At the local fair, 358 people waited in line for a boat ride. The boat can hold 8 people. How many trips will the boat have to take for everyone to get a ride? .​

The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

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The probability of both events occurring is  4/15

The given parameters are:

P(A) = 4/5

P(B) = 1/3

Because the events are independent, we have:

p(A and B) = P(A) * P(B)

This gives

P(A and B) = 4/5 * 1/3

Evaluate

P(A and B) = 4/15

Hence, the probability of both events occurring is  4/15

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The value of m is 14.5 and the three angles of the triangle are 32.5°, 57°, and 90.5°.

There are three angles in a triangle. Consider as ∠A, ∠B, and ∠C.

The sum of all the three angles gives 180° in a triangle. I.e.,

∠A + ∠B + ∠C = 180°.

The given triangle has three angles,

(m + 18)° , (2m + 28)°, and (3m + 47)°

On adding all these and equating to 180°,

(m + 18)° + (2m + 28)° + (3m + 47)° = 180°

⇒ 6m + 93 = 180

⇒ 6m = 180 - 93

⇒ 6m = 87

∴ m = 14.5

Then, the values of the three angles are:

(m + 18)° = (14.5 + 18)° = 32.5°

(2m + 28)° = (2 × 14.5 + 28)° = 57°

(3m + 47)° = (3 × 14.5 + 47)° = 90.5°

Therefore, the angles of the given triangle are 32.5°, 57°, and 90.5°.

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Answer:

C. 92.16π mi²

Step-by-step explanation:

Use the formula: 4 · π · r²

r=4.8

4 · π · 4.8²=

=4 · π · 23.04=

=92.16π mi²

Hope this helps!

If not, I am sorry.

Recall the Pythagorean identity.

[tex]\sin^2(x) + \cos^2(x) = 1 \implies \left\langle \begin{matrix} \tan^2(x) + 1 = \sec^2(x) \\ 1 + \cot^2(x) = \csc^2(x) \end{matrix} \right.[/tex]

[tex]\implies \sec^2(\beta) - \csc^2(\beta) = (\tan^2(\beta) + 1) - (1 + \cot^2(\beta)) \\\\ ~~~~~~~~= \tan^2(\beta) - \cot^2(\beta)[/tex]

Recall the difference of squares identity.

[tex]a^2 - b^2 = (a - b) (a + b)[/tex]

[tex]\implies \sec^2(\beta) - \csc^2(\beta) = (\tan(\beta) - \cot(\beta)) (\tan(\beta) + \cot(\beta))[/tex]

[tex]sec^2\beta -csc^2\beta \\(1+tan^2\beta )-(1+cot^2\beta )\\1+tan^2\beta -1-cot^2\beta \\tan^2\beta -cot^2\beta \\(tan\beta -cot\beta )(tan\beta +cot\beta )[/tex]

The Area of triangle is A= 58.02 (ft)^2

According to statement

Let

B is the measure of the vertex angle of the isosceles triangle ABC

A and C is the two congruent sides of the isosceles triangle ABC

we know that

The area of a triangle applying the law of sines is equal to the

A= 1/2 *AC *SinB

we have

A=C= 17.91 ft

And

B= 21.21

Substitute these values in the formula

A= 1/2* 17.91* 17.91 * Sin(21.21)

A= 58.02 (ft)^2

So, the Area of triangle is A= 58.02 (ft)^2

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The probability that the sample proportion of Republicans will differ from the population proportion by greater than 5% is 100%

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

It is given that 58% of voters are Republican. The sample is 536 voters.

0.58×536 = 310.88 can be rounded off to 311.

536 - 311 = 225 are not republicans

311-225 = 86 is the difference

[tex]\frac{86}{536}[/tex]×100 = 16.044%

Hence, the probability is 100%.

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The different sets of initials can be formed if every person has one surname (i.e., last name) and either one or two given names (i.e., a first name, or a first and middle name) is 15600.

There are 26 possible letters, each set of initials would have 3 letters in it, order doesn't matter, i.e. ABC does not equal ACB. using permutation   26P3 = 5600.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items in a certain order.

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Answer: 28.40 cans of soda

Step-by-step explanation:

Volume of cylinder: pi * r^2 * h

Volume of the can of soda = pi * 3.25^2 * 12 = 126.75 pi

Volume of the cylindrical pitcher = pi * 10^2 * 36 = 3600 pi

3600/126.75: 28.40 cans of soda

Answer:

28 whole soda cans or 28.4 soda cans (rounding to nearest tenth)

Step-by-step explanation:

The soda cans and the pitcher can be modeled as cylinders.

Volume of a cylinder

  [tex]\sf Volume=\pi r^2h[/tex]

where:

Diameter of circle

[tex]\sf d= 2r[/tex]

[tex]\sf \implies r=\dfrac{1}{2}d[/tex]

Volume of Soda can

Given values:

[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (3.25)^2 \cdot 12\\ & = \sf 126.75 \pi \:\:cm^3\end{aligned}[/tex]

Volume of Pitcher

Given values:

[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (10)^2 \cdot 36\\ & = \sf 3600 \pi \:\:cm^3\end{aligned}[/tex]

To calculate how many cans of soda the pitcher will hold, divide the volume of the pitcher by the volume of one soda can:

[tex]\begin{aligned}\implies \textsf{Number of soda cans} & = \dfrac{\textsf{Volume of Pitcher}}{\textsf{Volume of one soda can}}\\\\&= \sf\dfrac{3600 \pi}{126.75 \pi}\\\\& = \sf 28.402366...\end{aligned}[/tex]

Therefore, the pitcher can hold 28 soda cans (nearest whole can), or 28.4 soda cans (nearest tenth).

The equation of the line passing through the points is y = x + 2

The points are (-1, 1) and (4, 6).

The slope is calculated using:

m= (y2 - y1)/(x2 - x1)

So, we have:

m = (6 - 1)/(4 + 1)

Evaluate

m = 1

The equation of the line is then calculated as:

y = m(x -x1) + y1

This gives

y = 1 *(x + 1)  + 1

Evaluate

y = x + 2

Hence, the equation of the line passing through the points is y = x + 2

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The correct definition of dependent events is two events are dependent if the outcome of the first event affects the outcome of the second event.

Two events are dependent if the outcome of one of the event depends on the outcome of the first event.  An example of a dependent event is if it rains, the floor would be wet.

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Answer:

9x - 2

Step-by-step explanation:

f(x) = 4x - 8

g(x) = 5x + 6

because it's (f + g)(x), we can simply add the functions together

{note: don't get thrown off by the (x) being separate parentheses--distributing the x first can help it look familiar:

(x)(f + g)

fx + gx,

it's the same thing}

(4x - 8) + (5x + 6)

here, we want to combine like terms to simplify:

4x + 5x - 8 + 6

4x + 5x  -   2

9x - 2

So, (f + g)(x) = 9x - 2

hope this helps!! have a lovely day :)

The simplest form of  (–11.7y – 3.3x) + 1.2x + (5.2y + x) is -6.5y - 1.1x

(–11.7y – 3.3x) + 1.2x + (5.2y + x)

We have to open the brackets.

Therefore,

(–11.7y – 3.3x) + 1.2x + (5.2y + x)

-11.7y - 3.3x + 1.2x + 5.2y + x

combine like terms

Hence,

-11.7y + 5.2y - 3.3x + 1.2x + x

Therefore,

-6.5y - 1.1x

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Answer:   -6.5y - 1.1x

Step-by-step explanation:

The number of people coming in during the lunch hour is 160

The complete question is in the attached image

The random numbers are given as:

18, 38, 87, 16, 56, and 5

Regroup the numbers

Number           Group       Probability

5, 16, 18           1 - 20             3/6

38, 56             21 - 60           2/6

56                    61 - 90          1/6

Based on the individual numbers and the probability table, we have:

X      20      30     40

P     3/6     2/6    1/6

The expected value is:

[tex]E(x) = \sum xp[/tex]

This gives

E(x) = 20 * 3/6 + 30 * 2/6 * 40 * 1/6

Evaluate

E(x) = 160/6

There are six ten-minute intervals.

So, we have:

People = 6 * 160/6

Evaluate

People = 160

Hence, the number of people coming in during the lunch hour is 160

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Answer: $768

Step-by-step explanation:

Here, you'll just multiply:

16x8x6 = 768

Answer:

c. x=8

Step-by-step explanation:

make me a brain list.

Answer:

A ≈ 1194.5

The total surface area is 1194.53.

a = 24

b = 30

c = 7

h = 18

Rachel should perform better because of the spacing effect.

Given,

Rachel will study one hour each day for 5 days and Jennifer will study 5 hours the day before the exam.

What do you predict about their scores?  

Rachel should perform better because of the spacing effect.

The spacing effect demonstrates that learning is more effective when study sessions are spaced out. This effect shows that more information is encoded into long-term memory by spaced study sessions, also known as spaced repetition or spaced presentation, than by massed presentation.

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yd=

yd=

16x2+12x+18=3x=2x2+6x+9=3x=

sorry i try

Answer:

D

Step-by-step explanation:

Answer:

2700 - 2000 = 700 - 100 = 600 - 200 = 400 - 100 = 300

300 dollars

Answer:

1066

Step-by-step explanation:

5 mins = 410 words

410/5 = 82 so she is typing 82 words a minute

Then do 82 times 13

The ordered pair that is on g(x) is (2, -3/400)

determine the ordered pair:

The function is given as:

f(x)=3/4(10)∧-x

The rule of reflection across the x-axis is:

g(x) = -f(x)

So, we have:

g(x) = -3/4(10)∧-x

Set x = 2.

So, we have:

g(2) = -3/4(10)∧-2

Evaluate the exponent

g(2) = -3/4 * 1/100

Evaluate the product

g(2) = -3/400

This means that:

(x, y) = (2, -3/400)

Hence, the ordered pair that is on g(x) is (2, -3/400)

Ordered pairs are pairs of two numbers (or variables) that are enclosed in parentheses and separated by commas. For example, (1, 2) is an ordered pair. Coordinate geometry represents points, and set theory represents elements of relations / Cartesian products.

Ordered pairs are pairs of numbers in a particular order. For example, (1, 2) and (-4, 12) are ordered pairs. The order of the two numbers is important. (1, 2) is not equivalent to (2, 1)-(1, 2) ≠ (2, 1).

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The inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

The inverse of a matrix A is calculated by the formula:

A' = (1/|A|)(Adj A),

where A' represents the inverse of matrix A,

|A| represents the determinant value of matrix A, and

Adj A represents the Adjoin matrix of matrix A.

So, to calculate the inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] , we will first calculate its Adj.

Adj = [tex]\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}[/tex]= [tex]\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex].

Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.

Therefore A' = (1/|A|)(Adj A),

or, A' = [tex](1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex] ,

or, A' = [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

Therefore, the inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

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By the converse of the basic proportionality theorem, we can say DE║AB.

We need to check whether DE is parallel to AB.

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

In triangle ABC, we can see on side AC, D is midpoint (∵AD=DC) and on side BC, E is midpoint (∵BE=CE).

Therefore, by the converse of the basic proportionality theorem, we can say DE║AB.

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The proof is shown below:

The line segment joining the mid points of any two sides of a triangle is parallel to the third side.

△ABC in which D and E are the mid points of AB and AC,.

If D and E are the mid points of AB and AC,

then AD=DB and AE=EC.

Thus,

AD/DB = AE/ EC

​

by the converse of Thales theorem, DE∥BC.

As, by theorem we can say that DE∥BC.

So, there is no other side parallel to DE.

​

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Multiplying the binomials, we have (x - 7)(x - 2) = x² - 9x + 14.

Applying the distribution property of multiplication, the given binomials, (x - 7)(x - 2) can be multiplied as shown below:

(x - 7)(x - 2)

x(x - 2) -7(x - 2)

x² - 2x - 7x + 14

x² - 9x + 14

Therefore, (x - 7)(x - 2) = x² - 9x + 14.

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Answer:

Hence the expression [tex]$$(x-7)(x-2)=x^2-9x-14$$[/tex]

Step-by-step explanation:

The given expression is (x-7)(x-2).

We have to multiply the given expression.

Multiply the (x-7) by-2, multiply the (x-7) by x then add like terms.

[tex]$$\frac{\begin{matrix}{} & {} & x & - & 7 \\ \times & {} & x & - & 2 \\ \end{matrix}}[/tex]

____________

[tex]{\frac{\begin{matrix}{} & - & 2x & - & 14 \\ {{x}^2} & - & 7x & {} & {} \\ \end{matrix}}{\begin{matrix}{{x}^2} & - & 9x & - & 14 \\ \end{matrix}}}$$[/tex]

Using it's concept, it is found that the percentage of the students that do NOT like to travel out of state that like camping is:

B. 34%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, there are 112 students that do not like traveling out of the state, and of those, 38 like camping, hence the percentage is:

[tex]P = \frac{38}{112} \times 100\% = 34\%[/tex]

Hence option B is correct.

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Answer: The three triangles shown are similar triangles. We can tell this by the Angle Angle theory. You can tell the angles are congruent by the matching marks in each corner of the triangles, the marks or “ticks” are the same in the same corners. The length of the sides can change but the angle measurements will still be the same.

Step-by-step explanation: explained in answer

Answer: Each of the corresponding angles of one triangle equal the corresponding angles of the other triangle.