The ratio of adults to students on a class field trip is 2 to 5. If there are 12 more students than adults, which proportion and solution represent this situation?

Step-by-step explanation:

(2) (x+2)^2 + (-15x -3)

I hope this will be helpful for you.

Answer:

[tex]2(x + 2)^{2} + (-15x - 3)[/tex]

The guy above is correct

Proof :

[tex]2(x + 2)^{2} - 15x - 3 \\ 2((x + 2)(x + 2) - 15x - 3 \\ 2( {x}^{2} + 4x + 4) - 15x - 3[/tex]

[tex]2 {x}^{2} + 8x - 15x + 8 - 3 \\ 2 {x}^{2} - 7x + 5[/tex]

My workings are in the picture

My asnwer was 5/2 and -1

Answer:

y= -7

Step-by-step explanation:

This line is a horizontal line.

Horizontal lines all have the same form of y=k (where k is the y-intercept of the horizontal line).

The y-intercept is the point where the line meets the y-axis (the vertical axis). For this line, the y-intercept is in between -6 and -8, making it: (0,-7) or just -7.

Let's return to the form for horizontal lines.

y= k

The y-intercept is -7. Substitute -7 in for k.

y= -7

The equation of the line is y= -7

Answer:  The difference is approximately $44. Remember that is not an exact amount because the weeks are approximated and the second offer was also approximated.

Step-by-step explanation:

If one has $61,100 and the other has 63,400 annually which means that is the amount they will be offered a year. So first we need to determine how many weeks are in a year.There are approximately 52 weeks in one year so we will divide the salaries by 52 to find how much they each offer in one week.

First Offer:  61,100 / 52 =  1175  

Second Offer:  63,400/52=  approximately 1219    

Now find the difference between the numbers

1219. - 1175 =  $44

The difference in weekly pay for these two job will be around $0.04k.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Number of weeks in 1 year = number of weeks in 1 month × 12

Number of weeks in 1 year = 4 × 12 = 48

Annual salary in the first job = $61.1k

So weekly salary of first job =$1.28k

Annual salary in the second job = $63.4k

So weekly salary of second job = $1.32k per week

Difference between weekly pay = 1.32 - 1.28 = 0.04k

Hence "The difference in weekly pay for these two job will be around $0.04k".

To learn more about the arithmetic operators,

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Answer:

A

Step-by-step explanation:

The simpler way to calculate this question is just to calculate A and B

A - 4 x (7+2) = 4 x 9 = 36

B - (4 x 7) + 2 = 28 + 2 = 30

A = 36

=> Thus, our answer is A

Hope this helps!

Answer:

A. 4 * (7+2)

Step-by-step explanation:

Let's evaluate choice A and B. Solve each expression according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

The option that equals 36 will be the correct choice.

A.

4 * (7+2)

Solve the parentheses first. Add 7 and 2.

4 * (9)

Multiply 4 and 9.

36

B.

(4*7)+2

Solve the parentheses first. Multiply 4 and 7.

(28)+2

Add 28 and 2.

30

When evaluated, choice A equals 36. Therefore, A is correct. When the parentheses are arranged like so: 4 * (7+2) it will be equivalent to 36.

Answer:

The crowd would cover an area of 100000 square feet of the field.

Step-by-step explanation:

The length of the football field = 1[tex]\frac{1}{2}[/tex] miles

1 mile = 5280 feet

So that, 1[tex]\frac{1}{2}[/tex] miles = 7920 feet

Given that the field was 12 feet deep on both sides implies that the width = 24 feet.

To estimate the size of the crowd,

length of field = 5000 feet

width = 20

Area of the field covered by the crowd = length × width

                                              = 5000 × 20

                                              = 100000

The crowd would cover an area of 100000 square feet.

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

[tex]\triangle ABC[/tex] represents the 1st angle of elevation of sun i.e.  58°

[tex]\triangle ABD[/tex] represents the 2nd angle of elevation of sun i.e.  36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = [tex]h[/tex] m

Let side BC = [tex]x[/tex] m

Now, let us apply tangent rules in [tex]\triangle ABC, \triangle ABD[/tex] one by one:

[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)[/tex]

[tex]tan36^\circ = \dfrac{h}{x+90}[/tex]

Putting value of [tex]x[/tex] using equation (1):

[tex]tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}[/tex]

119.45 m is the height of pole.

Answer:

$578.87

Step-by-step explanation:

Find the area made by the circle made by the 3 ft. walk:

Radius = 17 + 3 = 20

Area = 22/7 x 20 x20 = 1257.14

Find the area made by the pond:

Area = 22/7 x 17 x 17 = 908.29

Subtract area 2 from area 1:

1257.14 - 908.29 = 348.85

Muliply this area by the cost er squar foot:

348.85 x $1.66 = 579.09

It depends on the value of pi used

Answer:

y2=16-x

x=0

y2=16-0

y2=16

y2/2=16/2

y=8

Answer:

quantity of red paint =  12.5 gallons

quantity of blue paint =  7.5  gallons

Step-by-step explanation:

Ratio of red and blue paint : 5:3

in ratio

a:b = ax:bx

let the

quantity of red paint be 5x

quantity of blue paint be 3x

then quantity of purple paint = quantity of red paint  + quantity of blue paint

                                                  = 8x

given quantity of purple paint is 20 gallons

thus,

8x = 20

x = 20/8 = 2.5

thus,

quantity of red paint = 5x = 5*2.5 = 12.5 gallons

quantity of blue paint = 3x = 3x*2.5 = 7.5  gallons

Answer:

7 and 12.5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The leading coefficient is the coefficient with a variable with the greatest exponent.The exponent is the number you would say "the power to". What I mean is let's say you have this number: [tex]3^{2}[/tex] . The exponent would be 2 in this equation because it's saying what power 3 is too. Therefore, 5 is the leading coefficient.

Answer:

the answer is 8. just think of it as subtraction. subtract +6 from +14. then you get the answer for +14+-6.

Answer:

This was an increase of 22%

Step-by-step explanation:

Given:

Initial/Old amount = $438.00

New amount = $534.36

The percentage increase = [tex] \frac{new amount - old amount}{old amount}*100 [/tex]

% increase = [tex] \frac{534.36 - 438.00}{438.00}*100 [/tex]

[tex] = \frac{96.36}{438.00}*100 = \frac{96.36*100}{438.00} [/tex]

[tex] = \frac{9636}{438.00} = 22 [/tex]

This was an increase of 22%.

Answer:

0.00387

To convert from meters to kilometers, you must divide the number pf meters by 1000.

3.87 ÷ 1000 = 0.00387.

So, that is the answer. Hope it helps!

Answer:

y=-2x+15

Step-by-step explanation:

First, write out the equation in slope-intercept form, with what you already have:

[tex]y=-2x+b[/tex]

Let "b" represent the y-intercept.

To find the y-intercept, substitute the point (6,3) in for the "x" and "y" variable of the equation and solve for "b":

[tex]3=-2(6)+b\\3=-12+b\\3+12=-12+12+b\\15=b[/tex]

Therefore, your y-intercept is 15.

That means your equation is slope-intercept form is y=-2x+15.

Answer:

3

Step-by-step explanation:

because it's being intersected

hope I helped?

Answer:

5/14

Step-by-step explanation:

you would just add the number of marbles which is 14 and add the green and red marbles which is 5 and your answer is 5/14

Probability helps us to know the chances of an event occurring. The probability of choosing a green or red marble from the bag is 5/14.

Probability helps us to know the chances of an event occurring. It is always the ratio of desired outcomes or the sample that is needed to the total number of outcomes.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that the bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles.

Now, the total number of marbles in the bag is 14.

Therefore, the probability of choosing a green or red marble from the bag is,

Probability = (Number of green and red marbles)/(Total number of marbles)

                  = (1+4)/(2+1+7+4)

                  = 5/14

Hence, the probability of choosing a green or red marble from the bag is 5/14.

Learn more about Probability:

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Answer:

1,3,4,6 answer

Step-by-step explanation:

Answer:

y = 4x + 3

Step-by-step explanation:

If he has x seed packets, Johnny can grow 4 * x = 4x plants. The 3 is a constant because he already has 3 so the equation is y = 4x + 3.

Answer:

x=3

Step-by-step explanation:

Hello,

The first thing you do is set up your equation, and we are solving for x so we are going to get x by itself on one side of the = sign.

       2x/3+1=3        First thing: subtract 1 from BOTH sides.

               -1  -1

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

          2x/3=2       Multipliy by 3 on both sides

              *3 *3

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

            2x=6         Divide by 2 on both sides

             /2 /2

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

           x=3

I hope this helped you!!!

Answer:

0.33

Step-by-step explanation:

We would like to find the probability that both beads are aqua.

There are 6 aqua beads. Let's calculate the number of ways we can select 2 aqua beads from these 6. We use combinations, which is [tex]_6C_2=\frac{6!}{(6-2)!*2!}[/tex], where the n! means n * (n - 1) * (n - 2) * ... * 2 * 1.

The value of the expression is:

[tex]_6C_2=\frac{6!}{(6-2)!*2!}=\frac{720}{24*2} =15[/tex]

So there are 15 ways to choose 2 aqua beads.

Now let's calculate the number of ways we can select any 2 beads. There are 6 + 4 = 10 beads in total, so we do the same thing as before using combinations:

[tex]_{10}C_2=\frac{10!}{(10-2)!*2!} =\frac{3628800}{40320*2} =45[/tex]

Our fraction is thus:

15 / 45 = 1/3 ≈ 0.33

The answer is thus 0.33.

~ an aesthetics lover

Answer: 3 people ordered soup.

Step-by-step explanation:

Let x be the number of people ordered salad and y  be the number of people ordered soup.

As per given,

x=2y           (i)

7.50x+6.25y= 63.75          (ii)

Substitute value of c =2y in (ii) , we get

7.50(2y)+6.25y= 63.75

⇒ 15y+6.25y =  63.75

⇒21.25y =  63.75

⇒ y= 3   [divide both sides by 21.25]

Then, x= 2(3) =6

So 6 people ordered salad and 3 people ordered soup.

Answer:

4 units

Step-by-step explanation:

The volume of a square pyramid is (a²)*h/3

256=a²*12/3

256=a²*4

256/4=a²

64=a²

a=8

Now we know that the square is 8 by 8.

The volume of a square prism is a²h

256=64h

256/64=h

h=4

Also, a square pyramid is 1/3 the volume of a square prism.

12÷3=4

Answer:

the answer is C    4 units

Step-by-step explanation:

Answer:

108 ft long

Step-by-step explanation:

they both form similar triangles like shape

therefore

[tex] \frac{4}{9} = \frac{48}{x} [/tex]

[tex]x = \frac{9(48)}{4} [/tex]

[tex]x = 108[/tex]

Answer:

1/6

Step-by-step explanation:

For a set of vectors a, b and c to be linearly dependent, the linear combination of the set of vectors must be zero.

C1a + C2b + C3c = 0

From the question, we are given the set S={u−3v,v−2w,w−ku}, the corresponding vectors are a(0, -3, 1), b(-2,1,0) and c(1,0,-k)

The values in parenthesis are the ccoefficients of w, v and u respectively.

On writing this vector as a linear combination, we will have;

C1(0, -3, 1) + C2(-2,1,0) + C3(1,0,-k) = (0,0,0)

0-2C2+C3 = 0........ 1

-3C1+C2 = 0 ........... 2

C1-kC3 = 0 ….......... 3

From equation 2, 3C1 = C2

Substituting into 1, -2(3C1)+C3 = 0

-6C1+C3 = 0

-6C1 = -C3

6C1 = C3.…..4

Substitute 4 into 3 to have

C1-k(6C1) = 0

C1 = k6C1

6k = 1

k = 1/6

Hence the value of k for the set of vectors to be linearly dependent is 1/6

Answer: 62°

Step-by-step explanation:

apply concept: the interior angle sum of triangle is = 180°

          a+b+c=180

a+68.5+49.5=180

            a+118=180

                  a=62

Answer:

Step-by-step explanation:

Since it's a triangle it's interior angles sum up to 180° .

In order to find x add up all it's known interior angles and subtract it from 180° to find x.

That's

x + 68.5 + 49.5 = 180

x + 118 = 180

x = 180 - 118

We have the final answer as

Hope this helps you

Answer:

The heaviest 5% of fruits weigh more than 747.81 grams.

Step-by-step explanation:

We are given that a particular fruit's weights are normally distributed, with a mean of 733 grams and a standard deviation of 9 grams.

Let X = weights of the fruits

The z-score probability distribution for the normal distribution is given by;

                              Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean weight = 733 grams

            [tex]\sigma[/tex] = standard deviation = 9 grams

Now, we have to find that heaviest 5% of fruits weigh more than how many grams, that means;

                    P(X > x) = 0.05       {where x is the required weight}

                    P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-733}{9}[/tex] ) = 0.05

                    P(Z > [tex]\frac{x-733}{9}[/tex] ) = 0.05

In the z table the critical value of z that represents the top 5% of the area is given as 1.645, that means;

                               [tex]\frac{x-733}{9}=1.645[/tex]

                              [tex]{x-733}}=1.645\times 9[/tex]

                              [tex]x = 733 + 14.81[/tex]

                              x = 747.81 grams

Hence, the heaviest 5% of fruits weigh more than 747.81 grams.

Answer:

Standard form:

Simplify the words.

6,090,036

Expanded form:

Take the standard number and expand it.

6000000 + 90000 + 30 + 6

I'm sorry if I misunderstood.

Good luck though! :)

Please add Brainliest if you'd like, not that it matters.

Answer:

Total number of votes- 145,000

Votes secured by winning candidate- 76,850

Step-by-step explanation:

Candidate A- 47%

Candidate B- 53%

6% difference or 8700 votes so

6%=8700

1%=1450

100%=145,000

53%= 76,850

Answer:

RK= 13      SK= 12

Step-by-step explanation

First, we find the missing length of RK using the given information: 65-52=13

Then we divide 65 by 13 to get a scale factor: 65/13=5

(To check, we multipuly: 13*5=65)

We then apply the scale factor to MK to find SK: 60/5=12

(To check we multipuly: 5*12=60)

We now have our answers: RK:13, SK:12