must be true:

A. △DCE≅△FCE: This statement is true because both triangles share the same side lengths of DE and FG and the common angle ∠DCE = ∠FCE.

B. arcDE = arcFG: This statement is false since congruent line segments do not necessarily correspond to congruent arcs in a circle.

C. △FCE≅△FCG: This statement is false since there is no given information to suggest that the line segment CG is congruent to CE.

D. ∠DCE≅∠GCF: This statement is false since there is no given information to suggest that ∠GCF is congruent to ∠DCE.

E. EF≅ED: This statement may or may not be true since we are not given any information about the length of either of these line segments.

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To find the percentage of M2 that M1 represents, we can use the following formula:(M1 / M2) x 100%Substituting the given values, we get:(1050 / 3500) x 100% = 30%Therefore, M1 represents 30% of M2.

Answer:

Hope this helps ^^

Step-by-step explanation:

Let's define the variables:

Let's call the cost of a burger "B" (in dollars).

Let's call the cost of a hotdog "H" (in dollars).

Now, we can set up a system of equations based on the given information:

Equation 1: 2B + H = 4.82 (Two burgers and one hotdog cost $4.82)

Equation 2: B + 2H = 3.70 (One burger and two hotdogs cost $3.70)

To solve this system of equations, we can use the method of substitution or elimination.

Using the method of elimination, we can multiply Equation 2 by 2 to eliminate the "B" term:

2(B + 2H) = 2(3.70)

2B + 4H = 7.40

Now, we can subtract Equation 1 from this new equation to eliminate the "2B" term:

(2B + 4H) - (2B + H) = 7.40 - 4.82

2H - H = 2.58

H = 2.58

Therefore, the cost of a hotdog is $2.58.

Labeling the answer: The cost of a hotdog is $2.58.

The height if the squared-based pyramid is given as 34 cm

We have BD / 2

= 10 / 2

= 5 cm

AC = [tex]\sqrt{AB^2-BC^2}[/tex]

= √12² - 5 ²

= 12 cm

The height is given as 10 + 12 + 12

= 34 cm

Hence the height if the squared-based pyramid is given as 34 cm

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The exponential model for the population of the city t years after 2010 is given by:

The population in 2020 can be estimated to be 187,000 × 1.01^10 = 200,270, which is rounded to 200,000.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &187000\\ r=rate\to 1\%\to \frac{1}{100}\dotfill &0.01\\ t=years \end{cases} \\\\\\ A = 187000(1 + 0.01)^{t} \implies A=y = 187000(1.01)^t \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{in 2020 is 10 years later}}{y=187000(1.01)^{10}}\implies y\approx 207000[/tex]

The length of the hypotenuse of the triangle is b = x√2 units

Given data ,

Let the triangle be represented as ΔABC

And , the triangle is a 45 - 45 - 90 triangle

So , the two legs are congruent to one another and the non-right angles are both equal to 45 degrees

And , the sides are in the proportion x : x : x√2

Now , the length of the sides of the triangle are

The measure of base BC = a units = x

The measure of height AB = c units = x

So , the measure of the hypotenuse of the triangle is = x√2 units

Hence , the triangle is solved and hypotenuse AC = x√2 units

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a.) The number of students that took the Algebra 1 for the whole three years = 672

b.) The empirical probability that Sharon will receive an A would be =0.061

For question a.)

To calculate the total number of students that took the Algebra 1 for the 3 years, the students that got the various grades are being added up. That is;

Grade A= 41

Grade B =183

Grade C =265

Grade D =96

Grade F =85

Incomplete = 2

Total = 41+183+265+96+85+2 = 672

For b.)

The probability = possible outcome/sample space

possible outcome = 41/672=0.061

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Answer:

x=58.74

Step-by-step explanation:

4x+5(-42)=25

4x+-210=25

4x=25+210

4x=235

x=235/4

x=58.75

Answer:

9.6 miles per hour

Step-by-step explanation:

The rate is 4/25 miles per minute

To convert to miles per hour, since there are 60 minutes in an hour, multiply:  4/25 x 60

= 240/25

= 9.6 miles per hour

Okay, let's break this down step-by-step:

In the beginning of BS 2077, Dolma deposited B? 120,000 in her account.

The interest rate is 9% per annum.

So in the first year (BS 2077), she earned 9% of 120,000 = B? 10,800 in interest.

Her principal amount increased to 120,000 + 10,800 = B? 130,800

In BS 2078, she earned 9% of 130,800 = B? 11,772 in interest.

Her principal now was 130,800 + 11,772 = B? 142,572

In BS 2079, she earned 9% of 142,572 = B? 12,781 in interest.

Her principal now was 142,572 + 12,781 = B? 155,353

In the beginning of BS 2080, her total balance was B? 155,353.

She paid 6% of her interest as income tax.

9% of 155,353 is 13,991.

6% of 13,991 is 839.

So her total interest received in BS 2080 after paying tax was 13,991 - 839 = B? 13,152.

Her total amount received in BS 2080 was:

Principal (155,353) + Interest (13,152) = B? 168,505

So the total amount Dolma received in the beginning of BS 2080 was B? 168,505

Let me know if you have any other questions!

Answer:

231002 = (2340)25 · 232 ≡ 125 · 529 = 529 ≡ 37 mod 41.

The height of the tree is 60 ft

Proportion is defined as as an equation that is made equal to another

From the information given, we have that;

The shadow casted by the tree = 30 ft

The height of the pole = 6ft

The shadow casted by the pole = 3ft

Then, we have that;

If 6ft = 3ft

xft = 30ft

cross multiply the values, we have;

3x = 30(6)

Multiply the values

3x = 180

Divide both sides by the coefficient of the variable

x = 60ft

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The equation that matched the graph of the greatest interger function is y = [x] - 4. The correct option is (A).

To know the graph, we recall the equation of a straight line which is:

y = mx + c

where m is the gradient and

c is the intercept on the y-axis

Checking the graph, we can find the the intercept made by the straight line curve on the y-axis is -4.

Then we can have an equation of line written as:

y = mx + (-4) = mx - 4

From the options provided, there is only 1 with intercept of -4

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Answer:

Hexagon

Step-by-step explanation: Count the sides, hex means 6, sept means 7, oct means 8

The features of the quadratic function are given as follows:

The zero is the value of x for which the function touches or crosses the x-axis, hence it is of:

x = -2.

As the graph only touches the x-axis, the zero has an even multiplicity of 2.

The vertex is the turning point of the graph of the quadratic function, hence the coordinates are given as follows:

(-2,0).

Meaning that:

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The solution is:

The area of the rectangular field is 2831.25 sq. yards.

The perimeter of the rectangular field is 153.1 yards

Here,

the length of the field =  62. 5 yards

The width of the field = 45.3 yards

PERIMETER OF A RECTANGLE = 2 (LENGTH + WIDTH)

⇒ The perimeter of the yard = 2 ( 62.5 + 45.3)

                                               = 2 x (107.8) = 153.1 yards

or the perimeter of the rectangular field is 153.1 yards

Area of a Rectangle = (LENGTH x WIDTH)

⇒ The area of the yard =  ( 62.5 x 45.3)

                                      = 2831.25 sq. yards

or the area of the rectangular field is 2831.25 sq. yards.

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complete question:

John has a rectangular-shaped field whose length is 62.5 yards and width is 45.3 yards.

The area of the field is square yards. The perimeter of the field is yards.

The total length of the chord PR is 30.

Given a circle Q.

Given a chord named as PR.

We have to find the length of the chord.

Here Q is the center of the circle.

Given that ∠QSP is a right angle.

Then clearly, ∠QSR is also a right angle.

Consider the triangle QSR and QSP.

QP = QR, since they are radius of the circle.

So, QP = QR = 17

QS ia a common side.

So QS = 8

Then it is clear that,

PS = SR

Using Pythagoras theorem,

(PS)² = 17² - 8²

        = 225

PS = √225 = 15

So the length of the chord, PR = 15 + 15 = 30.

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Answer:

Initially, national security was defined as the government's ability to protect its citizens from military attacks. Today, this definition also includes other non-military areas such as defense against crime and terrorism, economic security, environmental security, food security, energy security and cyber security.

The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1  using synthetic division is x³ +  2x² - 2x  + 7  and the remainder is 13

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

x⁴ - 3x³ + 9x + 6 ÷ x + 1

The synthetic set up is

-1  |   1  3  0   9   6

    |__________

Bring down the first coefficient, which is 1 and repeat the process

-1  |   1  3  0   9   6

    |__-1_-2_-2_7____

       1  2  -2  7  13

This means that the quotient is

x³ +  2x² - 2x  + 7  

And the remainder is 13

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Complete question

Find the quotient and remainder using synthetic division.

x^4-3x^3+9x+6/x+1

The quotient is

The remainder is

Answer:

Step-by-step explanation:

To use synthetic division, we need to set up the coefficients of the dividend polynomial in decreasing order of powers of x, including any missing terms with zero coefficients.

So we have:

Dividend: x^4 - 3x^3 + 9x + 6

Divisor: x + 1

We can represent the divisor as (x + 1) and set up the synthetic division table as follows:

-1 | 1 -3 9 0 6

| -1 4 -13 13

|___________________

| 1 -4 13 -13 19

The numbers on the first row of the table are the coefficients of the dividend polynomial in decreasing order of powers of x. The -1 on the left of the table is the opposite of the divisor, x + 1.

The first number in the second row is always 0, and we get it by bringing down the first coefficient, which is 1. To get the next number in the second row, we multiply the divisor, -1, by 1, and add the result to the second coefficient, which is -3. This gives us -1 x -3 = 3, which we write under -3 in the first row.

We repeat this process for the next numbers in the second row, always multiplying the divisor by the last number in the second row, and adding the result to the next coefficient in the first row. We continue until we reach the last coefficient in the first row.

The last number in the second row, 13, is the remainder of the division. The other numbers in the second row are the coefficients of the quotient polynomial in decreasing order of powers of x. So the quotient is:

x^3 - 4x^2 + 13x - 13

And the remainder is:

13

Therefore, the quotient is x^3 - 4x^2 + 13x - 13, and the remainder is 13.

Answer:

Line 2

Step-by-step explanation:

In the second line, 4 is taken as 4x and added with 6x resulting in 10x.

The line 2 should be written as follows:

6x - 5 = 6x - 5

6x - 6x = 5 - 5

0 = 0

Matrices are widely used in various fields, including solving word problems in mathematics because they provide a convenient way to organize and manipulate data, making complex problem-solving more manageable.

In word problem solutions, matrices serve as valuable tools for organizing and manipulating data, simplifying complex problem-solving endeavors. For instance, when faced with a system of linear equations, matrices provide a structured representation that enables efficient computation.

Consider a word problem involving multiple variables and equations, such as determining quantities and prices of diverse items. By formulating the problem as a matrix equation and employing matrix operations like Gaussian elimination or matrix inverses, we can decipher the unknown variables and unlock solutions.

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A graph that represents the compound inequality include the following: D. graph D.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the inequality symbol represents less than, we can logically deduce that the first point would be located at negative 3, followed by positive 1, with an open circle on both sides.

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The graph of the translations are attached

The red is the preimage while the blue is the image

The absolute value graph has equation f(x) = |2x| and the translation we want to obtain is y = f(x) + 4 and this is a translation 4 units up

This results to a graph of equation  y = f(x) + 4 = |2x| + 4

For the parabolic graph, the equation is written as

y = a(x - 2)² - 3

solving for a using (0, -5)

-5 = a(0 - 2)² - 3

-2 = 4a

a = -1/2, then the equation is g(x) = -1/2 (x - 2)² - 3

Applying the translation, the equation will be

y = g(x + 2) =  -1/2 (x - 2 + 2)² - 3 = -1/2 (x)² - 3

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The area of a right triangle is 70 yds².

We have,

Base= 17 yards

Height = 8 yards

The area of a triangle is given by the formula:

Area = (1/2) x base x height

Substituting the given values, we get:

Area = (1/2) x 17 x 8

Area = 68 square yards

Therefore, the area of a right triangle is 70 yds².

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The end behavior of [tex]g(x) = -3e^x[/tex] is As x approaches positive infinity, g(x) approaches negative infinity, As x approaches negative infinity, g(x) approaches 0.

To determine the end behavior of the function g(x) = -3e^x, we need to consider what happens to the output of the function as x gets very large (approaches positive infinity) or very small (approaches negative infinity).

As x approaches positive infinity, e^x also approaches positive infinity, since e is a positive number greater than 1. Therefore, -3e^x approaches negative infinity as x approaches positive infinity. We can write this as:

lim x → ∞ (-3[tex]e^x[/tex]) = -∞

This means that the function g(x) approaches negative infinity as x approaches positive infinity.

Similarly, as x approaches negative infinity, e^x approaches 0, since e to a negative power is equal to 1 divided by e raised to the absolute value of that power. Therefore, -3e^x approaches 0 as x approaches negative infinity. We can write this as:

lim x → -∞ (-3[tex]e^x[/tex]) = 0

This means that the function g(x) approaches 0 as x approaches negative infinity.

So, in summary, the end behavior of g(x) = -3[tex]e^x[/tex] is:

As x approaches positive infinity, g(x) approaches negative infinity.

As x approaches negative infinity, g(x) approaches 0.

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The mean of M1 + M2 is 1.4

The standard deviation is  1.104536.

The mean of the number of mistakes = 0.7

The standard deviation of the number of mistakes = 0.781

(a) Mean of M1 + M2:

Mean of (M1 + M2)

= Mean(M1) + Mean(M2)

= μ + μ

= 2μ

=  2 * 0.7

mean of M1 + M2= 1.4

(b) Standard deviation of M1 + M2:

Standard deviation of (M1 + M2)

= √(Variance(M1) + Variance(M2))

Variance for (M1) = (σ²) = (0.781)² = 0.610561

Variance for (M2) = (σ²) = (0.781)² = 0.610561

Standard deviation for (M1 + M2)

= √(0.610561 + 0.610561)

= √1.221122

Standard deviation = 1.104536

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