( 7 − 2 ) 2 + 3 ÷ 1 6 (7 − 2) 2 + 3 ÷ 6 1 ​

The slope (m) is equal to the tangent of the angle, so for a 30-degree angle, m = tan(30) = 1/√3. Since the ray contains the origin, the y-intercept (b) is 0. Therefore, the equation of the ray is y = (1/√3)x.

To determine the equation of the ray consisting of the origin and all points whose bearing is 30 degrees, we first need to find the slope of the ray.

The ray y = x, x > 0 contains the origin and all points in the coordinate system whose bearing is 45 degrees. This means that it forms an angle of 45 degrees with the positive x-axis.

Using trigonometry, we can determine that the slope of this ray is tan(45 degrees) = 1.

To find the slope of the ray we're interested in, which forms an angle of 30 degrees with the positive x-axis, we use the same process: tan(30 degrees) = 1/sqrt(3).

Since the ray passes through the origin, its equation will be of the form y = mx, where m is the slope we just calculated.

So the equation of the ray is y = (1/sqrt(3))x.

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The number is 62

What are the basic operations in mathematics?

The basic operations in mathematics are:

We can start solving the problem by using algebra. Let's call the unknown number "x". According to the problem, we know that:

814 = 12x + 70

To find the value of x, we can subtract 70 from both sides of the equation:

814 - 70 = 12x

744 = 12x

Now, we can divide both sides of the equation by 12:

x = 744/12

x = 62

So, the number is 62.

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Answer: n> or equals to 3

Step-by-step explanation:

Find explanation on the attachment

This plot will provide a visual representation of how the purchased cost of the shell-and-tube heat exchanger changes over the specified range of surface areas.

To plot the purchased cost of the shell-and-tube heat exchanger as a function of the surface area, we need to consider the variation in the purchased cost capacity exponent.

The purchased cost of the heat exchanger can be expressed as:

C = C0 * (A)^b

where C is the purchased cost, C0 is the cost constant, A is the surface area, and b is the purchased cost capacity exponent.

Given that the purchased cost capacity exponent is not constant over the range of surface area requested (10 to 200 m²), we need to consider different values of b for different ranges of surface area.

Let's assume the following ranges and their corresponding purchased cost capacity exponents:

For 10 m² ≤ A ≤ 50 m², let b = 0.8

For 50 m² < A ≤ 100 m², let b = 0.7

For 100 m² < A ≤ 150 m², let b = 0.6

For 150 m² < A ≤ 200 m², let b = 0.5

Now, we can calculate the purchased cost for different values of surface area using the corresponding purchased cost capacity exponents.

For each range, substitute the given values of C0 and b into the cost equation to find the purchased cost for the corresponding surface area.

Once we have calculated the purchased costs for different surface areas, we can plot them on a graph with surface area (A) on the x-axis and purchased cost (C) on the y-axis.

The graph will show the variation in purchased cost as a function of surface area, considering the different purchased cost capacity exponents for different ranges.

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Answer: its a

Step-by-step explanation:

i got the test all right trust me :)

hope it helped

To find the end behavior of the function:

We look at the graph of it:

And look at what happens when the x is to small and to big.

• When x goes to infinity the function goes to infinity.

• When x goes to minus infinity the function goes to infinity.

The other way to find this is taking the limits to infinity in each end:

The greatest percent change occurred in the first five-year period, between the first and second year, with a percent change of 60%.

Percentage is a number or ratio expressed as a fraction of 100.

We can calculate the percent change between two values using the following formula:

percent change = (new value - old value) / old value x 100%

To compare the percent change over a five-year period, we need to consider the percent change between each pair of values, as follows:

Percent change between the first and second year:

percent change = (320 - 200) / 200 x 100% = 60%

Percent change between the second and third year:

percent change = (400 - 320) / 320 x 100% = 25%

Therefore, the greatest percent change occurred in the first five-year period, between the first and second year, with a percent change of 60%.

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Answer:

10%

Step-by-step explanation:

You have the correct answer. Nice job!

Answer:

i just wanted to say god bless yall and im sry for not answerinng the question

Step-by-step explanation:

Answer:

2.7

Step-by-step explanation:

The answer to the question is 2.7

Answer:

36 minutes

Step-by-step explanation:

100 boxes in 3 hours is a rate. It is how fast you are working in boxes per hour 100/3 boxesperhour.

But 3 doesn't go into 100 very neatly and its going to make all kinds of ugly fractions or decimals. But lets look at minutes. 3 hours is 3 × 60 minutes (bc there's 60 minutes in an hour) So you loaded 100 boxes in 180 minutes. That's 100/180 boxes per minute.

100/180 = 10/18

10/18 means 10 boxes in 18 minutes.

So times 2 on the top and the bottom gives you 20/36.

20/36 means 20 boxes in 36 minutes.

This is your answer. It will take 36 minutes to load 20 more boxes.

Answer:

1. Given

2. Angle addition property

3. Angle addition property

4. Substitution property

5. Addition and subtraction property

Answer:

0.25 rad to the nearest hundredth radian

Step-by-step explanation:

Here is the complete question

Suppose a projectile is fired from a cannon with velocity vo and angle of elevation (theta). The horizontal distance R(θ) it travels (in feet) is given by the following.  

R(θ) = v₀²sin2θ/32

If vo=80ft/s what angel (theta) (in radians) should be used to hit a target on the ground 95 feet in front of the cannon?

Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a radian.

(θ)= ?rad

Solution

R(θ) = v₀²sin2θ/32

If v₀ = 80 ft/s and R(θ) = 95 ft

θ = [sin⁻¹(32R(θ)/v₀²)]/2

= [sin⁻¹(32 × 95/80²)]/2

=  [sin⁻¹(3040/6400)]/2

=  [sin⁻¹(0.475)]/2

= 28.36°/2

= 14.18°

Converting 14.18° to radians, we have 14.18° × π/180° = 0.2475 rad

= 0.25 rad to the nearest hundredth radian

Answer:

Theta= 0.32 rad

or Theta= 1.25 rad

Step-by-step explanation:

On the Aleks explanation

Yes, it is possible for three vectors of different magnitudes to add up to zero.

For three vectors to add up to zero, their magnitudes and directions must be carefully chosen. The vectors can have different magnitudes but must be arranged such that their sum cancels out.

To illustrate this, let's consider three vectors A, B, and C. Each vector has a different magnitude but when combined, their sum results in zero.

Let's say vector A has a magnitude of 3 units, vector B has a magnitude of 2 units, and vector C has a magnitude of 1 unit. To achieve a zero resultant vector, we can arrange these vectors in the following way:

Vector A is directed to the right with a magnitude of 3 units.

Vector B is directed to the left with a magnitude of 2 units.

Vector C is directed upwards with a magnitude of 1 unit.

By carefully choosing the directions and magnitudes, the sum of these vectors will be zero. Vector A cancels out the leftward component of vector B, and vector C cancels out the downward component of the resultant vector formed by A and B.

Therefore, it is possible for three vectors of different magnitudes to add up to zero if their directions and magnitudes are appropriately chosen to cancel each other out.

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The expression for g(x) is 9x + 26

A function can be defined as an expression, law or rule explaining the relationship between an independent and dependent variable.

Given the function;

g(x) = f(x + 4) - 10  

Where f = 9

Substitute into the function;

g(x) = 9( x + 4) -10

expand the bracket

g(x) = 9x + 36 - 10

collect like terms

g(x) = 9x + 26

Thus, the expression for g(x) is 9x + 26

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Answer:

Each brother will need 2 additional shots!

Step-by-step explanation:

If you add 3 to 18 it'll eventually lead to 24, as for 2 plus 20, if you add that up it also gets you to 24 which will make the game tied. And the tied score is 24.

The brothers will have a tied score in the game if both brothers are added with two more shots each.

Two or more expressions with an Equal sign is called as Equation.

Given,

The points started by Oscar was 20.

The points started by Oscars little brother was 18.

Oscar gets 2 points for every successful shot,

his brother, since he is younger, gets 3 points for each successful shot

If Oscar done 2 more shots his points will be 24.

If Oscars little brother two shots his points will be increased by 6 and will become 24. The brother will have a tied score in the game.

Hence, Each brother will need 2 additional shots

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Answer:

Step-by-step explanation:

2x-7 = 10^(22.3)

option (d) 40 would be the closest choice for the number of measurements required to detect a difference in the true standard deviation with a probability of at least 0.9, assuming α=0.05

several factors need to be considered, including the desired level of significance (α), the desired power of the test (1-β), and the effect size.

Given that α=0.05 and the desired probability is at least 0.9, we are considering a statistical test with a power of at least 0.9. However, the effect size is not provided in the question, which is necessary to determine the sample size required.

The required sample size can be determined using power analysis, which takes into account the effect size, significance level, desired power, and other statistical parameters.

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The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.

The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.

We have,

The absolute value function f(x) = |x – 2| is a piecewise function that returns the positive distance between the input value x and the number 2.

Geometrically,

It represents the distance of a point on the number line from point 2.

On the coordinate plane,

The graph of the absolute value function is V-shaped, with its vertex at the point (2, 0).

The two arms of the V extend indefinitely in opposite directions, passing through the points (-∞, 2) and (2, +∞) on the positive and negative sides of the x-axis, respectively.

Thus,

The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.

The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.

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The quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

The time taken by substance to reduce to its half of its initial concentration is called half life period.

We will use the half- life equation N(t)

N e^{(-0.693t) /t½}

Where,

N is the initial sample

t½ is the half life time period of the substance

t2 is the time in years.

N(t) is the reminder quantity after t years .

Given

N = 13g

t = 350 years

t½ = 1599 years

By substituting all the value, we get

N(t) = 13e^(0.693 × 50) / (1599)

= 13e^(- 0.368386)

= 13 × 0.691

= 8.98

Thus, we calculated that the quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

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1. We should understand that question is missing, but, the amount 1 that Mia has to pay back if she takes the loan will be Loan amount plus the interest on it.

2. The banks 2 and other financial institutions did offer cash loans to people that did not apply for it because they knew that had favorable credit worthiness, that is, they repay loan as at when due.

Creditworthiness is how a lender determines whether you will default on your debt obligations or whether you are creditworthy. Creditors consider your creditworthiness before approving new credit for you.

Several factors influence it, including your repayment history and credit score. When determining the likelihood of default, some lending institutions consider available assets as well as the number of liabilities you have.

The credit report shows how much debt you have, as well as the high balances, credit limits, and the current balance of each account. It will also flag any relevant information for the potential lender, such as past due amounts, defaults, bankruptcies, and collection items.

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The number of shoes she sells last week (b) 35

From the question, we have the following parameters that can be used in our computation:

Commission = $25 per shoe

Base salary = $450

Amount earned = $1325

The above means that

Amount earned = Commission x Number of shoes + Base salary

Substitute the known values in the above equation, so, we have the following representation

25 x Number of shoes + 450 = 1325

This gives

25 x Number of shoes = 875

So, we have

Number of shoes = 35

Hence, the number of shoes is (b) 35

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Answer:

c

Step-by-step explanation:

1. Yes, the relation defined by the table is a function.

This is because for each x value there is only one corresponding y value. Even though some of the y values are the same, as long as each x value has only one corresponding y value, the relation is a function.

The domain of the function is the set of all x values: {1, 2, 3, 8, 9}
The range of the function is the set of all y values: {-4, 5, 10}

2. (a) No, f(5 + 1)  is not equal to f(5) + f(1)

 f(5+1) = f(6) = 1 + 6 + 6^2 = 43, while f(5) + f(1) = 1 + 5 + 5^2 + 1 + 1 + 1^2 =39

So f(5+1) ≠ f(5) + f(1).

(b) f(x+h) =  1 + x + h + x^2 + 2xh + h^2

f(x+h) = 1 + (x+h) + (x+h)^2

1 + (x+h) + (x+h)^2 = 1 + x + h + x^2 + 2xh + h^2

Therefore:

f(x+h) =  1 + x + h + x^2 + 2xh + h^2

(c) No, f(x + h) is not equal to f(x) + f(h)

f(x+h) = 1 + x + h + x^2 + 2xh + h^2,

while f(x) + f(h) = 1 + x + x^2 + 1 + h + h^2.

So f(x+h) ≠ f(x) + f(h).

(d) No, f(x + h) is not equal to f(x) + h.

f(x+h) = 1 + x + h + x^2 + 2xh + h^2,

while f(x) + h = 1 + x + x^2 + h.

So f(x+h) ≠ f(x) + h.

(e) f(x+h) - f(x) = 1 + 2x + h

f(x+h) - f(x) = (1 + x + h + x^2 + 2xh + h^2) - (1 + x + x^2) = h + 2xh + h^2

(f(x+h) - f(x))/h = (h + 2xh + h^2)/h = 1 + 2x + h

3. (a) (P q)(t)= -0.1t^2 + 1670t + 112375

(Pq)(t) = P(q(t)) = P(650 + 10t) = 180(650 + 10t) - (650 + 10t)^2/100 - 400
= 117000 + 1800t - 4225 - 130t - 0.1t^2 - 400
= -0.1t^2 + 1670t + 112375

(b) The number of units produced is 820 units while the profit is $130,285.10.

On the seventeenth day of the month, t = 17.
The number of units produced is q(17) = 650 + 10(17) = 820 units.
The profit is (Pq)(17) = -0.1(17)^2 + 1670(17) + 112375 = $130,285.10.

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Answer: The hypotheses of this test are:

Null hypothesis: The average weight of the product on the line is equal to the specified value of 16 ounces.

Alternative hypothesis: The average weight of the product on the line is different from the specified value of 16 ounces.

Step-by-step explanation:

Answer:

base angle of isosceles triangle are equal..

hope it helps

The random variable x, which represents the amount of rain (in inches) that fell this spring, is a continuous random variable.

In this context, a continuous random variable is one that can take on any value within a certain range. The amount of rain can be measured with different levels of precision, such as 2.5 inches or 2.5342 inches, indicating that there is an infinite number of possible values between any two given points.

On the other hand, a discrete random variable would involve countable outcomes or a finite number of possible values. For example, if we were counting the number of rainy days during the spring, the random variable would be discrete since it can only take whole number values.

In the case of measuring the amount of rain, there can be infinitely many possible values within any given range, and therefore, it is considered a continuous random variable. So, the correct answer is option A.

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The complete question is:

Decide whether the random variable x is discrete or continuous. Explain your reasoning Let x represent the amount of rain (in inches) that fell this spring. Is the random variable x discrete or continuous? Choose the correct answer below.

A. Continuous, because x is a random variable that cannot be counted.

B. Discrete, because x is a random variable that can be counted.

Answer:

4. it would take greater than 31.25 hrs for tims price to be better.

Step-by-step explanation:

Answer:

\(\huge\boxed{x=0}\)

Step-by-step explanation:

\(x+1=1\\\\x+1-1=1-1\\\\\boxed{x=0}\)