bruce bought two books,one book equal 4 dollals more than three times the other book they both equal 72
what is x

Since the cafeteria is equidistant from the science building and the library, it means that the library is located at the same distance from the cafeteria as the science building. Therefore, the library will be located on the same line as the cafeteria and science building, making them collinear. Answer : The coordinates of the library will be (12 + √65, 16 + √65).

1. Given that the cafeteria is at point (12, 16) and the science building is at point (5, 12), we can use the concept of equidistance to find the coordinates of the library.

2. Calculate the distance between the cafeteria and the science building using the distance formula: √[(x2 - x1)^2 + (y2 - y1)^2]. In this case, it will be √[(12 - 5)^2 + (16 - 12)^2].

3. Simplify the expression: √[49 + 16] = √65.

4. Since the library is equidistant from the cafeteria, it will also be √65 units away from the cafeteria.

5. To find the coordinates of the library, we move √65 units in the same direction and along the same line as the cafeteria. Add √65 to the x-coordinate and y-coordinate of the cafeteria (12, 16) to get the coordinates of the library.

6. The coordinates of the library will be (12 + √65, 16 + √65).

7. Calculate the approximate values of the coordinates if necessary.

8. The coordinates of the library will be (12 + √65, 16 + √65).

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:a. sec(β) = `6/11`b. sin (β) = `5/6`c. Cot(β) = `2.01` (approximately)d. Sin(β - 90˚) = `√11/6` = `0.95` (approximately) are the exact values of each indicated trigonometric function.

Given function value is `cos(β) = √11/6` where `0˚ ≤ β ≤ 90˚` and `0 ≤ β ≤ π/2`.

To find the exact value of each indicated trigonometric function, we need to first find sin(β), tan(β), cos(β), csc(β), sec(β), and cot(β) where `0˚ ≤ β ≤ 90˚` and `0 ≤ β ≤ π/2`.

We know that `sin²(β) + cos²(β) = 1`.So, `sin(β) = ± √(1 - cos²(β))`Since `0˚ ≤ β ≤ 90˚`, `sin(β) = √(1 - cos²(β))`Now, `sin(β) = √(1 - (√11/6)²)`  = √(1 - 11/6)  = √(6/6 - 11/6)  = √(-5/6)

Since the value of β lies in the first quadrant, sin(β) is positive. Therefore, `sin(β) = √(5/6)`We also know that `tan(β) = sin(β)/cos(β)`.So, `tan(β) = (√(5/6))/((√11)/6)`

Now, `tan(β) = (6√5)/11`Similarly, we can find the values of all other trigonometric functions.a. sec(β) = `1/cos(β)` = `1/(√11/6)` = `6/√11` = `6/11`b. sin (β) = `√(5/6)` = `5/6`c. Cot(β) = `1/tan(β)` = `1/((6√5)/11)` = `11/(6√5)` = `(11/6) * (1/√5)` = `11/(6√5)` * `(√5/√5)` = `(11√5)/30` = `(11/5.48)` = `2.01` (approximately)d. Sin(β - 90˚) = `cos(β)` = `√11/6`

Therefore, the exact value of each indicated trigonometric function is:a. sec(β) = `6/11`b. sin (β) = `5/6`c. Cot(β) = `2.01` (approximately)d. Sin(β - 90˚) = `√11/6` = `0.95` (approximately).

Therefore, the options (a), (b), (c), and (d) are (6/11), (25/36), (11/5), and (11/6) respectively.

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Answer: To construct a box plot from the given data, we need to first find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

The minimum value is 47.

To find the quartiles, we first need to put the data in order from smallest to largest:

47, 49, 49, 52, 58, 59, 68, 71, 90, 91

There are 10 data points, so the median (Q2) is the average of the fifth and sixth values:

Q2 = (58 + 59)/2 = 58.5

To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively. The lower half of the data is:

47, 49, 49, 52, 58

So the median (Q1) of this half is:

Q1 = (49 + 49)/2 = 49

The upper half of the data is:

68, 71, 90, 91

So the median (Q3) of this half is:

Q3 = (71 + 90)/2 = 80.5

Now that we have found the minimum, Q1, Q2, Q3, and maximum values, we can construct the box plot:

  |     *

  |  *  |

  |-----|-----|-----|-----|-----|-----

 40    50    60    70    80    90   100

The line inside the box represents the median (Q2), the box goes from Q1 to Q3, and the whiskers extend from the box to the minimum and maximum values. The asterisk (*) represents an outlier, which is any data point more than 1.5 times the interquartile range (IQR) away from the nearest quartile. In this case, there are no outliers.

Step-by-step explanation:

The company should consider other factors to decide the number of items they should manufacture and sell per month.

Given that the company manufactures and sells Q items per month. The monthly cost and price-demand functions are as follows: TC(Q) = 62,000 + 50QP(Q) = 137The price-demand function P(Q) gives the price that the company can charge for an item if they manufacture Q items in a month.

The total revenue function is given by TR(Q) = P(Q) × Q Revenue is maximized when the derivative of the revenue function is zero.

Therefore, the first step is to find the derivative of the revenue function. We know that: P(Q) = 137, so TR(Q) = 137QTherefore, the derivative of the revenue function is given by: dTR(Q)/dQ = 137

Now, to find the maximum revenue, we set d T R(Q)/d Q = 0 and solve for Q.137 = 0Q = 0.

Therefore, the company should manufacture and sell 0 items in a month to maximize revenue.

However, this is not a feasible solution since the company is already manufacturing items.

Therefore, the company should consider other factors to decide the number of items they should manufacture and sell per month.

In conclusion, the question cannot be answered with the given information. There seems to be a mistake in the question since the company should not manufacture and sell 0 items in a month to maximize revenue.

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b < 45 represents the inequality of how many books can be put on the shelves.

An inequality is a mathematical statement that shows the relative size or ordering of two values. It is represented using symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), and "≠" (not equal to).

The inequality that represents how many books can be put on the shelves is:

b < 45

This inequality states that the number of books to be shelved, represented by b, must be less than 45 in order to fit on the bookshelf.

The inequality "b > 45" would represent a scenario in which the number of books to be shelved is greater than 45, which is not possible given the constraint that the bookshelf can hold a maximum of 45 books.

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Answer:

The symbol (∞) is read as infinity. and indicates that the set is unbounded to the right on a number line. Interval notation requires a parenthesis to enclose infinity. The square bracket indicates the boundary is included in the solution.

Step-by-step explanation:

Answer:

L = J + 5

Step-by-step explanation:

Let's use "L" to represent Leanne's age and "J" to represent Jose's age.

From the given information, we know that Leanne is 5 years older than Jose, so we can write:

L = J + 5

This equation states that Leanne's age "L" is equal to Jose's age "J" plus 5 years.

Answer:

12

Step-by-step explanation:

Mark brainliest pls

It is untrue to say that the exponential function f(x) has a base of 3.

A mathematical function termed an exponential function has the formula f (x) = axe, where x is a variable and a constant called the base of the function, which must be greater than 0. The most often used exponential function basis is the transcendental number e, or approximately 2.71828.

An exponential function has the form f(x) = bx for b > 0 and b 1. Like in any exponential expression, the base is b and the exponent is x. Bacterial growth serves as an example of an exponential function. Some bacteria grow by two per hour.

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The consecutive even numbers are 12 and 14.

Even numbers can be divided into two equal groups or pairs and are exactly divisible by two. For instance, 2, 4, 6, 8, and so on. These numbers can be divided into equal groups. Consecutive numbers are numbers that follow each other in descending order from smallest to greatest. Consecutive even numbers are even integers that are separated by a factor of two.

Let the consecutive even numbers be x and x+2.

The sum of the numbers is 340. This will be illustrated as:

x² + (x + 2)² = 340

x² + (x + 2)(x + 2) = 340

x² + x² + 4x + 4 = 340

Collect like terms

2x² + 4x + 4 - 340 = 0.

2x² + 4x - 336 = 0

Divide through by 2

x² + 2x - 168 = 0

x² - 14x + 12x -168 = 0

x(x - 14) + 12(x - 14) = 0.

(x + 12)(x - 14) = 0

This shows that the numbers are 12 and 14

Check: 12² + 14² = 144 + 196 = 340.

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Answer:

4 out of 14

Step-by-step explanation:

there is only 4 door bells and 14 bells in total

Answer: 3 burritos

Step-by-step explanation:

Fraction of tacos = 1/6

Fraction of empanadas = 25% = 1/4

Fraction of tamales = 1/3

Fraction of burritos = 1 - (1/6 + 1/4 + 1/3)

It should be noted that the lowest common multiple for 6, 4 and 3 is 12.

Fraction of burritos = 1 - (1/6 + 1/4 + 1/3)

= 1 - (2/12 + 3/12 + 4/12)

= 1 - 9/12

= 3/12 or 1/4

The number of burritos bought by Kelly will now be:

= 1/4 × 12

= 3 burritos

Burger Quick is able to estimate their wait time more consistently because it has a smaller IQR (Interquartile Range).

What is an IQR?

The IQR represents the range of the middle 50% of the data, and is a measure of the spread of the data. A smaller IQR indicates that the data is less spread out and more consistent. Therefore, since Burger Quick has a smaller IQR than Super Fast Food, it is able to estimate their wait time more consistently.

It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. The quartiles are values that split the data into four equal parts: Q1 represents the 25th percentile, Q2 (also known as the median) represents the 50th percentile, and Q3 represents the 75th percentile. The IQR therefore represents the range of the middle 50% of the data.

The IQR is a useful measure of variability because it is less sensitive to outliers than the range or standard deviation, which can be skewed by extreme values in the data. The IQR is often used in box plots to show the spread of the data and identify potential outliers.

What is Burger Quick?

Burger Quick is likely a hypothetical or fictional drive-thru restaurant used in a statistical analysis or problem. It was mentioned in a question about box plots and wait times at drive-thru restaurants, and may not actually exist as a real establishment.

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Answer:

64

Step-by-step explanation:

ITSSSS 64!!

Answer:

100

Step-by-step explanation:

The angles are on the same side of the transversal.  They are corresponding angles, so they are equal. Put algebraically

4a = 2a + 50                Subtract 2a from both sides.

4a-2a = 2a-2a + 50     Combine

2a = 50                        Divide by 2

2a/2 = 50/2

a = 25

<VYX = 4*a = 4*25 = 100

490

472 <490<500

it fits the criteria

Answer:

Step-by-step explanation:

let the number be x

20-x/2=10

40-x=20

40-20=x

x=20

Answer: it is 9

Step-by-step explanation: if you mean calculating range as in the highest and lowest number then yes. If you mean geometric or arithmetic calculation of range then it would just be the numbers you stated.

Answer:

The median 3.5 the mean is 3.5 and the min is 0 max is 9

Step-by-step explanation:

to find the median cross out the nubers on the end if theres two ansewrs in the middle then do whatever number .5

Answer:

1. -2x+24

2. 3x+21

3. 5x-17

4. 3x²+12x

5. 18

Step-by-step explanation:

2. 3(x)+3(7)=3x+21

3. 5(x)+5(-4)+3= 5x-20+3=5x-17

4. 3x(x)+3x(4)=3x²+12x

5. 3(10)-12=30-12=18

Answer:

1.) -2x + 24

2.) 3x + 21

3.) 5x - 17

4.) 15x

5.) 18

Step-by-step explanation:

1.) The first step to simplify this equation is to combine like terms. Also remember to always keep the sign before the number/variable to use when combining like terms.  

3x + 14 - 5x + 10

3x - 5x + 14 + 10

   -2x + 24

2.) Use distributive property to distribute the 3 to x and 7. Keep the sign.

3(x + 7)

3x + 21

3.) Use distributive property to distribute the 5 to x and 4 then add three. Keep the signs. Combine like terms.

5(x - 4) + 3

5x - 20 + 3

5x - 17

4.) Once again, use distributive property to distribute the 3x to x and 4. When multiplying 3x times x just think of x with a 1 in front of it (1x) and just multiply 3 times 1. Carry the x when multiplying 4x times 4. Combine like terms.

3x (x + 4)

3x + 12x

15x

5.) All you have to do is replace x in "3x" and solve.

3(10) - 12

30 - 12

18

If you have any additional questions feel free to ask me or your teacher so you can really master what you're learning. :)

To determine the optimal order quantity for Rocky Mountain Tire Center, you must consider ordering costs, storage costs, and the purchase price of the tires. The order quantity should minimize the total cost including both ordering cost and storage cost.

The EOQ formula is given by: EOQ = √((2DS) / H)

Where: D = Annual demand (7,000 go-cart tires)

S = Ordering cost per order ($40) H = Holding cost - percentage of the purchase price (40% of the purchase price)

we need to determine the purchase price per tire based on the quantity ordered.

EOQ = √((2 * 7,000 * 40) / (0.4 * 15))

=118 tires

they should order approximately 118 tires.

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Answer:

brainliest please

Step-by-step explanation:

6 dogs because 1/2 cup per dog 6 divided by 3 = 1/2 or 2

so2 dogs per cup

Answer:

D

Step-by-step explanation:

D

Answer:

The answer is B

Step-by-step explanation:

It's because the exponent have 6.

Answer:

Step-by-step explanation:

Common denominator is 45

(45/9)*2 = 10 and (45/15)*4 = 12

10/45 - 12/45 = - 2/45

The two trapezoids in the figure are similar. Thus, the value of x would be equal to 33.

A trapezoid is a quadrilateral with at least one pair of sides parallel.

The two trapezoids in the figure are similar.

Since the figures are similar, the corresponding sides have the same ratio.

Here, the side must be proportional

So,

\(\sf \dfrac{40.5}{x}=\dfrac{54}{44}\)

\(\sf 1782=54x\)

Divide 54 on both sides

\(\sf x= \dfrac{1782}{54}\)

\(\sf x=33\)

Thus, the value of x is 33.

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The probability P(3 < X < 6, Y) is 0.

To find the probability P(3 < X < 6, Y) based on the joint probability density function (pdf) f(x, y) = 10\(e^{-2x-5y}\), where x > 0 and y > 0, we need to integrate the joint pdf over the given region.

P(3 < X < 6, Y) can be calculated as follows:

P(3 < X < 6, Y) = ∫∫(3 < x < 6)∫(0 < y) f(x, y) dy dx

= ∫(3 < x < 6) ∫(0 < y) 10\(e^{-2x-5y}\) dy dx

To evaluate this double integral, we integrate with respect to y first, and then with respect to x.

∫(0 < y) 10\(e^{-2x-5y}\)  dy = [-2\(e^{-2x-5y}\) ] evaluated from y = 0 to y = ∞

= [-2\(e^{-2x-5}\) ∞] - [-2\(e^{-2x-5}\) *0)]

Since y > 0, the second term on the right side becomes zero.

= [-2\(e^{-2x}\)-∞] = 0

Thus, the integral with respect to y yields zero.

Now, we integrate the result with respect to x over the range (3 < x < 6).

∫(3 < x < 6) 0 dx = 0

Therefore, the probability P(3 < X < 6, Y) is 0.

In the 4th decimal place, the probability is 0.0000.

Hence, P(3 < X < 6, Y) is 0 (rounded to the 4th decimal place).

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Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is  (4x² - 7) (4x - 7) = 0

Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.

We have the equation,

16x³ +28x² - 28x - 49 = 0

In order to solve the equation by using factor by grouping:

We find common terms in between,

So, we arrange the terms,

16x³ +28x² - 28x - 49 = 0

4x² (4x - 7) -7 (4x - 7) = 0

Here, we have common term (4x-7).

Factor out the common binomial.

(4x² - 7) (4x - 7) = 0

Therefore, (4x² - 7) (4x - 7) = 0 is the factor.

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Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!