A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?

31 students
40 students
41 students
66 students

\(\bf\huge Question:\)

\(4c-3x=2y - 3\)

We need to find the value of c in the given Equation.

\(\bf\huge \: Solution:\)

\( \sf \longmapsto \: 4c-3x=2y - 3\)

\( \boxed{\bf Add \: 3x \: to \: both \: sides:}\)

\(\sf \longmapsto \: 4c - 3x + \red{ 3x} = 2y - 3 + \red{ 3x}\)

\( \underline{\bf \: \bf On \:Simplification :}\)

\(\sf \longmapsto \: 4c = 2y - 3 + 3x\)

\(\sf \longmapsto4c = 3x + 2y - 3\)

\( \boxed{\bf \: Divide \: both \: side s \: by \: 4 :} \)

\(\sf \longmapsto \: \dfrac{4c}{ \red4} = \dfrac{3x + 2y - 3}{ \red4} \)

\(\underline{ \bf \: \bf On \:Simplification :}\)

\( \sf \longmapsto \: c = \dfrac{3}{4} x + \dfrac{1}{2} y + \dfrac{ - 3}{4} \)

______________________________________

\( \underline{\bf \: Henceforth, The \: value \: of \: c \: is :} \)

\( \boxed{\red{\huge \tt{{c}}= \dfrac{3}{4} x + \dfrac{1}{2} y + \dfrac{ - 3}{4} }}\)

Or it can also be rewritten as :

\( \boxed{\red{\huge \tt \: c = \dfrac{1}{2} y - \dfrac{3}{4} + \dfrac{3}{4} x}}\)

Answer:

Step-by-step explanation:

?

Answer:

f(-1)= -1      

f(3)= -2

Step-by-step explanation:

I am in AP Calculus, I'm smart.  Brainliest????

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)

The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

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Answer:

6

Step-by-step explanation:

X=6

You can cross multiply.

72x3=36x

216=36x

216/36=x

6=x

Answer:

the ratio is the same

Step-by-step explanation:

Girls

12 out of 30

12/30

Divide top and bottom by 6

2/5

Boys

16 out of 40

16/40

Divide top and bottom by 8

2/5

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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The present value of $100 to be received after 3 years at 9% compounded quarterly is $73.67.

The formula for the present value of a future amount under quarterly compounding is:

PV = FV / (1 + r/4)⁴ⁿ

where PV is the present value,

FV is the future value, r is the interest rate per year, and n is the number of years.

In this case, FV = $100, r = 0.09 (9%), n = 3 years, and the interest is compounded quarterly

so the interest rate per quarter is r/4 = 0.0225.

Plugging these values into the formula, we get:

PV = $100 / (1 + 0.0225)¹² = $73.67

Therefore, the present value of $100 to be received after 3 years at 9% compounded quarterly is $73.67.

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25% percent of the females in Math town have brown eyes. To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes

what is percent  ?

A percent is a way of expressing a number as a fraction of 100. The symbol for percent is %, which means "per hundred".

In the given question,

Let's assume that there are 100 people in Math town.

60% of them are males, so there are 60 males and 40 females.

Out of the 60 males, 30% have brown eyes, so there are 18 males with brown eyes.

28% of the entire population have brown eyes, so there are 28 people with brown eyes.

To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes:

28 - 18 = 10

So, there are 10 females with brown eyes.

Out of the 40 females in Math town, what percentage have brown eyes?

10 brown-eyed females out of 40 females is:

10/40 = 0.25 or 25%

Therefore, 25% of the females in Math town have brown eyes.

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Answer:

3.5

Step-by-step explanation:

Test Scores

1, 1, 2, 3, 3, 4, 4, 5, 5, 5

median(middle #)

(3+4)/2 = 7/2 = 3.5

Answer:

3.5

Step-by-step explanation:

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The square root of 9 is 3.

√9=3

Hope this helps :)

Answer:

common denominator = 80        

3/80 and 24/30

Step-by-step explanation:

Same thing as last one, you multiply the denominators of each fraction together. 8x10=80 then multiply the fraction with the opposite denominator, 3x10=30 so 3/80 and 3x8=24 so 24/30.

Answer:

common denominator: 40

3/8 = 15/40

3/10 = 12/40

Step-by-step explanation:

8 x 5 = 40 and 10 × 4 = 40. This means 40 is the common denominator.

To get from 8 to 40 you multiply by 5 and so you multiply 3 by 5. This means the numerator is 15.

To get from 10 to 40 you multiply by 4 and so you multiply 3 by 4. This means the numerator is 12.

Answer:

The water level at Lake Willow is 9 feet after the rain

Step-by-step explanation:

Simply add 23 and -14

-14+23=9

Hope this helps

The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long  is 33.69 degrees

To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.

Given that:

The tree's height is 10 feet.

The length of the shadow is 15 feet.

Let's assume that the tree's height is "h"  feet.

Length of its shadow is represented by "s" feet

The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.

The angle can be determined using the tangent function.

\(tan\theta\) = \(\dfrac{h}{s}\)

Now, substitute the given values:

\(tan\theta\)= \(\dfrac{10}{15}\)

\(tan\theta\) = \(\dfrac{2}{3}\)

The angle of elevation can be obtained by  taking the inverse tangent of 2/3

angle of elevation =\(\tan^-1\dfrac{2}{3}\)

angle of elevation ≈ 33.66 degrees

So, the angle of elevation of the sun is approximately 33.69 degrees.

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Answer:

D. 9 inches

Step-by-step explanation:

(6/2)*3=9

Answer:

I say D.9 inches

Step-by-step explanation:

(6/2)×3=9

I don't know if i'm right though I just calculated the length side of RS

Answer:

$286.80

Step-by-step explanation:

First, find the price after the 150% markup:

478(1.5)

= 717

Now, calculate the price with the 60% discount:

717(0.4)

= 286.8

= $286.80

The angle LKN in the rhombus is 62 degrees.

A rhombus is a quadrilateral that has 4 sides equal to each other. The sum of angles in a rhombus is 360 degrees.

Opposite angles are equal in a rhombus. The diagonals bisect each other at 90 degrees. Adjacent angles add up to 180 degrees.

Therefore, let's find ∠LKN as follows:

m∠JMN = (-x + 69)

m∠LMJ = (-6x + 166)

Therefore,

1 / 2 (-6x + 166) = -x + 69

-3x + 83 = -x + 69

-3x + x = 69 - 83

-2x = -14

x = -14 / -2

x = 7

Therefore,

∠LKN = 1 / 2 (-6x + 166)

∠LKN = 1 / 2 (-6(7) + 166)

∠LKN = 1 / 2 (-42 + 166)

∠LKN = 62 degrees

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Answer:

what can I help you miss

Answer: A' = (1, 5)

              B' = (-3, 5)

              C' = (-3, 2)

              D' = (1, 2)

Step-by-step explanation:

Reflecting across the y-axis provides the opposite x-value.

   Z =  (x, y)    -->    Z' = (-x, y)

A = (-1, 5)       -->     A' = (1, 5)

B = (3, 5)       -->     B' = (-3, 5)

C = (3, 2)       -->     C' = (-3, 2)

D = (-1, 2)       -->     D' = (1, 2)

Answer:

Step-by-step explanation:

To save for a new car, Trafton invested $5,000 in a savings account that earns 6.5% interest, compounded continuously. After four years, he wants to buy a used car for $7,000. How much money will he need to pay in addition to what is in his savings account?

Answer:

The answer is c

The completed square form of the quadratic equation y = 2x² - 7x - 4 is:

y = 2(x - 7/8)² - 121/32

We have,

To complete the square of the quadratic equation y = 2x² - 7x - 4, we can follow these steps:

- Rewrite the quadratic equation in the form y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

- To get the value of h, we can use the formula h = -b/2a, where a = 2,

b = -7.

So,

h = -(-7)/2(2) = 7/4

- To get the value of k, we can substitute h into the equation and simplify.

y = 2(x² - (7/4)x) - 4

= 2(x² - (7/4)x + (7/8)²) - 2(7/8)² - 4

= 2(x - 7/8)² - 121/32

Therefore,

The completed square form of the quadratic equation y = 2x² - 7x - 4 is:

y = 2(x - 7/8)² - 121/32

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Answer:

8.60cm

Step-by-step explanation:

a/sinA=b/sinB

15/sin90⁰=x/sin35⁰

cross multiply

15sin35⁰=xsin90⁰

8.6036=x

x=8.60cm

9. The value of x is 7

10. In the figure  x = 10

11. The relationship is that their sum is 180 degrees

This relationship is known as the Same-Side Interior Angles Theorem.

12. The statement is true.

Supporting statement: If the two lines are parallel, then the alternate exterior angles created by the transversal line are equal

14 < 3 = 94 degrees

9. The value of x is solved using the knowledge of corresponding angles are equal

< A = < B

4x = 3x + 7

x = 7

10. In the figure < 3 and < 6 are alternate internal angles which is equal

7x - 10 = 5x + 10

7x - 5x = 10 + 10

2x = 20

x = 10

11. The relationship between the interior angles on the same side is that their sum is 180 degrees

This relationship is known as the Same-Side Interior Angles Theorem. It is a fundamental concept in geometry and is used to solve problems involving parallel lines and transversals.

12. The statement is true.

Supporting statement: If the two lines are parallel, then the alternate exterior angles created by the transversal line are equal

13. The measure of w is solved using the idea of vertical angels

w + 85 = 148

w = 148 - 85

w = 63

14. The mistake is that < 5 is not corresponding angle to < 2

The correct solution is < 3 = < 5 alternate internal angles

< 3 + 86 = 180 supplementary angles

< 3 = 180 - 86

< 3 = 94 degrees

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Answer:

sitting in his highchair modifies baby

Answer:

yes, each input would have exactly one output if you completed this table.

Step-by-step explanation:

Yes, there is only one output for each input. The table's linear equation provides exactly one value of y for each value of x.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

The general equation of a line is y = mx + c

where m is the slope of the line and c is the intercept.

A linear equation is defined as an equation in which the highest power of the variable is always one.

The table's linear equation provides exactly one value of y for each value of x.

Yes, there is only one output for each input.

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The weight of the male that has a body surface area of 2.3 would be = 108kg

The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.

The formula for BSA = √w×h/3600

The weight of the male = X

The height of the male = 176cm

The BSA = 2.3

From the formula, make w the subject of formula;

w = BSA²× 3600/h

w = 2.3²× 3600/176

w= 5.29×3600 /176

w = 19044/176

w = 108kg

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Answer:

509

Step-by-step explanation:

formula

L = a + (n - 1)*d

Givens

n = 57

a = 5

d = 9

Solution

t = 5 + (57 - 1)*9

t = 5 + 56*9

t = 5 + 504

t = 509

t = 556