In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?

Answer:  [tex]-3\sqrt{5}[/tex]

-3 times the square root of 5

=============================================

Explanation:

Let [tex]x = \sqrt{5}[/tex]

Replace all the root 5 terms with x and we go from

[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5}[/tex]

to

[tex]3x-8x+2x[/tex]

From here, combine like terms to get

[tex]3x-8x+2x = -5x+2x = -3x[/tex]

and the last thing to do is replace the x with sqrt(5)

[tex]-3x = -3\sqrt{5}[/tex]

Meaning that,

[tex]3x-8x+2x = -3x[/tex]

[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5} = -3\sqrt{5}[/tex]

Answer: Yes the sum of any two numbers is greater than the larger of the two numbers.

Step-by-step explanation:

Yes the sum of any two numbers is greater than the larger of the two numbers.

Let us assume that the two numbers are a and b and ab is the number.

a + b > a

b > a – a

b > 0

This therefore implies that b > 0.

This may however not be true when the value of b is zero(0) or a negative number.

Answer:

a. 3.5 inches by 4.5 inches

b. 1.5 inches

c. Divide 48 inches by 2 and multiply 1 inch by 12 to get a scale of 1 : 2

Step-by-step explanation:

A scale is a representative fraction showing the relationship between length on a drawing and actual length.

i.e scale = [tex]\frac{length on a drawing}{actual length}[/tex]

 scale = 1 inch : 4 feet

a. The dimensions in the drawing can be determined as;

1 inch : 4 feet implies an inch on the drawing equates 4 feet on actual length.

[tex]\frac{14}{4}[/tex] = 3.5 inches

[tex]\frac{18}{4}[/tex] = 4.5 inches

Dimensions on drawing is 3.5 inches by 4.5 inches.

b. The length of the sofa is 6 feet, its length on the drawing is;

[tex]\frac{6}{4}[/tex] = 1.5 inches

c. To enlarge the scale so as to double the dimensions of the drawing, we have;

12 inches = 1 feet

4 feet = 4 × 12 = 48 inches

given scale = 1 inch : 48 inches

Thus, divide 48 inches by 2 and multiply 1 inch by 12.

scale = 12 inch : 24 inch

scale = 1 : 2

To double the dimensions of the drawing, the scale required is 1 : 2. This implies that a unit measure on the drawing is synonymous to 2 measures on the actual reading.

Answer:

The balloon contains 456.3 kg of helium

Step-by-step explanation:

Density=mass / volume

Volume=2600 cubic meters of helium

Density=0.1755 kilograms per cubic meters

Mass=x

Find mass, x

Density=mass / volume

Mass=Density × volume

=0.1755 * 2600

=456.3 kg

The balloon contains 456.3 kg of helium

Explanation : As you can see, [tex]\sqrt{-16}[/tex] is not a real number, and hence should be expressed as 4[tex]i[/tex], [tex]i[/tex] being an imaginary number. Respectively [tex]\sqrt{-64}[/tex] will be 8[tex]i[/tex]. Therefore this expression boils down to [tex]\left(3+4i\right)\left(6-8i\right)[/tex]. All we have to do from now on is expand this expression.

Apply the rule [tex]\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i[/tex], in this case where [tex]a=3,\:b=4,\:c=6,\:d=-8[/tex],

[tex]\left(3\cdot \:6-4\left(-8\right)\right)+\left(3\left(-8\right)+4\cdot \:6\right)i[/tex]

Let's simplify each part, [tex]3\cdot \:6-4\left(-8\right)[/tex] and [tex]3\left(-8\right)+4\cdot \:6[/tex]. Afterwards we can add [tex]i[/tex], and refine.

[tex]3\cdot \:6-4\left(-8\right) = 50[/tex] ; [tex]3\left(-8\right)+4\cdot \:6 = 0[/tex]

Therefore our simplified expression will be [tex]50+0i[/tex], otherwise known as just 50. That is our solution.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

sin(180°-∅)=sin∅ as its in the 2nd quadrant

then tan(180°-∅)= -tan∅ as its in the 2nd quadrant and there only sin and cosec is positive and at last cos(180°-∅) = -cos∅ for the same reason

so by putting the values:

sin∅/sin∅ + -tan∅/tan∅ + -cos∅/cos∅ =1-1-1= -1

thanks ..

Answer:

7:15 am

Step-by-step explanation:

1. Add the times together by finding a common denominator

3/4 = 9/12

1/6 = 2/12

1/12 = 1/12

1/4 = 3/12

9/12 + 2/12 + 1/12 + 3/12 = 15/12

It took him 15/12 of an hour in total.

2. Convert to hours

15/12 = 1 3/12

3/12 = 1/4

1/4 of an hour is 15 minutes.

I took him a total of 1 hour and 15 minutes.

3. Subtract 1 hour and 15 minutes from 8:30

8:30 - 1:15 = 7:15

Answer:

The probability that 100 or fewer will have 3 ​girls is 0.00734.

Step-by-step explanation:

The complete question is:

In a family with ​3 children, the probability that all the children are girls is approximately 0.125. In a random sample of 1000 families with ​3 children, what is the approximate probability that 100 or fewer will have 3 ​girls? Approximate a binomial distribution with a normal distribution.

Solution:

Let X represent the number of families who has 3 girls.

The random variable X follows a Binomial distribution with parameters n = 1000 and p = 0.125.

But the sample selected is too large.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

 [tex]np=1000\times 0.125=125>10\\\\n(1-p)=1000\times (1-0.125)=875>10[/tex]

Thus, a Normal approximation to binomial can be applied.

So,  [tex]X\sim N(\mu=np,\sigma^{2}=np(1-p))[/tex]

The mean and standard deviation are:

[tex]\mu=np=1000\times 0.125=125\\\\\sigma=\sqrt{np(1-p)}=\sqrt{1000\times 0.125\times (1-0.125)}=10.46[/tex]

Compute the probability that 100 or fewer will have 3 ​girls as follows:

Apply Continuity correction:

[tex]P(X\leq 100)=P(X<100-0.50)[/tex]

                  [tex]=P(X<99.50)\\\\=P(\frac{X-\mu}{\sigma}<\frac{99.5-125}{10.46})\\\\=P(Z<-2.44)\\\\=0.00734[/tex]

*Use a z-table.

Thus, the probability that 100 or fewer will have 3 ​girls is 0.00734.

Answer:

8.5

Step-by-step explanation:

Applying pythagora's theorem,

hypotenuse^2 = opposite^2 + adjacent^2

but, hypotenuse = 9

opposite = X

adjacent = 1/2(base of triangle)= 1/2(6)

adjacent = 3

9^2 = X^2 + 3^2

X^2 = 81 - 9

X^2 = 72

X = 8.5

Answer:

I would say about 5 times but I am not sure so if it is wrong am sorry.

Answer:

Step-by-step explanation:

4x^5 + 7x^3

x^3(4x^2 + 7)

The GCF is x^3

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.

The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:

[tex]3x + 3x + (6x + 45) + (6x+45) = 360[/tex]

Combine like terms so we can get a simpler equation:

[tex]6x + 12x + 90 = 360\\18x + 90 = 360[/tex]

Now let's solve for x!

[tex]18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15[/tex]

So [tex]x = 15[/tex].

Hope this helped!

Answer:

15

Step-by-step explanation:

3x + 6x + 45 = 180

9x = 135

x = 15

Answer:

a = 0, i, -i, 1, -1

Step-by-step explanation:

What we're basically looking for here is a number, that when multiplied by itself any amount of times, will get us with the same number.

We know that 0 times and number will be 0, so 0 works.

1 times any number will be 1, and -1 would also work as -1² = 1.

i would also work as it represents the square root of a negative, and -i would also work.

Hope this helped!

Answer:

The height of the lighthouse is approximately 166.6 feet.

Step-by-step explanation:

Let the height of the lighthouse be represented by s, then;

Tan 48° = (opposite) ÷ (adjacent)

Tan 48° = s ÷ 150

⇒ s = 150 × Tan 48°

      = 150 × 1.1106

     = 166.59

s ≅ 166.6 feet

Therefore, the height of the lighthouse is approximately 166.6 feet.

Answer:

The height of the lighthouse is approximately 42.

Step-by-step explanation:

This situation forms a right triangle so the angles would be 90 and 48

90+48+x=180

138+x=180

x=180-138

x=42

Answer:

Height= 4.5 Volume= 91.125

Step-by-step explanation:

Answer:

Total number of matches need to win = 15

Step-by-step explanation:

Given:

Total number of race completed = 45

Total races win = 30

Success rate = 75% = 0.75

Find:

Total number of matches need to win

Computation:

Assume, extra number of matches = y

Extra number of win matches = x

So,

(30 + x) / (45 + y) = 0.75

Assume y = x

So,

(30 + x) / (45 + x) = 0.75

30 + x = 33.75 + 0.75 x

x = 15

Total number of matches need to win = 15

Answer:

48°

Step-by-step explanation:

arc BC = 136(2) -145 = 127

arc DC = 83(2) - 127 = 39

arc AD = 360 - 145- 127 - 39 = 48

Answer:

49 degrees

Step-by-step explanation:

Measure of arc ABC = 116*2 = 232 degrees.

Measure of arc BC = 232-145 = 87 degrees.

Measure of arc BCD = 83*2 = 166 degrees.

Measure of arc DC = 166-87 = 79 degrees.

Measure of arc AD = 360 - (145+87+79) = 360 - 311 = 49 degrees

Answer:

[tex]C. \left[\begin{array}{c}370\\228.5\\332\end{array}\right][/tex]

Step-by-step explanation:

Given the table of values for number of servings:

[tex]\begin{center}\begin{tabular}{ c c c c} & Small & Medium & Large\\ Cappuccino & 70 & 55 & 62 \\ Mocha & 42 & 34 & 39 \\ Latte & 59 & 63 & 47 \\ \end{tabular}\end{center}[/tex]

Cost of each coffee for a particular serving is same.

Cost of small serving = $1.50

Cost of medium serving = $2

Cost of large serving = $2.50

To find:

Matrix of revenue generated from sales of each coffee.

Solution:

Revenue generated by a particular coffee = Sum of (cost of each serving multiplied by number of particular servings)

So, revenue by Cappuccino = [tex]70 \times 1.5 +55 \times 2 + 62 \times 2.5 = \bold{\$370}[/tex]

So, revenue by Mocha = [tex]42\times 1.5 +34 \times 2 + 39 \times 2.5 = \bold{\$228.5}[/tex]

So, revenue by Latte = [tex]59\times 1.5 +63\times 2 + 47 \times 2.5 = \bold{\$332}[/tex]

So, the correct answer is:

[tex]C. \left[\begin{array}{c}370\\228.5\\332\end{array}\right][/tex]

Answer:

B. 255 m

Step-by-step explanation:

use similar triangle

L / 60 = 85 / 20

L = (85 * 60) / 20

L = 255 m

The distance across the lake will be 255 meters. Then the correct option is B.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the two triangles are similar, the ratio of the corresponding sides will be constant.

In an isosceles triangle, two angles and their opposite sides are equal.

The dimensions of the first triangle are L, 85, and y. And the dimensions of the second triangle are 60, 20, and x.

It is given that the triangles are similar.

Then the ratio of their corresponding sides will be

L / 60 = 85 / 20 = x / y

From first two terms, then the equation will be

L / 60 = 85 / 20

L / 60 = 4.25

       L = 4.25 x 60

       L = 255 m

The distance across the lake will be 255 meters.

Then the correct option is B.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ5

Answer:

Explained below.

Step-by-step explanation:

The question is:

Please answer me these questions or one: v please. My math class room is 700 m2, how much is 1/4 of the room? How long is 3/4 of the room? . How many minutes is 3/5 of a half hour? . It takes 4/7 of a liter of paint to paint a square meter of wall, if we want to paint 2/5 of a square meter of wall, how much paint will we need? . If it takes 2/5 of an orange to make a glass of orange juice, how many oranges do you need to make 2 and a half glasses?

(1)

Compute 1/4th of the math class room as follows:

[tex]=700\times\frac{1}{4}\\=175[/tex]

Thus, 1/4th of the math class room is 175 m².

(2)

Compute 3/4th of the math class room as follows:

[tex]=700\times\frac{3}{4}\\=525[/tex]

Thus, 3/4th of the math class room is 525 m².

(3)

Compute 3/5th of half an hour as follows:

[tex]=30\times \frac{3}[5}\\=18[/tex]

Thus, 3/5th of half an hour is 18 minutes.

(4)

A square meter of wall required 4/7 liter of paint.

Then 2/5 of a square meter will require,

[tex]=\frac{4}{7}\times \frac{2}{5}\\\\=\frac{8}{35}[/tex]

Thus, 8/35 liter of paint will be used to pain /5 of a square meter of the wall.

(5)

1 glass of orange juice can be made using 2/5 of an orange.

Then 2 and half glass will require,

[tex]=\frac{2}{5}\times 2\frac{1}{2}\\\\=\frac{2}{5}\times \frac{5}{2}\\\\=1[/tex]

Thus, 1 orange will be required to make 2 and half glass of orange juice.

Answer:

Assuming x is the number, then [tex]x=1.6[/tex]

Step-by-step explanation:

If the product of a number and 5 is 8, the equation becomes:

[tex]5x=8[/tex] (assuming x is the unknown number).

We can isolate the variable x by dividing both sides by 5.

[tex]5x\div5 = 8\div5\\x = 1.6[/tex]

Hope this helped!

Answer:

-25, -5

Step-by-step explanation:

Let's write a system of equations. Lets call x and y the numbers, where x is 5 times y.

x + y = -30

x = 5y

Plugging this in, we get:

5y + y = -30

y = -5

Since y = -5, we can plug this in, and see that x = -25.

Answer:

-5 & -25

Step-by-step explanation:

1st number=x

2nd number=5x

x+5x=-30

6x=-30

x=-5

5x=-25

So the numbers are -5 & -25

Answer:

2, 3, 4

Step-by-step explanation:

Since the question is asking which of the following are functions, lets define what it is first

Function: An equation for one answer for y for every x

This means that every x coordinate can have a y, but multiple x coordinates can have the same y coordinate

Because of this it has to be every one of them except the first one

Answer:

1. C = 10π, A = 25π

2. 9 cm³

Step-by-step explanation:

Formula for circumference = πd

Formula for area of a circle = πr²

1. Set up the equation for circumference

10π

2. Set up the equation for area (radius = 1/2diameter) and solve

π(5²) = 25π

Formula for volume of a square pyramid = 1/3s² · h

The volume of a square pyramid is equal to 1/3 of the volume of a cube. The formula for a volume of a cube is s³ which is equal to s² · h because a cube has the same side length for all sides. Therefore, the volume of a square pyramid that perfectly fits within a given cube would equal 1/3 the volume of the cube.

1. Set up the equation and solve

27 ÷ 3 = 9

Answer:

Step-by-step explanation:

3.

diameter is equal two radiuses

D = 10 = 2R   ⇒  R = 5

circumference:  C = 2πR = 2R•π = 10π

area:                    A = πR² = π•5² = 25π

4.

If square pyramid fit perfectly inside cube then its base is the same as a face of cube, and the height (H) of pyramid is equal to the edge (S) of its base.

[tex]A_p=\frac13S^2\cdot H =\frac13S^2\cdot S=\frac13S^3=\frac13A_c=\frac13\cdot27\,cm^3=9\,cm^3[/tex]

Answer:

3.66

Step-by-step explanation:

calculate their shares and then add the amount they gave to Jack

Answer:

c=5.9/6(G)

Step-by-step explanation:

first find the 2 distances.

a^2+b^2=c^2                    c=2.4+.7              

7^2+2.4^2=c^2                  c=3.1

.49+5.85=c^2                    

c^2=6.34

c=√6.34

c=2.51.

next subtract the two distances to find the difference.

c=2.51-3.1

c=.59

so the distance would be .59 which can be rounded up to .60/G

explanation on how I knew the answer.

Im reviewing for the math 8th grade staar.

Answer:

See below.

Step-by-step explanation:

There is an infinite n umber of systems of equations that has (1, 4) as its solution. Are you given choices? Try x = 1 and y = 4 in each equation of the choices. The set of two equations that are true when those values of x and y are used is the answer.

x - 3 = 27

add three to both sides

then x= 30

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Let's solve your equation step-by-step.

[tex]x-3=27[/tex]

Step 1: Add 3 to both sides.

[tex]x -3 + 3 = 27 +3[/tex]

[tex]x = 30[/tex]

So the answer is : [tex]x = 30[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

1/2 a minute (30 seconds)

Step-by-step explanation:

475/50=9.5

450/50=9

9-9.5=.5