A group of 12 students is deciding whether to go to the science center of the zoo. Science center tickets are 3 for $36.75 and zoo tickets are 4 for $51.
How much will a group of 12 students save by choosing the science center?

Since 87 + 33 = 120 and all angles in a triangle must add up to 180 degrees, the measure of angle A is 20 degrees.

Angle A is 20 degrees in length. This is so because the sum of the angles in a triangle must be 180 degrees, and the two arcs that angle A intercepts have measurements of 87 degrees and 33 degrees. In other words, the remaining angle must be 180 - (87 + 33), or 180 - 120, which is equivalent to 20 degrees. As a result, angle A is 20 degrees in length.The length of Angle A is 20 degrees. This is true since a triangle's total angles must equal 180 degrees, and angle A intercepts two arcs that measure 87 degrees and 33 degrees, respectively. In other words, the angle that remains must be 180 - (87 + 33), or 180 - 120, or 20 degrees. As a result, angle A has a length of 20 degrees.

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Answer:

13 cm

Step-by-step explanation:

The triangle perimeter size does not change because all the components rotate and reflect together.

The solution of the given linear system of equations is x = 2, y = 1 and z = 2.

Given that the linear system of equations is

2x + 4y + 2z = 16-2x - 3y + z = -52x + 2y - 3z = -3

To solve the system of equations by Cramer's rule method, arrange them in the form of Ax = B as below:

A = [2, 4, 2; -2, -3, 1; 2, 2, -3], x = [x, y, z] and B = [16, -5, -3]

To find the inverse of the coefficient matrix A⁻¹, first, find the determinant of A as below:

|A| = 2[-3 - 2] - 4[-2 + 2] + 2[-8 + 1] = -12

The determinant is non-zero, hence A is invertible

A⁻¹ = 1/|A| [adj A]

where adj A is the transpose of the cofactor matrix [C] of A:

adj A = [C]T

So, we find [C] by replacing each element of A with its cofactor and taking its transpose matrix as below:

C = [5, 2, 6; 2, -2, 2; -4, -4, -4]

Then [C]T = [5, 2, -4; 2, -2, -4; 6, 2, -4]So, A⁻¹ = 1/|A| [adj A] = 1/(-12) [5, 2, -4; 2, -2, -4; 6, 2, -4] = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2]

To solve the system of equations, we have x = A⁻¹B as below:

x = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2][16; -5; -3] = [2; 1; 2]

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Answer:

Tom wont need a longer ladder.

Step-by-step explanation:

Answer:

No the ladder is long enough.

Step-by-step explanation:

30x30=900

4x4=16

Sq. Root of (900+16)= 30.27ft distance from the ground to the roof, 4 ft away from the house.

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

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Answer:

AB = √(20^2 + 21^2) = √841 = 29

sin A = 21/29, cos A = 20/29, tan A = 21/20

If MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

The F statistic is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). Therefore, to increase the value of the F statistic, either the numerator (MSbetween) needs to increase, or the denominator (MSwithin) needs to decrease.

So, the answer is:

a. MSwithin > MSbetween

If the variance within groups (MSwithin) is reduced or the variance between groups (MSbetween) is increased, the F statistic will increase. Therefore, if MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

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Answer:

No. It is not possible to construct a triangle with lengths of its sides 4cm, 5cm and 9cm because the sum of two sides is not greater than the third side:

5 + 4 is not greater than 9.

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The slope of the roof is 0.25

What is a slope ?

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies).

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. And b is the value of b at the y-intercept (0, b).

To find slope

= 6.25 / 25

= 0.25

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Answer:

y = 4x + 6

Step-by-step explanation:

Turn the equation we are given into slope-intercept form.

y - 5 = -1/4(x + 8)

y - 5 = -1/4x - 2

y = -1/4x + 3

The slope of a perpendicular line is the opposite reciprocal of the original line.

-1/4 -> 4/1 -> 4

Find the new y-intercept using the point given.

y = 4x + b

2 = 4(-1) + b

2 = -4 + b

6 = b

Fill in everything we solved for.

y = 4x + 6

Best of Luck!

Answer:

50272

Step-by-step explanation:

Okay how I solve these equations is I take the problem apart like this:

3142 = 3000 + 100 + 40 + 2

Now we multiply each number by 16:

3000 * 16 = 48000

100 * 16 = 1600

40 * 16 = 640

2 * 16 = 32

Then we add all the totals together:

48000 + 1600 + 640 + 32 = 50272

Hope this Helps ;)

SOLUTIONS

Solve a given equations or algebraic symbols?

(A)

(B)

(C)

(D)

Answer:

x = 5 y − 35

Step-by-step explanation:

hope that helps

Brainliest if correct?

Answer:

Step-by-step explanation:

we calculate how much 0.3% is from 3280

y=3280*0.3/100=9.84$

months in 9y

12*9=108

the interest of 9y

108y=1062.72$

the sum of interest + the money borrowed

1062.72+3280=4342.72$

Answer And Explanation

Answer:

He neither earn profit nor gain loss

Step-by-step explanation:

Because he gain profit of 25 % by selling at price of 625 and gain loss of 25 % by selling second book at price of 375.

So if you add these profit and loss

    625 +375 = 1000

1000 which is his actual money

42 red blood cells are needed to make a line 1 inch long

The diameter of a red blood cell is 6 x \(10^{-6}\) m,

so we need to determine how many cells can fit in a

line 1 inch long (2.54 x\(10^{-5}\) m).

Dividing the length by the diameter gives the number of cells:

2.54 x \(10^{-5}\) m / 6 x \(10^{-6}\) m = 42.33.

So, approximately 42 red blood cells are needed to make a line 1 inch long.

This highlights the small size of red blood cells and the remarkable ability of the human body to produce and maintain billions of these cells for proper blood circulation and oxygen delivery.

Red blood cells, also known as erythrocytes, are one of the main types of blood cells. They are biconcave discs with a diameter of about 7.5 micrometers, and their primary function is to transport oxygen from the lungs to the tissues and carbon dioxide from the tissues to the lungs.

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the list of all possible outcomes is: {Comedy on Friday, Action on Friday, Comedy on Saturday, Action on Saturday}

What is possibility?

Possibility refers to the likelihood or chance that something may occur or be true. It is often expressed as a probability or a percentage, which indicates the relative frequency with which an event is expected to happen.

In everyday language, possibility is often used to describe something that could happen or be true, but is not necessarily guaranteed. For example, if there is a 50% chance of rain tomorrow, it is possible that it will rain, but it is not certain.

In mathematics and statistics, possibility is often used in the context of probability theory, which is the branch of mathematics that deals with the study of random events and their probabilities.

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Answer:

16.7% (to 3sf)

Step-by-step explanation:

Percentage decrease

= \(\frac{42-35}{42}\) × 100%

= \(\frac{7}{42}\) × 100%

= \(\frac{1}{6}\) × 100%

= 16.7% (to 3sf)

Answer:

see below

Step-by-step explanation:

Assuming the comma means and

a) P(A , E) = P(A) * P(E) = .1 * .5 = .05

b) P( A, L, E) =  P(A) * P(L) *P(E) = .1 *.4* .5 = .002

C This means that it snows in Abbostford, Lehtbridge and Estevan today  is .002 or .2%

To find the point of intersection between the curves r1(t) and r2(s), we need to equate their respective coordinates.

Equating the x-coordinates, we have t = 5 - s. Equating the y-coordinates, we have 3 - t = s - 2. Solving these two equations simultaneously, we can find the values of t and s. Substituting the value of s in terms of t into r1(t), we can find the corresponding (x, y, z) coordinates of the point of intersection.

To find the angle of intersection, theta, between the curves, we can calculate the dot product of the tangent vectors of the curves at the point of intersection and then find the angle using the dot product formula. The tangent vectors can be obtained by taking the derivatives of the respective parametric equations. Finally, we can use trigonometric functions to find the angle in degrees.

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Answer:

First, we find the area of the bread.

\(8 \times 5 = 40\)

Now, we need to divide this by 16 to get the size of each piece.

\(40 \div 16 = 2.5\)

Each piece will be:

\( {2.5cm}^{2} \)

Answer:

7x-2 = 12x-22

-7x

-2=5x-22

+22

20=5x

÷5

x=4

KL is 7x-2, so substitute the value of x.

7 x 4 - 2 = 26

KL = 26

Hope this helps!

The three positive numbers are 2, 2, and 2 and their sum is 6, and the sum of their squares is 12.

To minimize the sum of squares given the constraint,

let's set up the Lagrangian as follows:

L(a, b, c, λ) = a² + b² + c² - λ(a + b + c - 6)

Taking the partial derivatives with respect to each variable, we have:

∂L/∂a = 2a - λ = 0

∂L/∂b = 2b - λ = 0

∂L/∂c = 2c - λ = 0

∂L/∂λ = -(a + b + c - 6) = 0

From the first three equations, we find that 2a = 2b = 2c = λ.

Since a, b, and c are positive, we can conclude that a = b = c.

Substituting this into the fourth equation, we have:

-(3a - 6) = 0

3a = 6

a = 2

Therefore, the three positive numbers are a = b = c = 2.

The sum of their squares is 2² + 2² + 2² = 12.

Hence, the three positive numbers whose sum is 6 and the sum of whose squares is as small as possible are 2, 2, and 2. The sum of their squares is 12.

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Answer:

Step-by-step explanation:

5th term is 6 and the 7th term is 48, we know the nth term for a GP is  arn−1

 so let's substitute the given information in that formula for the nth term

ar3=6

  ar6=48

ar6ar3=486

The  a

and  a

cancelout hence we remain with  r3=8

 take a cube root on both sides and we end up having  r=2

Substitute the value of r in any given equation to get the value of a

ar3=6

a(2)3=6

8a=6

a=34

The formula for the nth term of this GP is given by  34(2n−1)

And when you substitute the value of n in the above formula of nth term you will get the following values; 3/4, 3/2, 3, 6…

The patient is recieving nearly 35.5 miligrams of the drugs for  per kilogram per 24 hours.

First, we need to convert the child's weight from pounds to kilograms:

99 lbs / 2.205 = 44.9 kg

Next, we calculate the recommended dose for this weight:

40 mg/kg/24h x 44.9 kg = 1796 mg/24h

Since the recommended dose is divided into four equal doses, each dose should be:

1796 mg/24h ÷ 4 doses = 449 mg/dose

However, the physician ordered 400 mg every 6 hours, which is not the same as 449 mg every 6 hours. To calculate the actual dose per kilogram per 24 hours, we need to convert the ordered dose to the recommended dose:

400 mg/dose x 4 doses = 1600 mg/24h

Then, we divide the actual dose by the child's weight in kilograms:

1600 mg/24h ÷ 44.9 kg = 35.6 mg/kg/24h

Therefore, the patient is receiving 35.6 mg/kg/24h, which is slightly lower than the recommended dose of 40 mg/kg/24h.

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Answer:

they go around

Step-by-step explanation: