Find the constant of variation when t varies directly as the square of s, and t = 64 when S = 4.
​

It would take the brave night 20 hours on his horse from one kingdom to another in 2 days.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let us assume that he travelled at 20 mph on the second day.  If he traveled exactly the same amount of time each day and went 300 miles, find how many hours it took the knight to travel from one kingdom to another.

Let t represent the time in hours travelled each day.

Total distance travelled in day one = 10t

Total distance travelled in day one = 20t

Hence:

10t + 20t = 300

t = 10 hours

Total time = 10 + 10 = 20 hours

It would take the brave night 20 hours on his horse from one kingdom to another in 2 days.

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Answer:

True. empty set is the subset of any set

Answer: 5.83

Step-by-step explanation:

[tex]\sqrt{(2-5)^2 + (1-6)^2}=\sqrt{34} \approx 5.83[/tex]

1. The amount of the adjusting entry for Uncollectible Accounts is $1,250.

2. The adjusted balances of Accounts Receivable Allowance for Doubtful Accounts Bad Debt Expense are:

Accounts Receivable = $3,545,000

Allowance for Doubtful = $7,250

Accounts Bad Debt Expense = $1,250

3. The net realizable value of the accounts receivable is $3,537.750 ($3,545,000 - $7,250).

                               Accounts Receivable    Allowance for Doubtful Accounts

Beginning balance     $645,000 DR               $6,000 CR

Sales                          2,900,000

Bad Debt Estimate = $7,250 ($2,900,000 x 0.0025)

Ending balance      $3,545,000                     $7,250 CR

Bad Debts Expense = $1,250 ($7,250 - $6,000)

Thus, the net realizable value of the accounts receivable shows the amount that the company expects to recover from customers after allowing for doubtful accounts.

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1. Determine the amount of the adjusting entry for uncollectible accounts.

2. Determine the adjusted balances of Accounts Receivable, Allowance for Doubtful Accounts, and Bad Debt Expenses.

3. Determine the net realizable value of accounts receivable

The unit rate of each of the brands are:

Brand A's unit rate = 37 cents per ounce.

Brand B's unit rate = 31 cents per ounce.

The unit rate of each brand is simply how much a brand of tomatoes will cost per ounce.

To find the unit rate of each brand, do the following:

Brand A's unit rate = 2.99/8 = $0.37 per ounce = 37 cents per ounce.

Brand B's unit rate = 4.99/16 = $0.31 per ounce = 31 cents per ounce.

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By definition of vectors exist as quantities that contain magnitude (positive or negative) and direction.

A) The unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]

B) The distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.

C) i.) Required vector = −4j − 5k

ii.) Required vector = 5i − 6j − 8k

To estimate the unit vector in the direction of V = 2i+3j+4k

|V| [tex]$= \sqrt{2^2+3^2+4^2}[/tex]

[tex]$= \sqrt{29}[/tex]

A) Unit vector

[tex]$F= \frac{V}{ |V|}[/tex]

[tex]$F= \frac{2i+3j +4k}{2}[/tex]

[tex]$F = \frac{2i}{2} + \frac{3j}{2} +\frac{4k}{2}[/tex]

[tex]$F= i + \frac{3j}{2} +2k.[/tex]

Therefore, unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]

B) To estimate the distance between [tex]F_{1}[/tex] = 3i+2j+ 5k and [tex]F_{2}[/tex] = 3i +4j +5k

[tex]$d = \sqrt{(3-3)^{2}+(4-2)^{2}+(5-5)^{2}}[/tex]

= 2

Therefore, the distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.

C) i.) P, (3,2,2), P₂(3,-2,-3)

Required vector =|[tex]P_{1}[/tex]P₂|=(3−3)i + ((−2)-2)j ​+ ((-3)-2)k

= −4j − 5k

ii.) P₂ (2,-3,-6), [tex]P_{3}[/tex] (-3,3,2) ​

Required vector =|P₂[tex]P_{3}[/tex]|=(-3-2)i + (3-(-3))j ​+ (2-(-6))k

= 5i − 6j − 8k

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Answer:

$21200

Step-by-step explanation:

6% × 20000 = 1200.

20000 + 1200 = 21200

basically yout find 6% of 20000 then add it the original 20000

Answer:

Step-by-step explanation:

Reflecting across the x-axis means (x,y) maps onto (x,-y).

So, A' has coordinates (-2,0), B' has coordinates (-6,-5), and C' has coordinates (-3, -4).

Answer:

8/3

Step-by-step explanation:

8/9

Answer:

x = 73

x = -35

Step-by-step explanation:

Here are the 8 numbers:

34, 31, 15, x, 17, 4, 20, 25

Here are the 8 numbers in ascending order with x as the greatest number:

4, 15, 17, 20, 25, 31, 34, x

x - 4 = 69

x = 73

Here are the 8 numbers in ascending order with x as the smallest number:

x, 4, 15, 17, 20, 25, 31, 34

34 - x = 69

-x = 69 - 34

-x = -35

x = -35

Answer:

x = 73

x = -35

Answer:

Step-by-step explanation:

The confidence interval for the population proportion, p is (0.766, 0.833)

The formula for calculating the confidence interval for proportion is expressed as:

CI = p±√pq/n

Given the following

p = 112/140 = 0.8

q = 1-p = 0.2

Substitute

CI = 0.8±√(0.8)(0.2)/140

CI = 0.8±0.0338

CI = (0.766, 0.833)

Hence the confidence interval for the population proportion, p is (0.766, 0.833)

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Answer:

the answer to the question is 1

Answer:

-26 Is the correct answer

Step-by-step explanation:

The exponential form of 6 × 6, is written as: 6².

Repeated multiplication involving base exponents and base can be written in exponential form, such as: a × a × a = a³.

Given the expression, 6 × 6, the number 6 will be the base while 2 will be the exponent if we want to express it in exponential form. Therefore:

6 × 6 = 6².

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The vertices of the feasible region are as follows,

(-14, -11), (9, -11) and (6, 4)

What is a Feasible Region?

The area of the graph where all constraints are satisfied is the feasible solution zone or feasible region. It might also be thought of as the point where each constraint line's valid regions intersect. Any decision in this region would lead to a workable resolution for our objective function.

Vertices of the Feasible Region

As it can be seen in the graph, the vertices of the feasible region surrounded by the given constraints are:

(-14, -11), (9, -11) and (6, 4)

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Using the normal distribution, we have that:

a) The probability of a student scoring less than 19 is 0.2709 = 27.09%.

b) The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.

c) The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.

d) The correct option is: B. The event in part (c) is unusual because its probability is less than 0.05.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 22.4, \sigma = 5.1[/tex]

Item a:

The probability is the p-value of Z when X = 19, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{19 - 22.4}{5.1}[/tex]

Z = -0.67.

Z = -0.67 has a p-value of 0.2709.

The probability of a student scoring less than 19 is 0.2709 = 27.09%.

Item b:

The probability is the p-value of Z when X = 27.1 subtracted by the p-value of Z when X = 17.7, hence:

X = 27.1:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{27.1 - 22.4}{5.1}[/tex]

Z = 0.92.

Z = 0.92 has a p-value of 0.8212.

X = 17.7:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{17.7 - 22.4}{5.1}[/tex]

Z = -0.92.

Z = -0.92 has a p-value of 0.1788.

0.8212 - 0.1788 = 0.6424.

The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.

Item c:

The probability is one subtracted by the p-value of Z when X = 33.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33.1 - 22.4}{5.1}[/tex]

Z = 2.1.

Z = 2.1 has a p-value of 0.9821.

1 - 0.9821 = 0.0179.

The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.

Item d:

Probabilities less than 0.05 are unusual, hence the correct option is:

B. The event in part (c) is unusual because its probability is less than 0.05.

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The length and width of the fence should be made 76.25 feet and 23.75 feet respectively. Also, the expression for the length is L = 3W + 5 and the perimeter is P = 2(4W + 5).

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Since the length of this fence is 5 more than 3 times the width, we have:

L = 3W + 5

Substituting the given parameters into the formula, we have;

200 = 2(3W + 5 + W)

200 = 2(4W + 5)

200 = 8W + 10

8W = 190

W = 190/8

W = 23.75 feet.

For the length, we have:

L = 3W + 5

L = 3(23.75) + 5

L = 76.25 feet.

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The probability of all three events happening when the dies are rolled is; 0.0083

A) On the first die, it has 6 sides and 3 must come out, that is, 1 event out of 6 possible, therefore the probability is: 1/6

B) On the second die, it has 20 sides and if 19 or 20 can come out, that is 2 events out of 20 possible, so the probability is: 2/20 = 1/10

C) On the third die, which is 12 sides, an odd number can come out. The odd numbers would be 1, 3, 5, 7, 9, 11; i.e, 6 events out of 12 possible numbers.

Thus, the probability would be: 6/12 = 1/2

The final probability would be;

(1/6) * (1/10) * (1/2) = 0.0083

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Answer:

d

Step-by-step explanation:

multiply by 2 then subtract 1

2(25)-1=49

2(49)-1=97

2(97)-1=193

Answer:

1. 60%

2. He paid Rs. 1285.71

Step-by-step explanation:

1.

He buys an item for x.

He sells the item with a 25% of the marked price, and he still makes a 20% profit over his cost x.

He must sell for x + 20% of x which is the same as 1.2x.

Let the markup be y%.

Since he gives a 25% discount over the marked price, he sells for 75% of the marked price.

0.75(x + y% of x) = 1.2x

0.75(x + xy/100) = 1.2x

x + xy/100 = 1.6x

Divide both sides by x.

1 + y/100 = 1.6

Multiply both sides by 100.

100 + y = 160

y = 60

Remember that y is in percent, so the markup must be 60%.

Check:

He buys an item for $10.

He applies a markup of 60%. 1.6 × $10 = $16.

He has a price of $16 for this item.

Now he gives a 25% discount. That means the discounted price is 75% of the marked price.

75% of $16 = $12

He sells at a 25% discount for $12.

Compare the actual selling price after the 25% discount with this cost.

$12 compared to $10.

$12/$10 = 1.2 = 120%

Since he sells for 120% of the original price, the markup is 20% which is what he wanted.

2.

The cost to the seller is x.

If he sells it at a 20% profit, then he sells it for 1.2x

Now he gives a discount of 5%, so the final selling price after discount is

0.95(1.2x)

The profit is the difference between what he sold it for, 0.95(1.2x), and what he bought is for, x, and it is Rs. 180.

0.95(1.2x) - x = 180

1.14x - x = 180

0.14x = 180

x = 1285.71

Answer: He paid Rs. 1285.71

From the given information,

a. The length of the belt is 180.28 ft

b. The height of the window from the ground is 100 ft

c. The length of the ramp needed is 141.42 ft

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²

It is given that,

The height of the silo is 150 feet

The distance from the belt to the silo is 100 feet

With the given measurements, a right-angled triangle is formed.

a. Finding the length of the belt:

From the diagram,

The height of the silo, sh = 150 ft

The base distance, sb = 100 ft

So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.

On applying the Pythagorean theorem,

bh² = sb² + sh²

⇒ bh² = (100)² + (150)²

⇒ bh² = 32500

⇒ bh = √32500 = 50√13

∴ bh = 180.28 ft

Thus, the length of the belt is 180.28 ft.

b. Finding the height of the window from the ground:

It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.

This creates a special right-angled triangle. I.e.,

The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)

So, the new triangle has angles of 90°- 45°- 45°

Thus, the new triangle is said to be an isosceles right angled triangle.

So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft

Therefore, the height of the window from the ground(sw) is 100 ft

c. Finding the length of the ramp(bw) to the window:

Since we have

sw = 100 ft and sb = 100 ft

On applying Pythagora's theorem,

bw² = sb² + sw²

⇒ bw² = (100)² + (100)²

⇒ bw = √20000 = 141.42 ft

Therefore, the length of the ramp to the window is 141.42 ft.

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The probability of selecting from the platter a chocolate cupcake and then a yellow cupcake is  0.10.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of selecting a chocolate cupcake and then a yellow cupcake = (number of chocolate cupcake / total number of cupcakes) x (number of yellow cupcakes / total number of cupcakes - 1)

(13 / 38) x (11 / 37) = 0.10

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The number makes the expression a perfect square trinomial is 25.

Hence, we have v² - 10v + 25.

Given the expression; v² - 10v

To determine the number that makes the expression a perfect square trinomial, we divide the coefficient of v by 2 and square the result.

( -1 × 10/2 )²

(-1 × 5)²

( -5 )²

25

We add 25 to the expression to get a perfect square trinomial.

v² - 10v + 25.

Therefore, the number makes the expression a perfect square trinomial is 25.

Hence, we have v² - 10v + 25.

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Answer:

35 and 7

Step-by-step explanation:

5x + 1x =42

6x=42

x=7

Answer:

Greater number: 35

Smaller number: 7

Step-by-step explanation:

1) Set up system of equations.

Let x = greater number

Let y = smaller number

----------------------------------------------

x + y = 42

x = 5y

2) Solve them using elimination or substitution.

x + y = 42

x - 5y = 0

----------------

6y = 42

y = 42/6

y = 7

3) Substitute the found answer into one of the two equations to find the value of x.

x = 5(7)

x = 35

Therefore, the greater number is 35, and the smaller number is 7.

The equivalent to the quotient shown in the task content for acceptable values of x is; √(5/(x-1)).

It follows from the task content that the expression given is; √(25(x-1)) ÷ √(5(x-1)²).

It therefore follows from the the laws of indices that the evaluation is thus;

= √{(25/5) ×(x-1)/(x-1)²}.

Ultimately, upon evaluation we have;

= √(5/(x-1))

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Answer:

about 19.31 years

Step-by-step explanation:

[tex]10000( {1.11}^{x} ) = 75000[/tex]

[tex] {1.11}^{x} = 7.5[/tex]

[tex]x ln(1.11) = ln(7.5) [/tex]

[tex]x = \frac{ ln(7.5) }{ ln(1.11) } = 19.31[/tex]

The number of board game sorted is 14

The games have been sorted into video games and board games.

The number of video games is 28 less than 6 times the number of board games.

Therefore,

the number of board games = x

number of video game = 6x - 28

The games are 80% video games. Hence,

80 / 100 × x + 6x - 28 = 6x - 28

4 / 5 × 7x - 28 = 6x - 28

4 / 5 (7x - 28) = 6x -28

28 / 5 x - 112 / 5  = 6x - 28

28 / 5 x  - 6x = -28 + 112 / 5

28x - 30x / 5 =  - 28 + 112 / 5

-2x / 5  = -28 / 5

-10x = -140

x = 14

Therefore, the number of board game sorted is 14.

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Answer:

14

Step-by-step explanation:

80 / 100 × x + 6x - 28 = 6x - 28

4 / 5 × 7x - 28 = 6x - 28

4 / 5 (7x - 28) = 6x -28

28 / 5 x - 112 / 5  = 6x - 28

28 / 5 x  - 6x = -28 + 112 / 5

28x - 30x / 5 =  - 28 + 112 / 5

-2x / 5  = -28 / 5

-10x = -140

x = 14

Answer: 57.59- 56.3=1.29

Step-by-step explanation:

57.59-x = 1.29

-x= 1.29-57.59

(—) -x= - 56.3

x=56.3