A) In a hostel , 30% of the beds are vacant. There are 210 guest beds at the hostel currently. How many beds are there at the hostel?

B) The hostel plans to increase its bed capacity by 15% over the next year. What is the planned bed capacity at the hostel?

C) The jeweler is trying to determine which box has the greatest weight. A box of gold weighs 0.55 kilograms and a box of silver weighs 14/25 kilograms. Which box is heavier?

The probabilities are (a) 0.4228, and (b) 0.8382

Define probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.

(a) probability of drawing first a white marble and then a red marble

= 4/(4+10+3) x 3(3+10+3) = 4/17 + 3/16 = 0.4228

(b) probability of drawing first a green marble and then a blue marble

= 10/(10+3+4) x 4(9+3+4) = 10/17 + 4/16 = 0.8382

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The equation has two solutions [tex]x_{1}[/tex] =  [-4 + 2√13]/3] and

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

Given the question:

(x + 4)^2 = 15 - 2x^2.

To solve the above Equation by using Quadratic Formula:
Solving Steps of Equation:

[tex](x+4)^2 = 15 -2x^2[/tex]

Expand the expression

[tex]x^{2} +8x+16=15-2x^2[/tex]

Move the expression to the left

[tex]x^{2} +8x+16-15+2x^2[/tex] = 0

Collect like terms

[tex]3x^{2} +8x+1=0[/tex]

Use the Quadratic formula:

x = [-b ± √(b2 – 4ac)]/2a

x = [-8 ± √(8^2 – 4x3x1)]/2x 3

Multiply and evaluate :

x = [-8± √(64 – 12)]/6]

Calculate:

x = [-8± 2√13]/6]

Separate the solutions

[tex]x_{1}[/tex] =  [-4 + 2√13]/3]

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

Hence, The equation has two solutions [tex]x_{1}[/tex] =  [-4 + 2√13]/3] and

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

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When the ratio of the number of miles run to the number of miles biked is equivalent for each row in the table, the value for A is C. 2 3/4.

It should be noted that based on the information, the table has been given and the appropriate figures have been put into it.

The constant rate will be:

7 / 3 1/2 = 2

Now we can then write the relationship and this is illustrated as:

B = 2R

where B is the distance biked

R = the distance that's run.

We want to find the missing value of A. This is illustrated as:

5 1/2 = 2 × A

2A = 5 1/2

A = 2 3/4

Therefore, based on the information given, the correct option is C.

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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table.

Complete the table for A

A 2 1/4

B 2 2/4

C 2 3/4

D 3 3/4

Original price: $16

Discount: 40%

First, multiply the original price by the percentage discount in decimal form (divided by 100)

16 x 40/100 = 16 x 0.4 = $6.4 ( discount amount)

Subtract the discount amount to the original price

16-6.4 = $9.6 new price

multiply by 7 :

9.6 x 7 = $67.2

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1 = 0.76r - 9 - 0.36r

1 + 9 = 0.76r - 0.36r

Simplify like terms

10 = 0.4r

Solve for r

r = 10/0.4

r = 25

Result

r = 25

b)

Result

z = 20

Principal = $3000

Rate = 5%

time = 2

Amount after 2 years =

= $3307.5

Option D is the correct answer

If 24 out of our 40 stickers glow in the dark, we would have 16 that don't

As a fraction relative to our total 40 stickers, those 16 would be:

Simplifying,

hereby, 2/5 of the sticketrs don't glow in the dark

The solution of the inequality expression in interval notation is;

-1/2 < x < 2/3 and the number line is attached

We are given the Inequality expression  as;

6x² - x  < 2

To express the function in quadratic form, we subtract 2 from both sides to get;

6x² - x - 2 < 0

We now factorize this expression to get;

(2x +1)(3x - 2) < 0

This means that we have two inequalities solution which are expressed as; (2x + 1) < 0 and (3x - 2) < 0

For (2x + 1) < 0, add 1 to both sides to get;

2x < 1

divide both sides by 2 to get;

x < 1/2

Similarly, for (3x - 2) < 0;

Add 2 to both sides and then divide by 3 to get;

x < 3/2

Thus, the solution to the inequality is x = -1/2 and x = 3/2

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The written and solved equation to determine the cost of the desserts, d is  5(9.75 + d) = 63.75; d = 3.00

Five friends ate lunch and spent a total of $63.75.

They each bought the same meal for $9.75, and they each bought the same dessert.

The equation to determine the cost of the dessert, d can be represented as follows:

They are 5 friends,

Hence,

5 (9.75 + d) = 63.75

48.75 + 5d = 63.75

Therefore, let's use the equation to solve for d.

48.75 + 5d = 63.75

63.75 - 48.75 = 5d

15 = 5d

divide both sides by 5

15 / 5 = 5d / 5

d = 3

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If a submarine was situated 800 feet below sea level. ​If it ascends 275 feet, its new position relative to the sea level is: -525 feet.

Given :

Initial position of the submarine = 800ft below sea level

Ascending =275ft.

Hence, the New position relative to the sea level  is calculated as:

New position relative to the sea level = (-800+ 275)

New position relative to the sea level = - 525 feet

Therefore the new position is: -525 feet.

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The shadow of the 4 feet stick is 3/4 feet or 0.75 feet.

It is a question of ratio and proportion.

It is given in the question that the 32 feet tall building had a shadow 6 feet long.

We have to find the length of the shadow of a 4 ft stick.

Let the  length of the shadow of a 4 ft stick be x.

We know that length and shadow of a 4 feet stick and a 32 feet building will be in proportion.

Hence, we can write,

Length of building/Length of stick = shadow of building/shadow of stick

32/4 = 6/x

8 = 6/x

x = 6/8 feet = 3/4 feet = 0.75 feet

x = 0.75 feet.

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The measure of the angle b is 61°.

In Euclidean geometry, an angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. The plane that contains the rays contains the angles created by two beams.

Vertical Angles (Vertically Opposite Angles): The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.

The figure describes two angles 61° and b.

Now, from the figure the angles 61° and b are vertically opposite angles.

Therefore, the angles are equal.

b = 61°

Hence, the measure of angle b is 61°.

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The most appropriate choice for relation, domain and range will be given by-

Domain of S = {3, 1, 4}

Range of S = {0 , 2, -1, 9}

What is relation, domain and range?

A relation over set A and B is the subset of the cartesian product A x B.

Domain of a relation is the set of values for which the relation is defined.

Range is the set of solution obtained on putting the values of domain.

The relation S is defined as follows

S = {(3, 0), (1, 2), (4, -1), (3, 9)}

Now the set of values for which the relation is defined is the domain of the relation

For each ordered pair, the first number gives the values to be put in S. So the first number of every ordered pair is the domain.

So domain of S = {3, 1, 4}

Now, the second number gives the solution after putting the numbers in S.

So the second number of every ordered pair represents the range.

So, range of S = {0 , 2, -1, 9}

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The difference between the population in City A and City B is 8.27 x [tex]10^{4}[/tex] and 82,700.

The numbers are written in scientific notation. Scientific notation is a method that is used in mathematics to compress large numbers. In order to write a number in scientific notation, the number is written as a decimal number between 1 and 10 and multiplied by a power of 10. For example, 3 x 10² is equivalent to 300

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers.

8.59 x [tex]10^{4}[/tex] - 3.2 x 10³

(0.859 x [tex]10^{4 - 1}[/tex]) - ( 3.2 x 10³)

(0.859 x  10³)- (3.2 x 10³)

0.827 x  10³

8.27 x [tex]10^{4}[/tex] = 82,700

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[tex] = 2(3( {(9})^{2} - 5) + 5(3)) \\ = 2(3(81 - 5) + 15) \\ = 2( 3(76) + 15) \\ = 2(228 + 15) \\ = 2(243) \\ = 486[/tex]

ATTACHED IS THE SOLUTION

YOU DID NOT PROVIDE FULL OPTIONS THEREFORE I WON'T BE ABLE TO CHOOSE.

GOODLUCK .

Answer:

-1.5 ≤ r < 9.5

Step-by-step explanation:

All you have to do is just insert the numbers

we use ≤ as it says in the question "no less"

It is given that,

By using parallelogram method,

The graph is as shown below:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:-\dfrac{1}{\sqrt{3-2x}} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

We newd to find the derivative of given function :

[tex]\qquad \tt \rightarrow \: y = \sqrt{3 - 2x} [/tex]

[tex]\qquad \tt \rightarrow \: y = (3 - 2x) {}^{ \frac{1}{2} } [/tex]

[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} (3 - 2x) {}^{ \frac{1}{2} } [/tex]

[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{2} \sdot(3 - 2x) {}^{ - \frac{1}{2} } \sdot( - 2)[/tex]

[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{ \cancel2} \sdot\frac{1}{(3 - 2x) {}^{ \frac{1}{2} } }\sdot( - \cancel2)[/tex]

[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ - 1}{ \sqrt{ (3 - 2x) {}^{ }} }[/tex]

Correct option : B

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The correct explanation for the expression 3.5p(4 − 0.3p) will be;

⇒ 14p - 1.05p²

Option C is true.

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called the Mathematical expression.

Given that;

The mathematical expression is;

⇒ 3.5p(4 − 0.3p)

Now, Solve the expression as;

The mathematical expression is;

⇒ 3.5p(4 − 0.3p)

Hence,

⇒ 3.5p(4 − 0.3p) = 3.5 x 4p - 3.5p x 0.3p

                         = 14p - 1.05p²

Thus, After simplify we get;

⇒ 3.5p(4 − 0.3p) = 14p - 1.05p²

Therefore, The correct explanation for the expression 3.5p(4 − 0.3p) will be;

⇒ 14p - 1.05p²

Option C is true.

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Distributive property is illustrated in Step 2.

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Let x represent the weight of the comic book to be sold

Let y represent the weight of the appraised book to be appraised

There are 15 copies of the comic book the individual wants to sell (S), and 8 copies of a comic book the individual wants appraised (A), with a combined weight of 49.9 oz. It means that

15x + 8y = 49.9 equation 1

If the individual brings 10 copies of the comic book he wants to sell (S), 4 copies to be appraised (A), the combined weight would be 30.2 oz, it means that

10x + 4y = 30.2 equation 2

Multiplying equation 2 by 2, it becomes

20x + 8y = 60.4 equation 3

Subtracting equation 3 from equation 1, it becomes

20x - 15x + 8y - 8y = 60.4 - 49.9

5x = 10.5

x = 10.5/5

x = 2.1

Substituting x = 2.1 into equation 2, it becomes

10(2.1) + 4y = 30.2

21 + 4y = 30.2

4y = 30.2 - 21 = 9.2

y = 9.2/4

y = 2.3

Weight of the comic(S) to be sold = 2.1 oz

The boat that sailed in the direction closest to due north is the both that has lesser angle to the vertical ,which is the boat that that sailed 30 miles west and 22 miles north.

Given data

One boat sails 30 miles west and 22 miles north

Another boat sails 55 miles west and 40 miles north

Say boat A sail 30 miles west and 22 miles north while boat B sails 55 miles west and 40 miles north

Boat A

let the angle boat A made with the vertical be a. This is given as

tan a = 30 / 22

a = arc tan ( 30 / 22 )

a = 53.746 degrees

Boat B

let the angle boat B made with the vertical be b. This is given as

tan b = 55 / 40

b = arc tan ( 55 / 40 )

b = 53.973 degrees

Comparing angle a and angle b shows that angle a is lesser hence boat A is the boat that sailed in the direction closest to the north

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{(2,9), (2,-5),(-6,3), (4, -7)} this pair doesn't represent a function

A mathematical function is a relationship that is established between two sets, through which each element of the first set is assigned a single element of the second set or none at all. The initial set or starting set is also called the domain; the final set or arrival set is called the rank.

Since in this set two elements of the range are associated with the same element of the domain [(2,9) and (2,-5)], we can conclude that it is not a function

Answer: 0

Step-by-step explanation: We have to 2 answers to choose between, 0 and 1. 0.0379 is closer to 0 because if your decimal was more than 0.5 it would round to 1 as its nearest whole number. Hope this helps!

After evaluating, we get

In the given question, we are given two expressions that include numerical in Roots. We have to calculate their values for each.

These are examples of Products. Product is when two numbers or terms are multiplied together.

The first expression is represented by:

=> 3 *√25, Calculating this expression we get

=> 3 * 5

=> 15

The second expression is represented by:

=> √(2 * 50), calculating this expression we get

=> √(100)

=> 10

Hence, after calculating both A. and B. expressions we get values 15, and 10 respectively

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We have the following:

1. Similar By SSS similarity

4/2= 2

7.3.5 = 2

6/3 = 2

2. Similar by AA similarity, same angles, 90°, 70° and 50°

3. Similar by SAS similarity

, same angles and related sides.::

4/2 = 2

6/3 = 2

4. Similar by SAS similarity, same angles and related sides:

12/6 = 2

8/4 = 2

If the ham costs $6.24 per pound, and the cheese costs $4.80 per pound. You spend twice as much on ham as you do on cheese. The amount spent in total is: $187.20.

Let number of ham bought = x + 4

Let number  of cheese bought = x - 3

Price of ham = $6.24

Price of cheese = $4.80

Hence,

Amount spent on ham = (x+4)×6.24

Amount spent on ham =6.24x + 24.96

Amount spent on cheese = (x−3)×4.80

Amount spent on cheese =4.80x−14.40

So,

6.24 x + 24.96 = 2 (4.80 x - 14.40)

6.24x + 24.96 = 9.60 x - 28.80

Combine like terms

24.96 + 28.80 = 9.60 x - 6.24 x

3.36 x = 53.76

Divide both side by 3.36x

x = 53.76/3.36

= 16x

Now let find the total money spent where x is 16

Total amount = 6.24(16) + 24.96+ 4.80(16) - 14.40

Total amount = $187.20

Therefore the amount of $187.20 was spent in total.

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Answer:

  1/36

Step-by-step explanation:

You want the fraction of villains that are both jay walkers and double-parkers, given that 1/9 of jay walkers are double-parkers and 1/4 of villains are jay walkers.

The fraction of villains that both jay walk and double park is 1/9 of 1/4 of all villains.

  1/9 × 1/4 = 1/(9×4) = 1/36

1/36 of all villains are both jay walkers and double parkers.