Two families go to a zoo. The Smith family of two adults and three children pay £61. The Jones family of three adults and five children pay £96. Work out the cost of an adult ticket and the cost of a child ticket. In your working, let 'a' stand for an adult ticket and 'c' stand for a child ticket.​

The system of equations models this problem:

x + y = 405

y = 8x

The correct answer is an option (c)

Here, the variable x represents the number of angelfish Carlos bought and the variable y represents the number of parrotfish he bought.

Carlos bought 8 times as many parrotfish as angelfish.

From this statement we get an equation,

y = 8x

Carlos bought 405 tropical fish for a museum display.

This means that the total number of fish = 405

so, we get an equation,

x + y = 405

Therefore, the system of equations would be,

x + y = 405

y = 8x

The correct answer is an option (c)

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Answer:

y=85°

p=100°

Step-by-step explanation:

Corresponding Angles Theorem

Alternate Exterior Angles Theorem

Answer:

y=85°

p=100°

I hope you get this right!!

:)

The Longest Increasing Subsequence (LIS) problem is a classic problem in dynamic programming. Given a sequence of numbers, the problem is to find the longest subsequence in which the numbers are in increasing order. For example, given the sequence {3, 1, 5, 2, 4}, the longest increasing subsequence is {1, 2, 4}, which has length 3.

The LIS problem can be solved using dynamic programming by defining an array to store the length of the longest increasing subsequence that ends at each position in the sequence. The array is initialized to 1, and then for each position i in the sequence, the length of the longest increasing subsequence that ends at i is calculated by finding the maximum length of any subsequence that ends at a position j < i and has a smaller value than the value at i. The final solution is the maximum length of any subsequence in the array.

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SOLUTION:

Step 1:

In this question, we have that the Quadrilateral ABCD will be dilated about the origin by a scale factor of 1/3 and then reflected across the y-axis:

From the graph, we can see that:

Step 2:

We need to dilate about the origin by a scale factor of 1/3, then

we have that:

Step 3 :

We need to reflect across the y-axis:

( x , y ) ------- ( -x, y )

From the graph,

a) The original polygon is in colour Red

b) The dilated image of the original polygon is in colour Blue

c) The reflection of the dilated image is in colour Green.

If Mr. yuan wants to use his credit to pay off the full amount that another customer's balance, then he can pay off for Wenner.

Customer          Balance ($)

Girardi                -85.23

Lewis                  20.44

Stein                   116.33

Yuan                    13.50

Wenner               -9.85

As he got the balance of -9.85 and Mr. yuan got the balance of 13.50. About the above problem is based on financial literacy which is the ability to understand and make full of our financial skills. Some of the basics of financial literacy which we can have practical applications are such as budgeting, banking, handling credit and debt, and investing. Financial literacy is essential just to avoid higher levels of debt and to have enough income for retirement.

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We can conclude that the value of r(2) which is -6 and x - 2 is not the factor for r(x).

So, we know that the equation is:

Now, calculate the equation when x = 2.

Now, we can conclude that:

Therefore, we can conclude that the value of r(2) which is -6 and x - 2 is not the factor for r(x).

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The point that is located at the ordered pair (4, -2) is given as follows:

Point B.

The general format of an ordered pair is given as follows:

(x,y).

In which the coordinates are given as follows:

On the coordinate plane, we have that:

Hence the coordinates for this problem are given as follows:

A(-2, 4), B(4, -2), C(-4, 2) and D(2, -4).

The graph is given by the image presented at the end of the answer.

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The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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(6,4) \(90^{o}\) around the origin is (4, - 6) by rotating anticlockwise.

Every point of a preimage is transformed in a plane via a rotation that rotates it around a fixed point at a certain angle and direction. The fixed point is referred to as the rotational center. The term "angle of rotation" refers to the rotation's magnitude and is expressed in degrees. Measure the given angle counterclockwise using a protractor.

The following principles make it straightforward to do a few rotations in the coordinate plane.

(6,4) \(90^{o}\) around the origin is (4, - 6).

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Answer:

See below

Step-by-step explanation:

The most important info is the rate ft^2 / min and how many minutes it took to mow.

From this, we need to know how much total area there is. We do this by multiplying the rate by the time.

\( \frac{ 4{ft}^{2} }{minute} \times 29minutes = 116 {ft}^{2} \)

Then we need to write out the sum of the whole area in terms of length times width

\(6ft \times 14 ft + x \times 4ft = 116 {ft}^{2} \)

Notice how we put x for the unknown variable, this turns it into an easy peasy algebra problem. I leave that to you, solve for x

molarity = moles of solute/liters of solution

44.9/16.9 = 2.66

Answer: 2.66

Answer:

Either 1.59 or 2.66

Step-by-step explanation:

I'm not sure but I think it's 1.59 more than 2.66

Answer:

1) word form

three million,two hundred and ninety eight thousand and seventy six

expanded form

5000000+3000+87

2)5,003,087

3)64,000,239

The measure of angle APB in the intersecting chords is 10⁰.

The measure of angle APB is calculated by applying intersecting chord theorem which that the angle at tangent is half of the arc angle of the two intersecting chords.

The value of m∠APB is calculated as follows;

m∠APB = ¹/₂ (arc AC - arc AB ) ( exterior intersecting secants)

The value of arc angle AC = 80⁰

The value of arc angle AB = 60⁰

Now substitute and solve for the value of angle APB as follows;

m∠APB = ¹/₂ (80 - 60 )

m∠APB = ¹/₂ ( 20 )

m∠APB = 10⁰

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The complete question is below:

In the accompanying diagram, tangent PA and secant PBC are drawn to circle O from point P. If mAC=80 and mAB=60, what is the measure of angle APB.

Answer:

c

Step-by-step explanation:

Answer:

A. -4

Step-by-step explanation:

Use the gradient formula (y2-y1)/(x2-x1)

Use the coordinates so (-2,17) = (x2, y2) and (-1, 13) = (x1, x2)

so 17-13/-2--1

= -4

Answer:

-4

Step-by-step explanation:

Each time 'x' changes by +1  the value of 'y' changes by -4

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

did you use google.if not use it it is good to use.

Answer:

17/2

Step-by-step explanation:

Work backwards. you have 10, then opposite of subtract 7 is add 7 which gives you 17. then opposite of double is half getting you 8.5 or 17/2

Answer:

Your number is 8.5 or 17/2

Step-by-step explanation:

Let's say your number is equal to the variable n.

Then we can set up an equation for this scenario: 2n - 7 = 10

Now, we need to use algebra to solve:

2n - 7 = 10 → add 7 to both sides

2n = 17 → divide both sides by 2

n = 17/2 = 8.5

Thus, the number you were thinking of was 8.5, or 17/2

Step-by-step explanation:

150 Square Yards =. 194,400 Square Inches. (exact result) Display result asNumberFraction (exact value) A square yardis a unit of area equal to the size of a square that is one yard on a side. It is equal to 9 square feet or about 0.836 square meters. A square inchis a unit of area.

(a) To find the eigenvalues of matrix A, we need to solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.

The matrix A is given as A = [0.6 0.8; 0.9 0]. Subtracting λI from A gives A - λI = [0.6 - λ 0.8; 0.9 0 - λ]. The determinant of A - λI is: det(A - λI) = (0.6 - λ)(-λ) - (0.8)(0.9) = -0.6λ + λ² - 0.72. Setting this determinant equal to zero and solving for λ gives the eigenvalues of A. (b) To find the eigenvectors corresponding to each eigenvalue, we need to solve the equation (A - λI)v = 0, where v is the eigenvector. (c) The long-term growth factor for the population is determined by the dominant eigenvalue of A. Since A is a 2x2 matrix, there will be one dominant eigenvalue and one eigenvalue that is less than 1 in magnitude. The dominant eigenvalue represents the long-term growth factor.

The long-term population distribution is given by the corresponding eigenvector to the dominant eigenvalue. The entries in the eigenvector represent the proportions of the population in each category (juveniles and adults) in the long term.

By calculating the eigenvalues and eigenvectors of matrix A, we can determine the long-term growth factor and population distribution for the given insect population.

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Answer: $46,619

»» 288.44 / 0.7%

»› 41,205

»» 45 x 120.33

»» 5,414

A=41,205

A=5,414

A=46,619

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Answer:

The answer would be $46,619

Step-by-step explanation:

Someone already explained it pretty well, goodluck! :)

Answer:

option D

Step-by-step explanation:

option D is the correct answer .

plz mark my answer as brainlist.

Variance and Standard deviation can tell us the variation of data within a group of samples.

What is a variance?

Variance is a term used in probability theory and statistics to measure how far a group of numbers are spread out from their mean value.

In the context of hypothesis testing, the variance of two groups of data is compared to see if they are statistically significant.

A smaller variance indicates that the data points are closer together, whereas a larger variance indicates that the data points are farther apart.

What is Standard deviation?

The standard deviation is the square root of the variance, and it is used to express the average distance that data points deviate from the mean in a group of samples.

It is used in statistics to measure how tightly a set of data is clustered around its mean.

What is Mean?

The average value of a group of numbers is referred to as the mean.

It is calculated by adding all of the numbers together and then dividing by the total number of numbers.

What is T-value?

The t-value is used to test the null hypothesis, which states that there is no significant difference between two groups of data.

The t-value is calculated by subtracting the mean of one group from the mean of the other group and then dividing by the standard deviation of the two groups combined.

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Answer:

An atom of sodium has 11 proton, 11 electrons, and 12 neutrons.

Answer

\(12\)

Step by step explanation

\(protons = electrons \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 12 = 12\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

1.6 ft.

Step-by-step explanation:

Given that the conical pylons had a radius (r) of 1 foot and a height (h) of 2 foot. The volume of the conical pylons is:

Volume = πr²h/3

Therefore substituting gives:

Volume = π(1)²(2)/3 = 2π/3 ft³

Since the same amount of concrete is used to construct a spherical barrier, hence the volume of the sphere would be the same as the volume of the conical pylon.

Volume of sphere = 4πr³/3

4πr³/3 = 2π/3

2r³ = 1

r³ = 1/2 = 0.5

r = ∛0.5 = 0.8 ft.

Therefore the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.

Answer:

the reasonable prediction for the number of unsuccessful rollls is 15 ÷ 18

Step-by-step explanation:

The computation of the number of unsuccessful rolls is as follow:

For a number cube, the probability of getting 6 would be 1 ÷ 6 and for not getting is 5 ÷ 6

Now for 18 rolls i.e. there is 3 group of 6 so the chance of not getting would be 15 ÷ 18

Hence, the reasonable prediction for the number of unsuccessful rollls is 15 ÷ 18

The same is to be considered

The exponential function that defines the number of teams remaining after n rounds is given as follows:

y = 64(0.5)^x, 0 ≤ x ≤ 6.

The standard definition of an exponential function is given as follows:

y = a(b)^x + c.

In which:

The initial number of teams is of 64, hence the parameter a is given as follows:

a = 64.

Each round, the number of teams is cut by half, as the losers of each game are eliminated, hence the parameter b is given as follows:

b = 0.5.

Hence the function is defined as follows:

y = 64(0.5)^x.

The domain is 0 ≤ x ≤ 6 as:

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Answer:

Step-by-step explanation:

a2 = -2

a + d  =  -2

a + 6d = 7

-5d  =  -9

d  =  9/5

a = -19/5

an  =  a + ( n-1 ) d

an =  -19/5 + ( n-1 ) 9/5