help please

The admission fee at an amusement park is $2.00 for children and $5.20 for adults. On a certain day, 355 people entered the park, and the admission fees collected totaled $1334. How many children and how many adults were admitted?


number of children equals------------

number of adults equals---------------

Answer:

a) x²/(6378.137)² + y²/(6378.137)² + z²/(6356.523)² = 1

b) x²/(6378.137)²/(1+m²) + z²/(6356.523)² = 1

Step-by-step explanation:

a)

We know that the general equation of the ellipsoid with center at the origin is  

x²/a² + y²/b² + z²/c² = 1  

Since the north pole is along the z-axis and north pole is at a distance of 6356.523 km from the center, so c = 6356.523  

And the distance between center to a point on the equator is 6378.137 km so we have, a = b = 6378.137  

Thus, the equation of the earth's surface as used by WGS-84 is  

x²/(6378.137)² + y²/(6378.137)² + z²/(6356.523)² = 1

b)

Meridians are traces in planes of the form y=mx, so the equation of paraboloid gives;

x²/(6378.137)² + m²x²/(6378.137)² + z²/(6356.523)² = 1

x²/(6378.137)²/(1+m²) + z²/(6356.523)² = 1

Answer:

Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.

Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.

Step-by-step explanation:

We are given the following hypothesis below;

Let p = proportion of people who write with their left hand

So, Null Hypothesis, \(H_0\) : p = 0.22     {means that the proportion of people who write with their left hand is equal to 0.22}

Alternate Hypothesis, \(H_A\) : p \(\neq\) 0.22      {means that the proportion of people who write with their left hand is different from 0.22}

Now, Type I error states that we conclude that the null hypothesis is rejected when in fact the null hypothesis was actually true. Or in other words, it is the probability of rejecting a true hypothesis.

So, in our question; Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.

Type II error states that we conclude that the null hypothesis is accepted when in fact the null hypothesis was actually false. Or in other words, it is the probability of accepting a false hypothesis.

So, in our question; Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.

The average consumption of the fruit juice would be 7.6 gallons for the year 2006.

Average consumption is derived by dividing the total measured consumption of that municipal service by that consumer during the three months before by three. It refers to the average consumption of a consumer of a municipal service during a certain time.

Utilizing the total of quantities consumed or dispersed over a period of time, typically 12 months, the average monthly consumption can be computed. The average number of units used each month is known as average monthly consumption, stock-outs corrected (CA).

Total consumption of the fruit juice in 2006=2.28x109 gallons.

Total population of the country in year 2006=3x108

Average Consumption=(2.28x109)/(3x108)

                = 7.6 gallons    

Hence the average consumption would be 7.6 gallons per person.

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Answer:

do you have a screenshot of the angle or something? is it a triangle or another shape? anyhwhooo I believe your answer should be 56°

Step-by-step explanation:

48° + 76° = 124°

180° - 124° = 56°

so your answer is 56°

The quantity of pounds of dog food that Mrs. Evans should buy that would be enough for her dog = 720 ounces.

The total number of days the food is required to last = 90 days.

The quantity of dog food in ounce the dog eat per day = 4 × 2 = 8 ounces.

Therefore the quantity of pounds that will be enough for the dog for the whole 90 days would be = ?

That is;

1 day = 8 ounces

90 days = X

Make X the subject of formula;

X = 90× 8

= 720 ounces

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Answer:

The commission is 1925

Step-by-step explanation:

This is because you are taking 3.5% of $55,000. After doing the percent you are left with $1925 which is the commission.

Hope I helped, Have a great day! :-)

The commission of the total sales of $55000 will be $1925.

A specific number in every hundred is what is meant by the percentage. The percentage symbol percent is used to denote a fraction with 100 as the denominator.

The percentage is just like the amount of that value but between 1 to 100 and it is very useful to predict for example if you say 678 then we have to know about the full number also but if you say 80% then it becomes clear.

The percentage is also called the indicating hundredths. Thus, 3% is two-hundredth, which means 3%=3/100=0.03.

Principle amount = $55000

Commision rate = 3.5%

3.5% of 55000 = (3.5 × 55000)/100

3.5% of 55000 = $1925

Hence the 3.5% commission of the amount of $55000 will be $1925.

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Answer:

120(2x² + 3x - 2) or 240x² + 360x - 240

Perimeter = 64x + 28

x = 3

Length = 60ft

Width = 50ft

Step-by-step explanation:

Area = (12x + 24)(20x - 10)

= 12(x + 2).10(2x - 1)

= 120(2x² + 3x - 2)

= 240x² + 360x - 240

Perimeter = 2(12x + 24) + 2(20x - 10)

= 24x + 48 + 40x - 20

= 64x + 28

64x + 28 = 220

64x = 192

x = 3

Length = 12(3) + 24

= 36 + 24

= 60

Width = 20(3) - 10

= 60 - 10

= 50

Answer:

Step-by-step explanation:

The area of the building is given by the formula ...

  A = LW

  A = (12x +24)(20x -10) . . . . . substitute given length and width

__

The perimeter is twice the sum of length and width:

  P = 2(L +W)

  P = 2((12x +24) +(20x -10)) = 2(32x +14)

  P = 64x +28

__

If the perimeter is 220 feet, we can use that fact to find the value of x.

  220 = 64x +28

  192 = 64x . . . . . . . subtract 28

  3 = x . . . . . . . . . . . divide by 64

Then the dimensions of the building are ...

  length = 12x +24 = 12(3) +24 = 60 . . . feet

  width = 20x -10 = 20(3) -10 = 50 . . . feet

The length and width of the building are 60 feet and 50 feet, respectively.

Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

Answer:

?

Step-by-step explanation:

uhhh less than is x < y greater than is x > y

can you please provide more info!

The x intercepts are 0, 1, -2, 2.

What is intercepts?

The term "intercept" refers to the x- and y-intercepts of of a given equation. The x-intercept is the point at which a line crosses the x-axis and the y-intercept is the point at which a line crosses the y-axis.

In the linear equation, we have the general form as y=mx+b

where m and b are constants.

We have to find the x intercept of the given function.

Given equation is \(x^{4} +x^{3} -4x^{2} -4x\)

put this equation equals to 0

x^{4} +x^{3} -4x^{2} -4x = 0

\(x(x^{3} +x^{2} -4x-4)=0\)

from this x = 0

x =1 is also the root of the equation

we get \(x^{2} -4=0\)

from this

x = -2, 2

The intercept are 0,1,2,-2.

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Answer:

146,736

Step-by-step explanation:

6114 divided by 24 is 146,736

The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6

To determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also identified with the presence of arithmetic operations,

These operations are;

From the information given, we have that;

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

collect the like terms

7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6

add the like terms

x^7+10x^4+4x^3-5x^11-10x^6

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Answer:

Sample means and the grand mean

Step-by-step explanation:

The total sum of squares present in the sample can be partitioned into two parts.

1) Within sum of squares ( also called error sum of squares)

2) Between sum of squares

The first part is the sum of squares of deviations of the observations from the sample mean and is called the within sum of squares ( also called error sum of squares).

The second part is the weighted sum of the square of deviations of the sample means from the grand mean and is called between sum of squares.

Thus symbolically

Totastal SS = Within SS + Between SS

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

36y² - 1

Factorize

We have the final answer as

\((y - \frac{1}{6} )(36y + 6)\)

Hope this helps you

Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1

Answer: The given equation is

f(x) = x^{4} - 1

x- and y-intercept of the graph of the function f(x) = x^4 - 1 is

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

A graph of the above point is attached

Step-by-step explanation:

Given equation, f(x) = x^{4} - 1

let's assume the above equation with respect to y to find intercept i.e

y = x^{4} - 1 .........................(i)

Now, for the x-intercept put y = 0 in eq.(i)

So, we get,

0 = x^4 - 1

x^4 = 1

x = -1, +1

from above we get the x-intercept (1,0), (−1,0)

Now, for the y-intercept put x = 0 in eq.(i)

So, we get

y = 0^4 - 1

y = -1

from above we get the y-intercept (0, -1)

Therefore, from all above

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

Graph of the given equation f(x) = x^4 - 1 with intercept is

Answer:

its b !

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

The answer is "Equiangular, Equilateral"

Step-by-step explanation:

please find the complete question in the file.

In this question, the answer is equiangular, in which the triangle was considered an equilateral triangle with 3 parallel inner angles. It's the measurement of each of these interior angles is 60 degrees, inside an equiangular triangle, and although there 3 parallel sides of an equiangular triangle, so it is just like an equilateral triangle.

Based on the sides and angles of a triangle, triangle PQR would be classified as: an equilateral triangle.

Recall:

In the diagram given (see image attached below), we have the following:

PQ = RQ = 14 (congruent sides)

PN = NR = 7 (N is the midpoint of PR)

Therefore:

PR = PN + NR

PR = 7 + 7 = 14

This shows that triangle PQR has equal side lengths measuring 14 units (PQ = RQ = PR = 14).

m<QPR = m<QRP = 60 degrees (two congruent angles).

m<NQR = 180 - (90 + 60) (sum of triangle)

m<NQR = 30 degrees

Therefore:

m<PQR = m<NQR + m<PQN

m<PQR = 30 + 30

m<PQR = 60 degrees.

This means that, triangle PQR has three equal angles measuring 60 degrees each (<PQR = <QPR = <QRP = 60 degrees).

Therefore, based on the sides and angles of a triangle, triangle PQR would be classified as: an equilateral triangle.

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The value of theta where we do not have a vertical asymptote is θ = 0.

The vertical asymptotes happen when the denominator becomes equal to zero.

For our case, we have:

tan(θ) = sin(θ)/cos(θ).

So the vertical asymptotes are for the values of θ where the cosine is equal to zero. Particularly, cos(0) = 1, then in θ = 0 the denominator is not equal to zero, which means that at that value we do not have an asymptote.

Then the correct option is B.

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Answer:

The equations are not equivalent

Step-by-step explanation:

2(3c +2) -2c

6c + 4 - 2c

combine like terms

4c +4 does not equal 4c +2

Answer:

they are NOT equivelent

Step-by-step explanation:

2(3c+2)-2c and 4c + 2

(6c+4)-2c

4c+4>4c+2

Answer:

x = 1

Step-by-step explanation:

5(2x - 8) + 15 = -15

First, let's move the 15 to the opposite side of the equation. We'll do this by subtracting 15 from BOTH sides of the equation.

5(2x - 8) + 15-15 = -15-15

5(2x-8) + 0 = -30

5(2x-8) = -30

Now let's expand that first term.

5(2x)-5(8) = -30

10x - 40 = -30

Now let's move the -40 to the opposite side of the equation. We'll do this by ADDING 40 to both sides of the equation.

10x - 40 + 40 = -30 + 40

10x -0 = 10

10x = 10

Now to solve for x, we divide BOTH sides by 10 to "isolate the variable" aka get x alone.

10x/10 = 10/10

x = 1

The answer is x = 1.

Let's check if our answer is correct!

Original equation: 5(2x - 8) + 15 = -15

Substitute 1 for x.

5(2*1-8) + 15 =

5(2-8) + 15 =

5(-6) + 15 =

-30 + 15 = -15 >>> which is exactly what we started with! So x is 1.

The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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Answer:

87km

Step-by-step explanation:

Volume is proportional to radius cubed, so radius is proportional to the cube root of volume.

Increase volume by a factor of 10^6 and radius increases by a factor of the cube root of 10^6, which is 10^(6/3) = 10^2 = 100.

100 * 0.87 km = 87 km

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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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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