Find all solutions in the interval [0, 2π).
7 tan^3x - 21 tan x = 0

A) pi/3, 2pi/3, 4pi/3, 5pi/3
B) 0, pi/5, π, 6pi/5
C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3
D) 0, pi/3, π, 4pi/3

To determine how long Mrs. Liu can drive before her car runs out of gas, one needs to analyze the slope of the graph that shows the rate of gasoline consumption, know the total capacity of the tank, and perform a calculation to estimate the remaining driving time assuming constant consumption.

The question asks to determine how long Mrs. Liu can drive her car before the gas tank is empty, based on the graph showing the amount of gas left as she drives at a steady speed for 2 hours. To answer this, we need to find the rate at which the gas is being used and then use it to estimate the time until the tank reaches empty.

To find the rate of gasoline consumption, you would typically look at the slope of the graph, which shows the decrease in gas over time. If the graph shows a linear decrease, the slope will give you the rate (e.g., gallons per hour). Suppose the graph indicates that the tank started full and decreased to half over 2 hours. In that case, the consumption rate is half the tank's capacity divided by 2 hours. If you know the total capacity of the tank, you can calculate the driving time until empty.

However, since the actual graph and numerical data are not provided here, we can only guide you through the process hypothetically. With the actual graph, you would:

Remember, this calculation assumes a constant rate of consumption, which may not be accurate in real-life scenarios due to variations in driving conditions and car performances.

Out of 400 students in school, 200 students would want sandwich in school.

The question is asking to predict how many students would want sandwiches for lunch in a school of 400 based on a sample of 24 students where 12 wanted a sandwich.

Calculate the proportion of students in the sample wanting a sandwich: 12/24 = 0.5

Apply the proportion to the larger school: 0.5 x 400 = 200 students.

Answer: [tex]y = 2x + 6[/tex]

Step-by-step explanation:

Let x represents the number of days .

Given : There are 6 quarters in a jar.

Jill adds 2 quarters to the jar every day.

Then, the number of quarters added in x days = 2x

Now, the total number of quarters in the jar after x days = 2x+6

Hence, the linear equation represents the total amount of quarters in the jar after x days will be:-

[tex]y = 2x + 6[/tex]

The number 9 can be expressed as a power of 3 by finding the appropriate exponent that, when raised to the base 3, equals 9. This exponent is 2, making 9 written as a power of 3 to be 3².

To write the number 9 as a power of the base 3, we look for an exponent that can be raised to the base 3 to result in the number 9. This is achieved by recognizing that 3 squared (3²) equals 9. So, 9 expressed as a power of 3 is 3².

When raising a number to a power, such as generating the cubing of exponentials, you cube the digit term normally and multiply the exponent by 3. However, in this case of 9 as a power of 3, we are not cubing but rather finding which power results in the number 9 when using the base 3. The process involves simple experimentation or recollection that 3¹ = 3, 3² = 9, and so on.

In mathematics, writing numbers in exponential form is essential, as it simplifies operations and understanding of scale. It's a useful concept, not only for integer powers but also when dealing with decimal or negative exponents.

The slope intercept form of the given equation of a line is y= -3/2 x -15.

The given equation of the line is -3x-2y=30.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Now,

-3x-2y=30

⇒ -2y=3x+30

⇒ y= -3/2 x -15

Therefore, the slope intercept form of the given equation of a line is y= -3/2 x -15.

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Answer:

the answer is 16

Answer: Olivia needs 110 points on her final exam in order to earn at least a B in Math.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

Here, given that,

Olivia must earn 475 points out of 550 to receive a b in math.

so far she had earned 240 test points

85 quiz point

and 40 homework points.

Solution: 240 + 85 + 40 = 365

Now, we get,

475 - 365 = 110

Hence, Answer: Olivia needs 110 points on her final exam in order to earn at least a B in Math.

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By the definition of the functions of trigonometry, the sine of  is equal to the -coordinate of the point with polar coordinates , giving . Similarly, , since it is the -coordinate of this point. Filling out the rest trigonometric functions then gives

Answer:

30 feet, 24 feet, 24 feet

Step-by-step explanation:

A kite is a quadrilateral with two pairs of congruent adjacent sides.

One of the longer sides measures 30 feet. According to the definition, the kite has two sides of length 30 feet. Let x feet be the length of another side.

The perimeter of the kite is

[tex]2\cdot 30+2\cdot x\ feet[/tex]

Since the kite has a perimeter of 108 feet, we have

[tex]2\cdot 30+2\cdot x=108\\ \\60+2x=108\\ \\2x=108-60\\ \\2x=48\\ \\x=24[/tex]

The length of two another sides is 24 feet. The kite has two sides of 30 feet and two sides of 24 feet.

Answer: Hello mate!

The kite has two equal-length long sides and two equal-length shorter sides. We also know that the perimeter is the addition of the four sides, where we have two long sides, L, and two short sides, S.

Then 2S + 2L = 108ft

S + L = 54 ft

if L = 30 feet

S + 30 ft = 54ft

S = 54ft - 30 ft = 24ft

Then the other long side also has 30ft length, and the two shorter sides have 24ft length.

Answer:

C just did this

Step-by-step explanation:

Answer:

∠ NLO ≅ ∠ NPM Corresponding Parts of Congruent Triangles Are Congruent

Step-by-step explanation:

It's on my chart on the test this is 100% right

Final answer:

Hector used the Angle-Angle-Side Postulate to show congruency between two triangles. Therefore, the corresponding angles are congruent with the CPCTC principle. Thus, option 3 is correct.

Explanation:

Hector claims that ΔLNO ≅ ΔPNM is based on the Angle-Angle-Side Postulate.

Since the triangles are congruent, their corresponding parts must also be congruent.

Therefore, the statement that ∠NLO ≅ ∠NPM is supported by the principle that Corresponding Parts of Congruent Triangles Are Congruent (CPCTC).

The question is about finding the first and second derivatives of y with respect to x. The first derivative dy/dx is found to be (1+t)e^-2t, and the second derivative d2y/dx2 is found to be -2e^-2t.

The derivatives are found by differentiating each function with respect to t first, using the product and chain rules, respectively: the derivatives dy/dt and dx/dt are dy/dt = e^-t - te^-t and dx/dt = e^t. Then, dy/dx can be found as (dy/dt)/(dx/dt), and the second derivative d2y/dx2 can be obtained by differentiating dy/dx with respect to x, which will utilize the quotient rule. Specifically, dy/dx = (e^-t(1+t))/(e^t) which simplifies to (1+t)e^-2t, and after a relatively complex differentiation for d2y/dx2, we get -2e^-2t.

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Answer:

[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]

Step-by-step explanation:

Let premium p for age of a , (p,a)

# An insurance company charges a 35-year old non-smoker an annual premium of $118 for a $100,000 term life insurance policy.

(35,118)

# An insurance company charges a 45-year old non-smoker an annual premium of $218 for a $100,000 term life insurance policy.

(45,218)

# An insurance company charges a 55-year old non-smoker an annual premium of $563 for a $100,000 term life insurance policy.

(55,563)

Let quadratic model be p=Aa²+Ba+C

Substitute the points into equation

[tex]118=35^2A+35B+C[/tex]

[tex]118=1225A+35B+C[/tex] -------------(1)

[tex]218=45^2A+45B+C[/tex]

[tex]218=2025A+45B+C[/tex] -------------(2)

[tex]563=55^2A+55B+C[/tex]

[tex]563=3025A+55B+C[/tex] -------------(3)

Solve system of equation and find out A, B and C using calculator.

[tex]A=\dfrac{49}{40},B=-88,C=\dfrac{13579}{8}[/tex]

Quadratic model:

[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]

Answer:

235 workers

Step-by-step explanation:

Factory operates on a standard work week shift for 5 days = 8 hours per day

In one week working hours are = 8 × 5 = 40 hours.

Company has an order for 7,500 new cars to be delivered in one week.

One car requires time to be fitted with a new hood ornament that requires to install = 1 hour and 15 minutes ( 1.25 hours )

In 40 hours (one week) cars will install with one worker = [tex]\frac{40}{1.25}[/tex] = 32 cars

To fulfill the order of 7,500 cars, Company needs workers = 7,500 ÷ 32 = 234.375 ≈ 235 workers.

235 workers must be assigned this job to meet the deadline.

we know that

a) A box of ground nutmeg weighs [tex]1 1/3[/tex] ounces

b) There are [tex]20[/tex] teaspoons of nutmeg in the box

Step 1

Convert mixed number to an improper fraction

[tex]1\frac{1}{3} \ ounces= \frac{1*3+1}{3}= \frac{4}{3}\ ounces[/tex]

Step 2

By proportion

Find the weight of one teaspoon

[tex]\frac{(4/3)}{20} \frac{ounces}{teaspoons} =\frac{x}{1} \frac{ounces}{teaspoon} \\ \\x= \frac{4}{20*3}\\ \\x= \frac{4}{60}\ ounces\\\\x=\frac{1}{15}\ ounces[/tex]

therefore

the answer is the option

[tex]\frac{1}{15}\ ounces[/tex]