The senior class of a high school needs to decide where to go for their senior trip. They have four choices: A cruise, a camping trip, a snorkeling trip, or to the Great Wall of China.

Due to budget constraints they cannot survey all 800 people in the senior class so they randomly select 150 people from the class and ask them their preference. The table shows the results.

Using the sample results, estimate the proportion of the entire population that would like to take a cruise to Bermuda.

Starting from the Pythagorean identity, we deduce

[tex]\sin^2(x)+\cos^2(x) = 1 \iff \cos^2(x) = 1-\sin^2(x) \iff \cos(x) = \pm\sqrt{1-\sin^2(x)}[/tex]

If we plug in the value 7/10 for sin(x), we have

[tex]\cos(x) = \pm\sqrt{1-\dfrac{49}{100}} = \pm\sqrt{\dfrac{51}{100}}=\pm\dfrac{\sqrt{51}}{10}[/tex]

Answer:

d. 3x³ and 2x³

Step-by-step explanation:

In standard form, the terms of a polynomial expression are written in order of descending powers of the variable. There will be only one term for any given power of the variable.

Here, there are two terms that have x to the third power. These terms must be combined to write the expression in standard form. They are the only terms that can be combined: 3x³ + 2x³ = 5x³.

Answer:

[tex]t=7.4years[/tex]

Step-by-step explanation:

Let's clear t from the equation [tex]N=16.10^{0.15t}[/tex]. In order to clear t, we have to apply [tex]log_{10} (x)[/tex] in both side of the equations.

[tex]log_{10}N=log_{10}(16.10)^{0.15t}[/tex]

By using properties of the logarithm

[tex]log_{10} (a.b)}= log_{10}a+log_{10}b[/tex]

We obtain:

[tex]log_{10}N=log_{10}(16)+log_{10} (10^{0.15t})[/tex]

Ordering using the logarithm property  [tex]log_{10}a^{n} =nlog_{10}a[/tex] and [tex]log_{10} 10=1[/tex]

[tex]log_{10}N=log_{10}(16)+0.15tlog_{10}10[/tex]  

[tex]log_{10}N=log_{10}(16)+0.15t[/tex]

Clearing t

[tex]t=\frac{log_{10}N-log_{10}(16)}{0.15}[/tex] using the logarith property [tex]log_{10}a-log_{10}b=log_{10}\frac{a}{b}[/tex]

we obtain:

[tex]t=\frac{log_{10}\frac{N}{16} }{0.15}[/tex]

The number of Elm trees is N = 204

Solving

[tex]t=\frac{log_{10}\frac{204}{16} }{0.15}\\t=\frac{log_{10}12.75}{0.15}=7.370[/tex]

Round to the nearest tenths place [tex]t=7.4years[/tex]

Answer:

7x

Step-by-step explanation:

Sorry this is the best way I could show the work as the equation maker on this site does not support doing something in this format

To divide the expression (14x^2 - 21x) by (2x - 3), you can use long division to get the answer 7x.

To divide the expression (14x^2 - 21x) by (2x - 3), we can use long division. Here are the steps:

Therefore, the answer is 7x.

Answer:

26

Step-by-step explanation:

80 divided by three = 26.666666

26 times 3 = 78

2 leftover

The number sticker each student get is 26 and the number stickers teacher got is 2.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, three friends buy one pack of 80 stickers.

Now, number of stickers each friend = 80/3

3|80|26

  78
_____
   2

Therefore, the number sticker each student get is 26 and the number stickers teacher got is 2.

To learn more about the division visit:

https://brainly.com/question/1575906.

#SPJ5

Answer:

the third one.

Answer: C) V = 562.5π [tex]in^{3}[/tex] ; S = 225π [tex]in^{2}[/tex]

Step-by-step explanation: Please see the image below!

Answer:

20√2 meters (approximately 28.28 m)

Step-by-step explanation:

It may help to make a diagram. Because this is a 45 45 90 triangle, you can use those rules to help solve.

Final answer:

The distance from the top of a totem pole to the end of its shadow, when the angle of elevation of the sun is 45 degrees, is approximately 28.28 meters.

Explanation:

The student has presented a problem that involves using trigonometry to calculate the distance from the top of a totem pole to the end of its shadow when the angle of elevation of the sun is 45 degrees. To solve this, we can use the concept of right-angled triangles and the properties of special triangles, specifically a 45-45-90 triangle where the two legs are congruent. Since the angle of elevation is 45 degrees and the length of the shadow is given as 20 meters, we know that in this special right triangle, the lengths of the two legs are equal. Therefore, the distance from the top of the totem pole to the end of the shadow (the hypotenuse of the triangle) is the length of the shadow times the square root of 2, based on the Pythagorean theorem.

Using the formula hypotenuse = leg × √2, we substitute the leg length of 20 meters to get hypotenuse = 20 m × √2, which equals approximately 28.28 meters.

Fluid ounces, 47 more

Answer:

A

Step-by-step explanation:

(x−2) means the graph is shifted 2 units to the right.

+3 means the graph is shifted 3 units up.

So the graph of g(x) is shifted 2 units right and 3 units up.

see picture attached.

i hope this helped !!

ANSWER

Point-slope form:

[tex]y + 5 = -3(x - 1)[/tex]

Slope-intercept form;

[tex]y = - 3x - 2[/tex]

EXPLANATION

The point-slope form of a line is given by:

[tex]y-y_1=m(x-x_1)[/tex]

We need to find the slope using the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

Let us substitute the point (1, –5) and (–3, 7).

This implies that,

[tex]m = \frac{7 - - 5}{ - 3 - 1} [/tex]

[tex]m = \frac{12}{ - 4} = - 3[/tex]

The point slope form now becomes,

[tex]y - - 5 = - 3(x - 1)[/tex]

[tex]y + 5 = -3(x - 1)[/tex]

To find the slope intercept form, we expand to obtain;

[tex]y = - 3x + 3 - 5[/tex]

[tex]y = - 3x - 2[/tex]

Let [tex]a_1,\ldots,a_4[/tex] denote the ages of the 4 candidates. Then

[tex]\dfrac{a_1+a_2+a_3+a_4}4=40[/tex]

[tex]a_1+a_2+a_3+a_4=160[/tex]

[tex]\dfrac{a_1+a_2+a_3}3+\dfrac{a_4}3=\dfrac{160}3[/tex]

The average age of the first 3 candidates is 42, so

[tex]\dfrac{a_4}3=\dfrac{160}3-42[/tex]

[tex]\implies\boxed{a_4=160-3\cdot42=34}[/tex]

Answer:

3 1/4

Step-by-step explanation:

I'll assume you meant 3/4 + (1/3 / 1/6) - (- 1/2) and not 3/4 + (1/3 \ 1/6) - (- 1/2)

So we start with 3/4 + (1/3 / 1/6) - (- 1/2)

The toughest part is (1/3 / 1/6) , but remember that when dividing with a fraction, it's like multiplying by the inverse of that fraction, so...

[tex]\frac{1/3}{1/6} = \frac{1}{3} * \frac{6}{1} = \frac{6}{3} = 2[/tex]

Then we return to the original problem with the new value for the parenthesis:

3/4 + 2 + 1/2 = 3/4 + 8/4 + 2/4 = 13/4 or 3 1/4

Answer:

The correct answer is 3 1/4

Step-by-step explanation:

It is given that,

3/4 + (1/3 \ 1/6) - (- 1/2)

To find the value of given expression

3/4 + (1/3 \ 1/6) - (- 1/2) for finding the answer we have to find the value of

(1/3 / 1/6) = 1/3 * 6/1 = 2

3/4 + (1/3 \ 1/6) - (- 1/2 = 3/4 + 2 + 1/2

 = 3/4 + 8/4 + 2/4 = (3 + 8 + 2)/4 = 13/4 = 3 1/4

The correct answer is 3 1/4

m<6 = 180° - m<3

m<6 = 180° - 130°

m<6 = 50°

Answer: m6 equals 50 degrees

Step-by-step explanation: Since AB and CD are parallel u just solve for m2 which is the same as m6 which would be 180-130=50

Answer: 45°

Step-by-step explanation:

There are 180 degrees in a triangle so

180-80=100-55=45°

Answer:

Option a) x = −1, 5.4

Step-by-step explanation:

we have

[tex]f(x)=x^{2} -x-12[/tex]

[tex]g(x)=3.4x-6.6[/tex]

equate f(x) and g(x)

[tex]x^{2} -x-12=3.4x-6.6[/tex]

Solve the quadratic equation by graphing

The solutions are x=-1 and x=5.4

see the attached figure

Answer:

x= -1, 5.4

Step-by-step explanation:

[tex]f(x)= x^2-x-12[/tex]

[tex]g(x)= 3.4x -6.6[/tex]

f(x) is a quadratic equation and g(x) is a linear equation

To find f(x)= g(x) we need to find the point where the graph  of f(x) and g(x) intersects.

The quadratic equation f(x) and linear equation g(X) intersects at two points

from the graph f(x)= g(x) at x= -1 and x=5.4

Answer:

Step-by-step explanation:

x² + 5x – 104 = 0

Factor using the AC method.  Here, a = 1 and c = -104.  Multiplied together, ac = -104.  Factors of -104 that add up to +5 are +13 and -8.

(x + 13) (x - 8) = 0

x = -13, 8

A negative width doesn't make sense, so x = 8.  Therefore, the width is 8 inches and the length is 5 more than that, or 13 inches.

Answer:

width = 8

length = 13

Step-by-step explanation:

All that is left to do is factor the results that you have

x^2 + 5x - 104 = 0

You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.

The two numbers are 8 and 13

More formally stated, the quadratic can be factored to

(x + 13)(x - 8) = 0

x - 8 =0

x - 8 + 8 = 8 + 0

x = 8

x + 13 = 0 has no meaning.

That means that the width ( a positive number ) = 8

The length is 5 more = 13

Answer:

The smallest box dimensions are 4 x 4 cm.

Find the diagonal and this would be the diameter of the smallest circle.

Using the Pythagorean theorem:

4^2 + 4^2 = c^2

16 + 16 = c^2

c^2 = 32

c = √32

c = 5.658 cm ( Round answer as needed.)

Answer:

7ab+5

Step-by-step explanation:

add like terms (3ab+4ab=7ab)

5 doesn't have a like term so it stays by itself

Hey there! :)

3ab + 4ab + 5

In order to simplify this, we must add like terms. In addition, when simplifying, you can ONLY add like terms.

Since both "3ab" & "4ab" contain "ab," you are able to combine them together!

When combining like terms, you only add the numerical value, not the letters.

This leaves us with : 7ab + 5

Therefore, your answer is 7ab + 5

~Hope I helped!~

Answer:

The Answer is likely 60.

Step-by-step explanation:

Two standard deviations from 70 is 60, because the actual deviation is 5, so 2 of those equals 10. 10 - 70 = 60.

Answer:

60

Step-by-step explanation:

Two standard deviations below the mean is:

70 - 2(5) = 60

Let's call dimes x and the quarters x+3 since we have 3 more of them.

x+x+3=45

2x=42

x=21

we have 21 dimes and 23 quarters

21*0.10=2.1

23*0,25=5.98

if we add those together it equals 8.08

Answer:

$8.10

Step-by-step explanation:

Let d and q represent the # of dimes and quarters, respectively.  Then write equations reflecting this story:

q = d + 3, and d + q = 45.  Substitute d + 3 for q in the second equation, obtaining:

d + d + 3 = 45, or 2d = 42, or d = 21.  Then there are 21 dimes and 24 quarters.  That comes to $2.10 + $6.00, or $8.10.

Answer:

$179.17

Step-by-step explanation:

You already know the formula but you have it typed incorrectly.  The rt is raised as a power to the e.  Just in case you didn't know that.  Filling in our formula with what we have gives us:

[tex]A(t)=125e^{(.18)(2)[/tex]

Simplify that power to .36 and we have

[tex]A(t)=125e^{.36}[/tex]

Now raise e to the power of .36 on your calculator and get

A(t)= 125(1.433329415)  and

A(t) = $179.17

Answer:

C 179 is the answer.

Step-by-step explanation:

Answer:

Option B is correct.

Step-by-step explanation:

A city has population = 10000

Population increase each year = 4%

So, Population increase after 1 year = 10000 * 4%

                                                           = 10000*4/100

                                                           = 400

Adding in the current population:

10000+400 = 10,400

Population increase after 2 year = 10,400*4%

                                                     = 10400*4/100

                                                      = 416

Adding in the current population:

10400+416 = 10816

Population increase after 3 year = 10,816*4%

                                                     = 10816*4/100

                                                      = 433

Adding in the current population:

10816+433 = 11,249

Population increase after 4 year = 11,249*4%

                                                     = 11249*4/100

                                                      = 450

Adding in the current population:

11249+450 = 11,699

Population increase after 5 year = 11,699*4%

                                                     = 11699*4/100

                                                      = 468

Adding in the current population:

11699+468 = 12167

So, the population after 5 yeras will be 12167.

Option B is correct.

The population of the city will be approximately 12,167 people after 5 years, calculated by using the formula for exponential growth with a 4% annual increase from the initial population of 10,000.

The question involves calculating the future population of a city that is experiencing exponential growth over a period of time. To find the population of a city 5 years later when the population increases by 4% per year, we use the formula for exponential growth, which is:

P = [tex]P0 * (1 + r)^t[/tex]

Where:

P is the future population

P0 is the initial population (which is 10,000)

r is the annual growth rate (which is 4% or 0.04)

t is the number of years (which is 5)

Using the formula, we calculate:

P = 10,000 × (1 + 0.04)⁵

P = 10,000 × (1.04)⁵

P = 10,000 × 1.2166529

P = 12,166.529

So, the population will be approximately 12,167 people 5 years later.

Answer:

E = (3b+28)/2

T=3b+28

E= t/2

Step-by-step explanation:

The coat of the 4 pizzas would be $28, and an unknown amount of breadsticks that cost 3 dollars each.

Im going to use B as the amount of breadsticks bc i dont know what its supposed to be but that should be the correct answer.

T=3b+28

E= t/2

Answer:

To eliminate x multiply the first equation by 3 and the second equation by 4

To eliminate y multiply the first equation by 3 and the second equation by 2

Step-by-step explanation:

We are given a system of linear equations;

4x-2y=7

3x-3y=15

solving by elimination means that we shall be getting rid of one of the variables in order to determine the other. In this case we can either eliminate x or y. In order to eliminate any of these variables, we first must make their coefficients equal in both equations. To eliminate x;

Multiply the first equation by 3 and the second equation by 4.

To eliminate y;

Multiply the first equation by 3 and the second equation by 2.

Answer:

a) Function

b) Not a function

c) Function

d) Not a function

Step-by-step explanation:

a) Domain = { 7,-6,2}

   Range = {5,0,3}

It is a function as every value in domain has some and unique value mapped to it in Range

b)

Domain = { 7,-6,2}

   Range = {5,0,-2,3}

It is not a function as -6 value in domain has two values mapped to it in Range

c)

Domain = { 7,2}

   Range = {-6,-7}

It is a function as every value in domain has some and unique value mapped to it in Range

d)

Domain = { 7,-6}

   Range = {5,0,3}

It is not a function as 7 value in domain has two values 3 and 5 mapped to it in Range

Answer:

https://socratic.org/questions/how-do-you-write-the-equation-of-the-quadratic-function-with-roots-6-and-10-and-

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given the roots are x = 6 and x = 10, then

the factors are (x - 6) and (x - 10)

The quadratic is then the product of the roots

y = a(x - 6)(x - 10) ← a is a multiplier

To find a substitute (8, 2) into the equation

2 = a(2)(- 2) = - 4a ( divide both sides by - 4 )

a = - [tex]\frac{1}{2}[/tex]

Hence

y = - [tex]\frac{1}{2}[/tex](x - 6)(x - 10) ← expand factors

y = - [tex]\frac{1}{2}[/tex](x² - 16x + 60) ← distribute

y = - [tex]\frac{1}{2}[/tex] x² + 8x - 30

I hope it’s correct

Answer:

65 men

91 women

Step-by-step explanation:

the ratio is 5 to 7 and there are 156 total

5+7 is 12

so this gives us

5/12*156=65 men

7/12*156=91 women

65 + 91 = 156

Answer:

If you could insert a picture of the graphs that would help! thank you!

Step-by-step explanation:

Answer:

x = -9

Step-by-step explanation:

Multiply both sides by √(x - 6) to eliminate the fraction:

√(3x) = 3√(x - 6)

Now square both sides:  

3x = 9(x - 6), or 3x = 9x - 54.  

Combining the x terms results in -6x = -54, and thus x = 9.

Answer:

The correct answer is option D.  x = 9

Step-by-step explanation:

From the attached question we get an expression,

√3x/√(x - 6) = 3

To find the solution of given expression

√3x/√(x - 6) = 3

Squaring both side we get,

3x/(x - 6) = 9

3x = 9 * (x - 6)

3x = 9x - 54

9x - 3x = 54

6x = 54

x = 54/6 = 9

Therefore the correct option is D.  x = 9