Mr. Tom bought a Paqui #OneChip Challenge for $3.50. He also bought some water for $2.50 per gallon.
He spent $12 total. How many gallons of water did he buy?

Answer:

First don't forget the [ tex ] [ /tex ] in order to execute the latex code.

Step-by-step explanation:

\( \sin A=\frac{5}{\sqrt{89}}sinA= 89 \)

\( \cos AcosA \) = \( \cos \)

The exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is 8√(89)/89

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

\(\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\\)

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

\(|AC|^2 = |AB|^2 + |BC|^2\)

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Given that:

\(\sin A=\dfrac{5}{\sqrt{89}}\)

So, from this, we are given the ratio of perpendicular and hypotenuse from the perspective of angle A.

There must be existing a right triangle with same measure of angle A such that:

Perpendicular's length = P = 5 units

and Hypotenuse' length = H = \(\sqrt{89}\) units.

Using Pythagoras theorem, we get:

Base' length = B as:

\(P^2 + B^2 = H^2\\B = \sqrt{H^2 - P^2}\\\\B = \sqrt{(\sqrt{89})^2 - 5^2}\\\\B = \sqrt{89-25} = \sqrt{64} = 8\)

(took positive root as B is representing length, a non-negative quantity).

Thus, Base is of 8 units length.

Thus, we get:

\(\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\cos(A) = \dfrac{B}{H} = \dfrac{8}{\sqrt{89}}\)

Rationalizing, we get:

\(\cos(A) = \dfrac{8}{\sqrt{89}} =\dfrac{8}{\sqrt{89}} \times \dfrac{\sqrt{89}}{\sqrt{89}} \\\\\cos(A) = \dfrac{8\sqrt{89}}{89}\)

Thus, the exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is \(\dfrac{8\sqrt{89}}{89}\)

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Answer:

Step-by-step explanation:

(Not an answer) but im stuck on the same one! Lol.

According to the Second-Derivative Test for Local Extrema, f(x,y) has a critical point if f x(a,b) = 0 and f y(a,b) = 0, and all second-order partial derivatives of f(x,y) exist in some circular region containing (a,b) as center.

The Second-Derivative Test is as follows:

Case 1: If AC - B2 > 0 and A < 0, then f(x,y) has a local maximum at (a,b).

Case 2: If AC - B2 > 0 and A > 0, then f(x,y) has a local minimum at (a,b).

Case 3: If AC - B2 < 0, then f(x,y) has a saddle point at (a,b).

Case 4: The test fails if AC - B2 = 0. The steps to apply the Second-Derivative Test for Local Extrema are as follows:

Find the critical point of f(x,y). Calculate A, B, and C using second-order partial derivatives of f(x,y). Evaluate AC - B2 and A.

Using the above cases, determine whether f(x,y) has a local maximum, minimum, or a saddle point.

Thus, we need to apply the Second-Derivative Test for Local Extrema to find the local extrema of the function f(x,y). The Second-Derivative Test can be used to determine whether a function has a local minimum, a local maximum, or a saddle point, which can help solve optimization problems in various fields.

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Answer:

a

Step-by-step explanation:

thats what i put

Answer:

Reflect across segment AB, and across AC.

Step-by-step explanation:

Reflecting the triangle across segment AB will move triangle ABC onto DBA, and reflecting it over AC will move triangle ABC onto AEC. Showing that they have the same angles.

To solve the equation 24x equals 2100, we need to divide both sides by 24. This gives us x equals 87.5. Therefore, each dose should contain 87.5 milligrams of the antibiotic.

As we know that the patient needs to receive 2100 milligrams of antibiotic over a period of every 2 hours. To find out how much antibiotic should be given in each dose, we can divide the total amount of antibiotic by the number of doses. This is called the unitary method.

Since the antibiotic is to be given every 2 hours starting immediately for about 48 hours, there are:

48/2 = 24 doses in total.

Therefore, each dose should contain:

2100 mg / 24 = 87.5 milligrams of the antibiotic.

This is equivalent to saying that each dose should contain 1/24th of the total amount of antibiotic needed for the patient.

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After 6 hours, the population of bacteria in the Petri dish would be 4800.

If the population of bacteria in a Petri dish doubles every 2 hours, we can calculate the population at any given time using the formula

P = P₀\(\times 2^{(t/d),\)

where P is the final population, P₀ is the initial population, t is the time elapsed, and d is the doubling time.

In this case, the initial population (P₀) is 600 bacteria, and the doubling time (d) is 2 hours. Let's calculate the population after a certain time, say 6 hours:

\(P = 600 \times 2^{(6/2)}\\P = 600 \times 2^3\\P = 600 \times 8\\P = 4800\)

Therefore, after 6 hours, the population of bacteria in the Petri dish would be 4800.

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The number of incorrect answers is 8.

linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Let,

number correct of answer = x

number of incorrect answer = y

Given that,

Total number of answer  x+y = 30 ......(1)

Total score = x-\(\frac{1}{4}\)y = 20  .......(2)

In equation (2) multiply by -1 on both side.

-x+\(\frac{1}{4}\)y = -20   .......(3)

Now,

Adding both the equation (1) and (3)

x+y-x+\(\frac{1}{4}\)y = 30-20

\(\frac{5}{4} y\) = 10

y = 8

Hence, The number of incorrect answers is 8.

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We want to write and solve an algebraic equation to find how many milliliters of medicine a person uses each month.

The solution is 2 ml per month.

We know that in each pen injector we have 0.75mg of active component in 0.5 mL of liquid (written as 0.75mg/0.5 mL).

So, if the person takes 4 of these in a month, then the amount of mass that you get is given by:

x = 4*0.75mg = 3mg of active component per month.

And the volume that the person takes each month is:

y = 4*0.5 mL = 2 mL

Then, answering the question, the person gets 2 mL each month.

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When a plane intersects only one nappe of a double-napped cone such that it is parallel to a generating line, it forms a parabola.

When a plane intersects only one nappe of a double-napped cone parallel to a generating line, it forms a conic section known as a parabola. This is because a parabola is defined as the set of all points that are equidistant to a fixed point (known as the focus) and a fixed line (known as the directrix).

When a plane intersects a double-napped cone parallel to a generating line, it intersects all the generatrices at the same angle, resulting in a curve that is symmetric and opens in one direction. This curve is a parabola, and it is commonly found in nature, such as the path of a thrown ball, the shape of a satellite dish, or the reflector of a car's headlights.

The properties of a parabola make it useful in various fields, including optics, physics, and engineering, where it is used to model and analyze a wide range of phenomena, such as the trajectory of projectiles, the behavior of lenses and mirrors, and the design of antennas and reflectors.

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Answer:

ok I will help you because I am a nice person:)

Answer:

It will take them 7.89 days

Answer:

the number 3 is being subtracted from it because you want to get by itself

Equation that best models the situation is where c = 11

Living plants are used in phytoremediation technologies to purify contaminated soil, air, and water. According to the definition, it involves "the use of green plants, associated microbes, suitable soil amendments, and agronomic techniques to either contain, remove, or render dangerous environmental toxins harmless." The word is a combination of the Greek words phyto (plant) and remedium (remedy) (restoring balance). Despite being appealing due to its low cost, phytoremediation hasn't been shown to significantly address any environmental issues, at least not to the point where contaminated space has been returned. A cost-effective plant-based method of environmental cleanup called phytoremediation is being proposed. It makes use of plants' capacity to concentrate elements and chemicals from the environment and to detoxify different contaminants. The ability of certain plants, known as hyperaccumulators, to bioaccumulate substances is what causes the concentrating effect. The impact of cleanup is very different. Organic contaminants, which can be destroyed, are typically the main targets for phytoremediation while toxic heavy metals cannot. Several field tests supported the viability of employing plants to clean up the environment.

Let the number of crops needed to remove pollution = c

Since one crop can remove 15 mg of pollution per square meter.

Then, "c" number of crops may remove "15 C" mg of pollutant per square meter.

Now, the total amount of pollution per sq. meter Equals 170 mg

Additionally, it is necessary to reduce pollution to 5 mg per square meter.

Consequently, the equation for the scenario is given by,

Pollutants 'c' crops can remove from the total amount of pollution equal the amount of pollution required, or 170-15c=5.

Upon solving the equation, we get, c= 11.

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Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

Answer

When a input uses two outputs, say we have

5,6

5,8

3,4

6,2

9,1

Notice how 5 uses two instead of one meaning the function is unfunctional

Step-by-step explanation:

Answer:

x = 60

Step-by-step explanation:

The angle 30 is on the same vertical line as the angle that is adjacent to the missing angle x. they form 90 degrees.

Answer:

V=2.8cm^3

Step-by-step explanation:

The volume of a pyramid with a square base should be considered as the 2.8 cubic centimeter.

Since

perimeter of the base is 6.9 cm and the height of the pyramid is 2.8 cm.

So, here

we know that

volume of a pyramid = \(1/3(length * width * height)\)

And,

perimeter of a square = \(4 * length\)

6.9 = 4 x length

So,

length = 1.725

Now the volume is

\(= 1/3 * (1.725 * 1.725 * 2.8)\)

= 2.8

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Answer:

C≈81.68cm is the answer.

The branch of statistics that draws conclusions about a large set of data based on a smaller set of data is often referred to as inferential statistics.

Inferential statistics is the branch of statistics that analyzes a sample to draw conclusions about a larger population. In inferential statistics, we make use of a sample of data to reach conclusions about the population.

For instance, we could gather data from a small sample of voters and use inferential statistics to reach conclusions about a larger population of voters.

Inferential statistics are used to make predictions, generalizations, and decisions about a population based on a sample of data. Inferential statistics allows us to test hypotheses and draw conclusions from the data. In contrast, descriptive statistics describe the basic features of the data in the study.

Inferential statistics is important because it allows us to make decisions and predictions about large populations based on smaller samples of data.

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Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

8 is the correct answer

.

.

.

Answer:

7

Step-by-step explanation:

Jenny is 8 years older than twice her cousin Sue's age.

The 1st equation will be :

J = 8 + 2S ---------(1)

The sum of their ages is less than 32.

The 2nd equation will be :

J + S < 32  ----------------(2)

Now rearrange both equations :

8 + 2S + S < 32

3S < 32 - 8

3S < 24

S < 24/3

S < 8

S = 7

The age of Sue I think will be 7 years.

Hope that help <3

Answer:

0.5 in fraction form its 1/2.

Step-by-step explanation: hope this helps you <3.

The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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