A ship is tied to a dock with a rope
length 10 m. At low tide, the rope is
stretched tight, forming an angle of 45⁰ with the horizontal. At high tide, the stretched rope makes an angle of 30° with the horizontal. How much closer to the dock, horizontally, is the ship at low tide than at high tide?

Answer:

$0.50 per ounce

Step-by-step explanation:

To find the cost per ounce of the chocolate, you will need to divide the price of the box by the weight of the box in ounces. Since there are 16 ounces in a pound, the weight of the box in ounces is 1 * 16 = <<1*16=16>>16 ounces.

To find the cost per ounce, divide the price of the box by the weight of the box in ounces: $8.00 / 16 ounces = $0.50 per ounce.

Therefore, the cost per ounce of the chocolate is $0.50.

The resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.

In the set-builder form, a short, statement, or formula is written inside a pair of curly braces, as opposed to the roster form, where the listed items are enclosed in a pair of curly braces and separated by commas.

Roster or tabular form: In roster form, all of the components of a set are listed, with commas used to divide them and braces used to enclose them.

For instance, Z = the set of all integers = {…,−3,−2,−1,0,1,2,3,…}.

So, we have:

B = {x:x is an integer and -4 < x < 6}

B has numbers from -4 and 6.

Now, write B in roster form as:

B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}

Therefore, the resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.

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Complete question:

Write the following sets in roster form:

B = {x:x is an integer and -4 < x < 6}

Based on the fact that Hannah's investment will triple in 10 years and 10 months when compounding occurs every six months.

The process through which interest is added to the existing principal sum and the interest that has previously been paid is known as compounding.

As a result, compounding, sometimes known as the "magic of compounding," can be thought of as interest on interest, which has the effect of making returns on interest larger over time.

The amount of time required to triple the investment is as follows:

$2500 was invested.

3.4% interest rate.

Compounding: Every 6 months (Semiannually)

Now think about a time frame of two years:

3.4 * 6/12 = 1.7%

The effective interest rate will be 1.7%.

The current value of the 1.7% compounded rate over 65 factors is equivalent to 2.9913.

The value will therefore be $2,500 2.9913 = 7,478.25.

Six years divided by 65 months yields a total of 10.833 years.

10 months make up a year, or 0.833 * 12.

Therefore, based on the fact that Hannah's investment will triple in 10 years and 10 months when compounding occurs every six months.

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Answer:

Step-by-step explanation:

You want the number of tickets of each kind sold if 169 tickets were sold for $1795, and lower box tickets were $12.50 while upper box tickets were $10.

Let x represent the number of lower box tickets sold. Then 169 -x is the number of upper box tickets sold. The total revenue is ...

  12.50(x) + 10.00(169 -x) = 1795.00

Simplifying, we get

  2.50x +1690 = 1795

  2.5x = 105 . . . . . . . . . . . subtract 1690

  x = 42 . . . . . . . . . . . . divide by 2.5; the number of lower box ticket sold

  169 -42 = 127 . . . . . . the number of upper box tickets sold

42 lower box and 127 upper box tickets were purchased.

The expression given as 89 ∛9 cannot be further simplified

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

89 ∛9

The above expression is a radical expression

And the radicand is ∛9

The radicand ∛9 implies that the cube root of 9

The cube root of  9 is a decimal number

So, it is better to leave the expression without changing its form

Hence. 89 ∛9 cannot be further simplified

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The standard quadratic equation is (c) y = x² + 5x - 66

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

Zeros  -11 and 6

This means that

x = -11 and x = 6

The quadratic equation can then be calculated as

y = (x - 6) * (x + 11)

Evaluate the products

y = x² - 6x + 11x - 66

Evaluae the like terms

y = x² + 5x - 66

Hence, the equation is y = x² + 5x - 66

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Answer:  the cost is $35.51, That must mean it would be driven 33.0 miles.

Step-by-step explanation: The given function c(r) represents the cost of a one-day truck rental when the truck is driven x miles. This means that the cost in dollars is a linear function of the number of miles driven.

To answer the first part of the question, we can plug in x = 80 into the function to find the truck rental cost when we drive 80 miles:

$$c(r) = 0.47x + 20 = 0.47(80) + 20 = \boxed{35.6}$$

To answer the second part of the question, we can solve the equation $c(r) = 0.47x + 20 = 35.51$ for x to find the number of miles driven when the cost is $35.51:

$$35.51 = 0.47x + 20 \Rightarrow 15.51 = 0.47x \Rightarrow x = \boxed{33.0}$$

Therefore, when the cost is $35.51, we must have driven 33.0 miles.

She earned 0.91 pounds for every $1 US dollar when a visitor traded $1,000 US dollars for 910 British pounds.

A proportion is an equation that sets two ratios equal to each other. For example, if there is one guy and three girls, the ratio may be written as 1: 3. (for every one boy there are 3 girls) One-quarter are males and three-quarters are girls. 0.25 are males (by dividing 1 by 4). According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.

Here,

For 910 pounds, she spent $1000 US dollars.

For $1,

=910/1000 pound

=0.91 pounds

For each $1 US dollar, she received 0.91 pounds as tourist exchanged $1,000 US dollars for 910 British pounds.

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Answer:

Below

Step-by-step explanation:

log x = 2 log 6 + log 3    using properties of logs, this becomes

log x = log 6^2 + log 3

       = log (6^2 * 3 ) = log (108)

x = 108

Answer: 6.

Step-by-step explanation: We can solve this problem by using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

In this case, n is the number of choices (the digits 2, 3, 4, 5, 6, and 9) and r is the number of items in each combination (4 digits).

Plugging in the values, we get:

C(6, 4) = 6! / (4! * 2!) = (6 * 5 * 4 * 3) / (4 * 3 * 2) = 30

Therefore, there are 30 four-digit odd numbers that can be formed using the digits 2, 3, 4, 5, 6, and 9. However, not all of these numbers will be less than 5000, so we need to further filter the list to only include those that meet this requirement.

The four-digit odd numbers that can be formed using these digits are:

2359, 2395, 2539, 2593, 2935, 2953, 3259, 3295, 3529, 3592,

3925, 3952, 5239, 5293, 5329, 5392, 5923, 5932, 9235, 9253,

9352, 9523, 9532

Out of these numbers, only 2359, 2539, 2935, 3925, 5239, and 9523 are less than 5000. Therefore, there are 6 four-digit odd numbers less than 5000 that can be formed using the digits 2, 3, 4, 5, 6, and 9.

Therefore, the final answer is 6.

Application acceptance requires a minimum score of 392, which is required.

Make "x" the required minimum score.

Given:

The average score is 500.

Standard deviation () is equal to 100

Admission percentage, P > 86 percent, or 0.86

Thus, the area under the normal distribution curve to the right of the z-score, which is 86%, is provided.

The portion of the score left over is displayed in the z-score table. As a result, we will calculate the z-score value for area as 100 - 86 = 14% or 0.14.

The z-score is therefore equal to -1.08 for value of 0.1401.

P(x>x0) = P(z > -1.08)

= -1.08 = x0 - 500 /100

x0 - 500 = -1.08 × 100

x0 = -1.08 + 500 = 392.

As a result, 392 is the minimal score needed for admission.

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The unit rate or the number of miles run in one hour is 12 miles thus, 4 miles in 1/3 hour will be the faster.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

4 miles in 1/3 hour ⇒ 4 x3/1 = 21 miles/hour

1.3 miles in 4 hours ⇒ 1.4/4 mile/hour

1/2 mile in hours ⇒ 0.5 miles/hour

Hence "The unit rate or the number of miles run in one hour is 12 miles thus, 4 miles in 1/3 hour will be the faster".

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Answer:

Step-by-step explanation:

Using the laws of sines and cosines, answers to the questions are as follows,

1. A=52°, b=120, c = 160,  

SAS property,  a=128

2. a=13.7, A=25.43°, B=78°,

AAS property, b=31.21

3. A=38°, B=63°, c=15,

ASA property, b=14

4. a=1.5, b=2.3, c=1.9,

SSS property, B=84

5. b=795.1, c=775.6, B=51.85°,

SAS property, C=50

6. b=40, c=45, A=51°,

SAS property, a=37

8. a=20, b=12, c=28

SAS property, C=120

9. a=125, A=25°, b=150

SAS property, 2 solutions are there, B1=149, B2=30.4

10. b=15.2, A=12.5°, C=57.5°

SAS property, c=14

What are the laws of sine and cosine?

We can determine a triangle's one side's length or one of its angles' measurements using the laws of sine and cosine.
In most cases, the unknown sides or angles of an oblique triangle are calculated using the law of sines formula.
The equation that connects the lengths of the triangle's sides and the cosines of its angles is known as the law of cosine or cosine rule.

1. Given A=52°, b=120, c = 160.

If we construct the triangle, we see that it is satisfying the SAS property

By using the law of cosine we get,

[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{120^{2}+160^{2}-2.120.160.\cos 52}\\a=127.9[/tex]

2. Given, a=13.7, A=25.43°, B=78°

From angle A, angle B, and side a, we calculate side b, by using the Law of Sines,

[tex]\frac{b}{a}=\frac{\sin B}{\sin A}\\b=a.\frac{\sin B}{\sin A}\\b=13.7. \frac{\sin 78}{\sin 25.43}\\b=31.21[/tex]

3. A=38°, B=63°, c=15

From angle A and angle B, we calculate angle C,

[tex]A+B+C=180\\C=180-A-B\\C=180-38-63\\C=79[/tex]

Next, From angle A, angle C, and side c, we calculate side a, by using the Law of Sines

[tex]\frac{a}{c}=\frac{\sin A}{\sin C}\\a=c.\frac{\sin A}{\sin C}\\a=15. \frac{\sin 38}{\sin 79}\\a=9.41[/tex]

Calculation of the third side b of the triangle using a Law of Cosines,

[tex]b^{2}=a^{2} +c^{2}-2.a.c.\cos B\\b=\sqrt{a^{2}+c^{2}-2.a.c.\cos B}\\b=\sqrt{9.1^{2}+15^{2}-2.9.41.15.\cos 63}\\b=13.68[/tex]

4. a=1.5, b=2.3, c=1.9

Calculation of the inner angles of the triangle using a Law of Cosines

[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{1.5^{2}+1.9^{2}-2.3^{2} }{2 . 1.5.1.9}\\B=84.15[/tex]

5. b=795.1, c=775.6, B=51.85°

From angle B, side c, and side b, we calculate side a. by using the Law of Cosines and quadratic equation:

[tex]b^2 = c^2 + a^2 - 2.c. a. {\cos B} \\ 795.1^2 = 775.6^2+a^2-2. 775.6. a . \cos 51\ \\ a > 0 \\ a = 989.175[/tex]

Calculation of angle C of the triangle using a Law of Cosines

[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{989.175^{2}+795.1^{2}-775.6^{2} }{2 . 989.795}\\C=50.5[/tex]

6. b=40, c=45, A=51°

Calculation of the third side a of the triangle using a Law of Cosines

[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{40^{2}+45^{2}-2.0.45.\cos 51}\\a=36.87[/tex]

8. a=20, b=12, c=28

Calculation of angle C of the triangle using a Law of Cosines

[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{20^{2}+12^{2}-28^{2} }{2 . 20.12}\\C=120[/tex]

9.  a=125, A=25°, b=150

2 solutions are possible for this,

solution for B1:

From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:

[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 28.21[/tex]

Calculation of angle B of the triangle using a Law of Cosines

[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+28.21^{2}-150^{2} }{2 . 125.28}\\B=149[/tex]

solution for B2:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:

[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 243.679[/tex]

Calculation of angle B of the triangle using a Law of Cosines

[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+243^{2}-150^{2} }{2 . 125.243}\\B=30.28[/tex]

10.  b=15.2, A=12.5°, C=57.5°

From angle A and angle C, we calculate angle B:

[tex]A+B+C=180\\B=180-A-C\\B=180-12.5-57.5\\B=110[/tex]

From the angle A, angle B, and side b, we calculate side a, by using the Law of Sines.

[tex]\ \\ \dfrac{ a }{ b } = \dfrac{ \sin A }{ \sin B } \\ a = b \cdot \ \dfrac{ \sin A }{ \sin B } \\ a = 15.2 \cdot \ \dfrac{ \sin 12.30 }{ \sin 110\degree } = 3.5[/tex]

Calculation of the third side c of the triangle using a Law of Cosines

[tex]c^{2}=a^{2} +b^{2}-2.a.b.\cos C\\c=\sqrt{a^{2}+b^{2}-2.a.b.\cos C}\\c=\sqrt{15.2^{2}+3.5^{2}-2.15.4.\cos 57.30}\\c=13.64[/tex]

Therefore, we have found the solutions of all of the above bits using the law of sine and cosine.

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Answer:

91

Step-by-step explanation:

[tex]\frac{89+82+69+79+70+x}{6}[/tex] = 80  Combine like terms

[tex]\frac{389+ x}{6}[/tex] = 80  Multiple by sides by 6

380 + x = 480  Subtract 389 from both sides.

x = 91

Step-by-step explanation:

If M is the midpoint of AB then,

AM = BB so we can write the following equation:

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

Now on to the length of BM, we can replace x with 4 to find it.

3*4 + 17 = 29

The plane is perpendicular to the axis but does not go through the vertex. The plane intersects the double cone at only the vertex is ellipse.

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Answer:

D, I've taken the test already!

Step-by-step explanation:

there

Answer:

A

Step-by-step explanation:

A box plot shows the five-number summary of a set of data.

Five-number summary:

Therefore, from inspection of the given box plot:

The median of a set of data is the middle value when all data values are placed in order of size.

Therefore, the only answer option that has a maximum value of 34 and a median of 31 is answer option A.

A) The break-even sales level in shillings XYZ Company needs to achieve is Shs.1,096,443.

B) The break-even sales level in units XYZ Company needs to achieve is 27,444 units to make a profit of Shs.195,000.

The break-even point is the sales level when total revenue equals total costs (fixed and variable).

At the break-even point, there is no profit or loss.

Selling price per unit = Shs.66

Variable production cost per unit  = Shs.44

Variable selling cost per unit = Shs.4

Total variable cost per unit = Shs.48 (Shs.44 + Shs.4)'

Contribution margin per unit = Shs.18 (Shs.66 - Shs.48)

Contribution margin ratio = 27.27% (Shs.18/Shs.66 x 100)

Fixed production cost (total)  = Shs.200,000

Fixed selling and administrative cost (total) Shs.99,000

Total fixed costs = Shs. 299,000 (Shs.200,000 + Shs.99,000)

Target profit = Shs.195,000

a) Break-even sales in shillings = Fixed costs/Contribution margin ratio

= Shs.1,096,443 (Shs.299,000/27.27%)

b) Break-even sales in units to achieve target profit = (Fixed costs + Target profit)/Contribution margin per unit

= (Shs.299,000 + Shs.195,000/Shs.18)

= Shs.494,000/Shs.18

= 27,444 units

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XYZ Company manufactures a product called "PERMA". Pertinent cost and revenue data relating to the manufacture of this product are given below:

Selling price per unit = Shs.66

Variable production cost per unit  = Shs.44

Variable selling cost per unit = Shs.4

Fixed production cost (total)  = Shs.200,000

Fixed selling and administrative cost (total) Shs.99,000

Required:

a) Calculate the break-even sales level in shillings;

b) Suppose the company desires to make a profit of shs.195,000, what should be the output in units?

The solutions to the equations using function machine are x = 7, x = 5, b = 10, b = 5, n = 7, w = -4, k = 8 and h = 3

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

Using a function machine, we have:

Equation (a)

3x + 4=25

This becomes

x  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

x  ⇒ [ 21 ] ⇒ [ +4 ]  = [ 25 ]

This means that

x = 21/3

x = 7

Equation (b)

3x - 4 = 11

This becomes

x  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

x  ⇒ [ 15 ] ⇒ [ -4 ]  = [ 11 ]

This means that

x = 15/3

x = 5

Equation (c)

4b - 10 = 30

This becomes

b  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

b  ⇒ [ 40 ] ⇒ [ -10 ]  = [30]

This means that

b = 40/4

b = 10

Equation (d)

4b + 10 = 30

This becomes

b  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

b  ⇒ [ 20 ] ⇒ [ +10 ]  = [30]

This means that

b = 20/4

b = 5

Equation (e)

5n + 2 = 37

This becomes

n  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

n  ⇒ [ 35 ] ⇒ [ +2 ]  = [37]

This means that

n = 35/5

n = 7

Equation (f)

2w + 10 = 2

This becomes

w  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

w  ⇒ [ -8 ] ⇒ [ +10 ]  = [2]

This means that

w = -8/2

w = -4

Equation (g)

3k + 4 = 28

This becomes

k  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

k  ⇒ [ 24 ] ⇒ [ +4 ]  = [28]

This means that

k = 24/3

k = 8

Equation (h)

6h - 7 = 11

This becomes

h  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

h  ⇒ [ 18 ] ⇒ [ -7 ]  = [11]

This means that

h = 18/6

h = 3

Hence, the value of h is 3

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The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)

From the question, we have the table of values as the parameters that can be used in our computation:

From the table, we have

Table 1

(x, y) = (0, -3) and (4, 13)

A linear equation is represented as

y = mx + c

Where

Slope = m

c = y when x = 0

This means that

c = -3

So, we have

y = mx - 3

The point (4, 13) implies that

13 = m * 4 - 3

So, we have

4m = 16

m = 4

So, the equation is

y = 4x - 3

Table 2

(x, y) = (0, 4) and (4, 6)

A linear equation is represented as

y = mx + c

This means that

c = 4

So, we have

y = mx + 4

The point (4, 6) implies that

6 = m * 4 + 4

So, we have

4m = -2

m = -1/3

So, the equation is

y = -1/3x + 4

Substitute y = -1/3x + 4 in y = 4x - 3

-1/3x + 4 = 4x - 3

So, we have

-x + 12 = 12x - 9

Evaluate the like terms

13x = 21

Divide

x = 21/13

y = -1/3x + 4 implies that

y = -1/3 x 21/13 + 4

So, we have

y = -7/13 + 4

Evaluate

y = 45/13

So, the solution is (21/13, 45/13)

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Answer: 19/36

Step-by-step explanation:

First the LCM (Least Common Denominater) must be found, the LCM of 9 and 4 is 36

Since 9 x 4 is 36, the numerator and denominator of 7/9 will be multiplied by 4 making it 28/36

Since 4 x 9 equals 36, the numerator and denominator of 1/4 will be multiplied by 4 making it 9/36

Now that they have common denominators the numerators can be subtracted from each other as well as the denominators

28/36 - 9/36 = 19/36

19/36 cannot be simplified therefore 7/9 - 1/4 = 19/36

Answer: 475 minutes.

Step-by-step explanation: To compare the cost of these two plans, you need to find how many minutes of calls are needed for the cost of each plan to be the same. Let's call this number of minutes x.

For plan A, the total cost will be $19 plus $0.11 for each minute of calls, or a total of 19 + 0.11x dollars.

For plan B, the total cost will be $0.15 for each minute of calls, or a total of 0.15x dollars.

Since the cost of the two plans is equal, we can set these expressions equal to each other and solve for x:

19 + 0.11x = 0.15x

Subtracting 0.11x from both sides, we get:

19 = 0.04x

Dividing both sides by 0.04, we get:

475 = x

Therefore, the number of minutes of calls needed for the cost of the two plans to be the same is 475 minutes.

The remainder you got when 3x³ - 5x² - 23x + 24 is divided by x - 3 is -9.

Polynomials are expressions in algebra which consist of both variables and coefficients. Sometimes, variables are also known as indeterminates. Polynomials are classified as monomials, binomials, and trinomials based on the degree of the variables in the expression.

Variables in the monomials, binomials and trinomials have the highest degree equals 1, 2 and 3 respectively.

By doing the long division method, we will bet the quotient as 3x² + 4x - 11 and the remainder equals -9.

Let's check this using division algorithm.

Dividend = 3x³ - 5x² - 23x + 24

Divisor = x - 3

Quotient = 3x² + 4x - 11

Remainder = -9

By division algorithm,

Dividend = (Divisor × Quotient) + Remainder

3x³ - 5x² - 23x + 24  = [(x - 3) (3x² + 4x - 11)] + -9

                                 = [3x³ + 4x² - 11x - 9x² - 12x + 33] + -9

                                 = 3x³ + 4x² - 9x² - 11x - 12x + 33 - 9

                                 = 3x³ - 5x² - 23x + 24

Hence -9 is the remainder of this division process.

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