A group of 328 people consists of men ,women, and children. There are five times as many men than children and twice as many women then children. How many women are there

The distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A boat is heading towards a lighthouse, where Mason is watching from a vertical distance of 122 feet above the water. Mason measures an angle of depression to the boat at point A to be 16°.

We can draw the above situation as a form of a right-angle triangle.

From the figure, the distance between AB is x ft

From the right angle triangle DBC:

tan66 = 122/CB

CB = 54.31 ft

From the right angle triangle DAC

tan16 = 122/AC

AC = 425.46 ft

x = AC - CB

x = 425.46 - 54.31

x = 371.15 ft ≈ 371 ft

Thus, the distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.

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Answer:

[tex]-\dfrac{69}{14}[/tex]

Step-by-step explanation:

Substitute the given values of the variables into the given expression:

[tex]\implies \dfrac{60 \left(\dfrac{1}{3}\right)\left(-\dfrac{1}{5}\right)\left(\dfrac{1}{4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

When multiplying fractions, simply multiply the numerators and the denominators:

[tex]\implies \dfrac{60 \left(\dfrac{1 \cdot -1 \cdot 1}{3\cdot 5 \cdot 4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

[tex]\implies \dfrac{60 \left(-\dfrac{1}{60}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

When adding or subtracting fractions, make the denominators the same:

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20}{60}-\dfrac{12}{60}+\dfrac{15}{60}\right)}{\left(\dfrac{5}{15}-\dfrac{3}{15}\right)\left(\dfrac{4}{12}+\dfrac{3}{12}\right)}[/tex]

Now add the numerators and put that over the denominator:

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20-12+15}{60}\right)}{\left(\dfrac{5-3}{15}\right)\left(\dfrac{4+3}{12}\right)}[/tex]

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{23}{60}\right)}{\left(\dfrac{2}{15}\right)\left(\dfrac{7}{12}\right)}[/tex]

Again, multiply the fractions:

[tex]\implies \dfrac{\left(-1 \cdot \dfrac{23}{60}\right)}{\left(\dfrac{2 \cdot 7}{15 \cdot 12}\right)}[/tex]

[tex]\implies \dfrac{-\dfrac{23}{60}}{\dfrac{14}{180}}[/tex]

To divide the fractions, turn the second fraction upside down, then multiply it by the first fraction:

[tex]\implies -\dfrac{23}{60} \cdot \dfrac{180}{14}[/tex]

[tex]\implies -\dfrac{4140}{840}[/tex]

Finally, simplify:

[tex]\implies -\dfrac{4140 \div 60}{840 \div 60}[/tex]

[tex]\implies -\dfrac{69}{14}[/tex]

Answer:

y=4/5x-3.5

Step-by-step explanation:

You should keep the Y and X as variables in your slope-intercept equation. The slope-intercept formula is y=mx+b. Your M would be your slope which is rise over run. Based on the points, you go up four and right five. Your b is where the line intersects the Y-axis. You're welcome.

Answer:

x = 60

Step-by-step explanation:

The sum of the angles of a triangle is 180

95+25 +x = 180

120 +x = 180

Subtract 120 from each side

120+x-120 = 180-120

x = 60

Answer: Choice D) set of even integers

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

Explanation:

U = universal set = {all positive integers} = {1, 2, 3, 4, 5, ...}

A = {stuff in set U that is odd} = {1, 3, 5, 7, 9, ...}

[tex]A^c[/tex] = {stuff in set U but NOT from set A} = {2, 4, 6, 8, ...}

[tex]A^c[/tex] = {set of even numbers from set U}

In set theory, the complement is simply the complete opposite. If the number 7 is found in set A for instance, then 7 is not going to live in the complement [tex]A^c[/tex]

The opposite of the odd numbers is the set of even numbers.

Therefore, we go for choice D as our final answer.

Side note: if we union set A with its complement [tex]A^c[/tex] then we get the universal set as a result. [tex]A \cup A^c = \text{universal set} = \text{set of all positive integers}[/tex]

The solution is Option D.

Ac =  {x|x ∈ U and is an even positive integer} where Ac represents the complement of set A

What is union and intersection of sets?

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set U be = {all positive integers}

So , the values of set U = { 1 , 2 , 3 , 4 , 5 .. }

And , let the set A = {x|x ∈ U and x is an odd positive integer}

So , the value of set A = { 1 , 3 , 5 , 7 , ... }

And , the complement of set  A is Ac

The value of set Ac is all the even positive odd integers

So , the value of set Ac = { 2 , 4 , 6 , 8 .. }

Therefore , the value of set Ac = { 2 , 4 , 6 , 8 .. }

Hence , the set Ac = {x|x ∈ U and is an even positive integer}

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]12z^{2} -10z -12[/tex]

Step-by-step explanation:

Let the number be z

2 more than 3 times z ==> 3z + 2

6 less than 4 times z ==> 4z - 6

Product of the above two is
[tex](3z + 2) (4z - 6) \\= (3z)(4z) + (3z)(-6) + (4z)(2) + (2)(-6)\\= 12z^{2} -18z + 8z - 12\\= 12z^{2} -10z -12[/tex]

Answer:

The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).

The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒

The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number)

The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number) = P(head) × P(even number)

P(even number)Assuming a fair coin and a fair die:

P(even number)Assuming a fair coin and a fair die:P(head)

P(even number)Assuming a fair coin and a fair die:P(head) =50%

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number)

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50%

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number)

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number) =50%×50%=25%

Answer:

w = -1/5

OR

w = -3

Step-by-step explanation:

Given equation:

−16w-3 = 5w²

Solution:

Subtracting 5w^2 from both sides,we get

Factor the LHS of this equation using middle term factor:

Now,

Solving for equation 1:

Solving for equation 2:

[tex] - 16w - 3 = 5 {w}^{2} \\ \\ 0 = 5 {w}^{2} + 16w + 3 \\ \\ 5 {w}^{2} + 16w + 3 = 0 \\ \\ 5 {w}^{2} + w + 15w + 3 = 0 \\ \\ (5 {w}^{2} + w) + (15w + 3) = 0 \\ \\ w(5w + 1) + 3(5w + 1) = 0 \\ \\ (w + 3)(5w + 1) = 0. [/tex]

The value of w is -3 and -1/5 .

Answer:.20

Step-by-step explanation:

According to what are written in the table the probability for x=-10 is .20

350 tickets sold of children and 425 tickets sold for adult.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Let x be the number of adult tickets that were sold and y be the number of children's tickets that were sold.

Total 775 tickets were sold for the game.

So,

x + y = 775

If adults tickets sold for 2.50 and children's tickets sold for 1.50 and all the tickets were sold for a total of 1587.5, it means that

2.5x + 1.5y = 1587.5

put x = 775 - y

2.5(775 - y) + 1.5y = 1587.5

1937.5 - 2.5y + 1.5y = 1587.5

-y = 1587.5- 1937.5

y = 350

and, x = 775 - y = 775 - 350

x = 425

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Answer:

[tex]area \: of \: rectangle \: = length \: \times breath[/tex]

[tex]length \: = distance \: between \: f \: and \: g \: or \: between \: e \: and \: h \: [/tex]

F = (3,7)

G = (6,4)

H = (5,3)

E= (2,6)

= (3 units)

= 1 units

Area = 3* 1

= 3 units²

The number of cubes needed to fill the rectangular prism 4608 cubes.

volume of rectangular prism = lwh

where

Therefore,

volume of the rectangular prism = 8 × 4 × 9 / 4 = 72 inches³

volume of the cube = l³

where

Therefore,

volume = (1 / 4)³

volume of the cube = 1  / 64 inches³

Therefore,

The number of cubes needed to fill the rectangular prism = 72 ÷ 1 / 64

The number of cubes needed to fill the rectangular prism = 72 × 64 = 4608

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Step-by-step explanation:

first a little help, how they got the equations :

in total they need 15 liters.

so, whatever x and y are, but together they must be 15 L.

x + y = 15

then, we are mixing x liters of 20% alcohol with y liters of 100% alcohol, that have to result in a 40% solution of (x+y) liters :

0.2x + y = 0.4(x+y)

we know from the first equation that x+y = 15, so the second equation is actually

0.2x + y = 0.4 × 15 = 6

so, we have

x + y = 15

0.2x + y = 6

do you notice something ? there is a "+ y" in both equations.

so we can actually subtract the second equation from the first, eliminate y and solve for the remaining x. and then use one of the original equating to get also y :

x + y = 15

- 0.2x + y = 6

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

0.8x 0 = 9

0.8x = 9

x = 9/0.8 = 11.25 liters

x + y = 15

11.25 + y = 15

y = 15 - 11.25 = 3.75 liters

The total amount at the lowest price is $936, the total amount at the highest price is $1224, and the amount saved is $288.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The table is in the picture, please refer to the picture.

Tony needs to purchase 3,600 oz of vegetable oil for his catering business.

Lowest unit price = 26 cents per ounce

Total price at this rate = 3600×26 = 93600 cents = $936

The highest unit price = 34 cents per ounce

Total price at this rate = 3600×34 = 122400 cents = $1224

Total saving he purchases the container that has the lowest unit price:

= 1224 - 936

= $288

Thus, the total amount at the lowest price is $936, the total amount at the highest price is $1224, and the amount saved is $288.

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In the given graph point B is a relative maximum with the coordinates (0, 2).

The given function is [tex]y=x^{4}-2x^{2} +1[/tex].

In the given graph, we need to find which point is a relative maximum.

The function's graph makes it simple to spot relative maxima. It is the pivotal point in the function's graph. Relative maxima are locations where the function's graph shifts from increasing to decreasing. A point called Relative Maximum is higher than the points to its left and to its right.

In the graph, the maximum point is (0, 2).

Therefore, in the given graph point B is a relative maximum with the coordinates (0, 2).

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a short sale is when a house is sold for less than what the mortgage is.

answer: B. for less than the mortgage owed on it

Answer:

9

Step-by-step explanation:

10x + 8x = 162

18x = 162

x = 9

The equation can be used to find the time it took student  to hike the trail will be 3t= 5(3-t)

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

The formula for the distance for the to and fro motion is;

x= v × t

The total time required for to and fro motion is;

[tex]\rm t_1 + t_ 2 = 3 \\\\ \frac{x}{v_)1} +\frac{x}{v_2}=3 \\\\ \frac{x}{3} +\frac{x}{5}= 3 \\\\ x = \frac{45}{8} \\\\ x = 3 \times \frac{15}{8} \\\\\ x =v \times \frac{15}{8} \\\\ x = v \times t[/tex]

From the equation B;

3t= 5(3-t)

3t=15-5t

8t=15

t=15/8

The equation can be used to find the time it took Stu to hike the trail will be  3t= 5(3-t)

Hence option B is correct.

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The series diverges. You Consider concluding this because the series is in arithmetic progression.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

[tex]a_n = a_1 + (n-1)d[/tex]

where d is the difference and a₁ is the first term of the sequence.

The given series of numbers 1/4+3/2+11/4+4+21/4+.... is an arithmetic series because the difference between any two consecutive terms is 5/4. Therefore, the blanks can be filled as,

The series diverges. You Consider conclude this because the series is in arithmetic progression.

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definetly not a

Step-by-step explanation:

because it is an incompetent answer

Answer:

C

Step-by-step explanation:

We have

y - 5 = -2(x + 4)

Expanding the RHS by multiplying by 2 gives us

y - 5 = -2x -8

Moving -5 from LHS to RHS (reverses sign)
y = -2x -8 + 5   or
y = -2x -3

C. y=-2x - 3 , equation describes the same line as y- 5 = -2(x+4).

Here, we have,

We have been given an equation in point-slope form and we are asked to find the equation of same line.

y- 5 = -2(x+4)

Upon using distributive property , we will get,

=> y- 5 = -2x - 8

We have

y - 5 = -2(x + 4)

Expanding the RHS by multiplying by 2 gives us

y - 5 = -2x -8

Moving -5 from LHS to RHS (reverses sign)

y = -2x -8 + 5   or

y = -2x -3

Therefore, the equation y = -2x -3 represents the same line as our given equation.

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Answer:

Step-by-step explanation:

The last one: 79, 79, 79, 79, 79, 79, 79, 79, 79, 79 because there isn't any difference in the numbers.

S.D.: 0

Answer:

none of them match

Step-by-step explanation:

maybe something is typed wrong. the answer I got for the equation was 108 and none of them match

Answer:

     [tex]\frac{15*7^{x} }{7^{x} +9}[/tex]

Step-by-step explanation:

→ Substitute f(x) into g(x)

     [tex]\frac{15*7^{x} }{7^{x} +9}[/tex]

Answer:

(-4,-18) and (5,90)

Step-by-step explanation:

I'll assume the first equation is supposed to be y – 10 = 11x + x^2

This is a parabola.  The second equation is a straight line:  

y – 12x = 30

We want to find the points at which these lines intersect.  They will intersect for any (x,y) that

Let's rearrange the second equation to isolate y:

y – 12x = 30

y  = 30 + 12x

Now we can take the this value of y and substitute it into the first equation:

y – 10 = 11x + x^2

(30 + 12x) – 10 = 11x + x^2

20 + 12x = 11x + x^2

0 = x^2 -x -20

We can factor this into (x+4)(x-5)

That means x can be either -4 or 5.

Find the value of y using these values of x in both original equations:

For x = -4

y – 10 = 11x + x^2

y  = 11x + x^2 + 10

y = 11(-4)+(-4)^2 +10

y = -44 + 16 + 10

y = -18    The point both lines meet is at (-4, -18) which was already given in the problem.  

For x = 5

y – 10 = 11x + x^2

y  = 11x + x^2 + 10

y  = 11(5) + (5)^2 + 10

y  = 55 + 25 + 10

y = 90

The second point both lines meet is (5,90).

We should use both solutions in the second equation to verify these values, but I'll graph them, instead.  See the attached graph to prove these points are correct.

The radical is 2√21.

The √ symbol that is used to denote square root or nth roots.

Given :

√84

= √2*2*21

=2√21

Hence, the radical is 2√21.

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