The base of triangle exceeds the height by 4cm the area is 30cm² then find the the length ofbase & hight of triangle​

When Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

One fourth of the part of a circle is said to be the quadrant of the circle.

Given the angle Ф lies in quadrant IV.

As we know, cos Ф is positive only in first and fourth quadrant i.e when Ф lies in 0<Ф<90 and 270<Ф<360.

cosФ range from [-1,1]

So, cos Ф is positive when Ф lies in 1st and 4th quadrant.

&  cos Ф is negative when Ф lies in 2nd and 3rd quadrant.

If cos ∅ lies in the quadrant IV, anything between [0, 1] can be the value of cos ∅.

Hence, when Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

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Answer:

slope: 150

y-intercept: 250

y= 150x+250

Step-by-step explanation:

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

50%

Step-by-step explanation:

The question asks who has taken fewer than 19 courses.

So first we look at how many are fewer than 19.

There are 4 that are fewer than 19: 12, 9, 5, 17

So.. 4/8    (8 is the total number of options)

To find the percentage you...

Answer:

x = 11

Step-by-step explanation:

The lower base angles are congruent, so

4x + 41 = 85 ( subtract 41 from both sides )

4x = 44 ( divide both sides by 4 )

x = 11

The probability that at least 1 patient will arrive during this time is approximately 0.9967 or 99.67%. This information will help you staff the ER with the optimal number of doctors and nurses to handle the patient load.

As the human resource manager for the Cookeville Regional Medical Center's Emergency room, we need to calculate the probability that at least 1 patient will arrive between 11pm and midnight on Friday night.

Since the number of patients follows a Poisson distribution with a mean of 5.7, we can use the Poisson distribution formula:

P(X ≥ 1) = 1 - P(X = 0)

where X represents the number of patients arriving during this time.

To calculate P(X = 0), we can use the Poisson distribution formula:

P(X = 0) = (e^-λ * λ^0) / 0!

where λ is the mean number of patients, which is 5.7 in this case.

Plugging in the values, we get:

P(X = 0) = (e^-5.7 * 5.7^0) / 0! = 0.0030

Therefore,

P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.0030 = 0.9970

So the probability that at least 1 patient will arrive between 11pm and midnight on Friday night is 0.9970 or approximately 99.7%.

This information can be used by the Human Resources Director to staff the ER with the optimal number of doctors and nurses to handle the expected patient volume during this time.

As the human resource manager for the Cookeville Regional Medical Center's Emergency room, you need to calculate the probability that at least 1 patient will arrive between 11pm and midnight on a Friday night. The number of patients follows a Poisson distribution with a mean of 5.7 patients.

To find the probability that at least 1 patient will arrive, we will first calculate the probability that no patients arrive (P(X=0)) and then subtract it from 1. The formula for the Poisson distribution is:

P(X = k) = (e^(-λ) * λ^k) / k!

where λ is the mean (5.7 patients in this case), k is the number of patients, and e is the base of the natural logarithm (approximately 2.71828).

To calculate P(X=0):

P(X = 0) = (e^(-5.7) * 5.7^0) / 0!
         = (e^(-5.7) * 1) / 1
         ≈ 0.0033

Now, to find the probability of at least 1 patient arriving, we will subtract the probability of no patients arriving from 1:

P(X ≥ 1) = 1 - P(X = 0)
        = 1 - 0.0033
        ≈ 0.9967

So, the probability that at least 1 patient will arrive during this time is approximately 0.9967 or 99.67%. This information will help you staff the ER with the optimal number of doctors and nurses to handle the patient load.

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Answer:

im pretty sure it would be 27 degrees

Answer:

The answer to your question is C.

Step-by-step explanation:

Because the number of people with 4-5 pets is 9 and the 2-3 pets number is 4 9-4=5.

Integration by ordinary substitution is a general technique for simplifying integrals by changing variables, while integration by trigonometric substitution is a specific technique for evaluating integrals involving square roots and trigonometric functions.

Integration by ordinary substitution and integration by trigonometric substitution are two different techniques used to evaluate integrals in calculus.

Integration by ordinary substitution, also known as u-substitution, involves making a change of variables to simplify the integral. It is based on the chain rule for differentiation. The general steps for integration by ordinary substitution are as follows:

1. Identify a part of the integrand that can be replaced by a single variable, denoted by u.

2. Compute the derivative du/dx of the new variable u.

3. Substitute the expression for u and du into the integral, replacing the original integrand.

4. Integrate the resulting expression with respect to u.

5. Replace the variable u with the original variable or expression to obtain the final result.

Integration by trigonometric substitution, on the other hand, is a technique specifically used for integrals involving square roots of quadratic expressions or expressions with a combination of squares. It is based on trigonometric identities and is particularly useful when dealing with integrals that can be simplified using trigonometric functions. The general steps for integration by trigonometric substitution are as follows:

1. Identify a part of the integrand that can be expressed in terms of a trigonometric function.

2. Make a substitution using a trigonometric identity to replace the relevant part of the integrand.

3. Express all other terms in the integrand in terms of the same trigonometric function.

4. Simplify the integral using trigonometric identities and algebraic manipulations.

5. Integrate the resulting expression with respect to the new variable (usually denoted by θ).

6. Replace the trigonometric function with the original variable or expression to obtain the final result.

In summary, integration by ordinary substitution is a general technique for simplifying integrals by changing variables, while integration by trigonometric substitution is a specific technique for evaluating integrals involving square roots and trigonometric functions.

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Given:

Length of leg = 16.5

Angle = 31 degrees.

Let's find the length of the hypotenuse.

To find the length of the hypotenuse, apply the trigonometric ratio formula for sine:

Where:

Opposite side is the side opposite the angle = 16.5

θ is the angle = 31 degrees.

Hence, we have:

Therefore, the length of the hypotenuse is 32.0 units.

ANSWER:

32.0

Answer:

Step-by-step explanation:

Total hours constraint:

Number of session constraint:

So the system is:

Answer:

3/4m + 1/2f ≤ 30

f ≤ 30

Step-by-step explanation:

Step-by-step explanation:

When two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. This means that their measures add up to 180 degrees.

In this case, the two interior angles on the same side of the transversal 't' are (2x-8) degrees and (3x-7) degrees. Since these angles are supplementary, we can write the equation (2x-8) + (3x-7) = 180.

Solving this equation for x, we get:

(2x-8) + (3x-7) = 180

5x - 15 = 180

5x = 195

x = 39

Substituting this value of x into the expressions for the two interior angles, we find that their measures are:

(2x-8) = (2*39 - 8) = 70 degrees

(3x-7) = (3*39 - 7) = 110 degrees

So, the measure of each of these angles is 70 degrees and 110 degrees.

The cost of one book is £37.50 if Mark has sold thousands of tickets and the total collected amount is  £375.

The given data is as follows:

Number of books = 10

Number of tickets = £375

The total Mark collected is £375 for all 1000 tickets.

The unitary method is used here for solving this given problem by the first value of a single book and then calculating the value by the product of the single book.

Number of books = 1000/10 = 100

Here, Mark sold 100 books of tickets

$375 divided by 10 for 10 books,

= 375/ 10

cost of each book =  $37.75

Therefore, we can conclude that the cost of one book is £37.50

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Answer:

4 pack priced at £2.04 is the better pack

Step-by-step explanation:

2.04/4=£0.51 per roll

4.68/9=£0.52 per roll

I think the 9pack is better

I hope it was helpful to you

Among the given options, the annual expense would be A) car insurance

Car insurance is typically paid on an annual basis, providing coverage for potential damages or accidents involving the insured vehicle.

The policyholder pays a premium to the insurance company, which covers the cost of the insurance over the course of a year.

The other options listed, such as the electric bill (Choice B), savings (Choice C), and rent (Choice D), do involve financial transactions, but they may occur on different schedules.

The electric bill is typically a monthly or quarterly expense, while savings is a personal financial strategy involving setting aside money regularly. Rent is usually paid on a monthly basis for the use of a property.

Car insurance is the option that specifically relates to an annual expense, as it is a recurring payment made once a year for the coverage of an insured vehicle.

Correct option is A)car insurance.

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Answer:

.

Step-by-step explanation:

The missing operations from the given equations would be:

To get - 6, you would need to divide 48 by a negative number which is - 8 :

= 48 / - 8

= - 6

The same applies to getting - 5 from - 40. You need to divide with a positive 8 this time because 40 is already negative :

= - 40 / 8

= - 5

The operation for 12 ? ( -2) = 14 needs to be a subtraction because two subtraction signs would become positive:

= 12 - - 2

= 12 + 2

= 14

For 18 ? ( - 12 ) = 6

= 18 + ( - 12 )

= 18 - 12

= 6

The same applies to 18 ? ( - 20 ) = 2

= 18 + ( - 20 )

= 18 - 20

= - 2

The last operation would be:

= 22 x - 0. 5

= - 11

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Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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Answer:

This number is rational because there is a repeating pattern. Following the decimal, there is one 0 then a 2. This process repeats by adding a 0 each time the number 2 is passed.

Step-by-step explanation:

If both measurements are equal to the radius of the circle, then side RT is tangent to the circle. We can also use the Pythagorean Theorem to determine if side RT is tangent to the circle.

Pythagorean Theorem is a fundamental geometry theorem that states that in any right triangle, the sum of the squares of the lengths of the two sides that form the right angle equals the square of the length of the hypotenuse. It is written as \(a^{2} +b^{2}= c^{2}\), where a and b are the lengths of the two sides and c is the length of the hypotenuse.

In order to determine if side RT of triangle GTR is tangent to the circle, we can use the properties of tangency. A tangent line is always perpendicular to the radius of the circle at the point of tangency. This means that if side RT is tangent to the circle, the angle formed by the radius of the circle and side RT must be 90°. Furthermore, the length of side RT must be equal to the radius of the circle.

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The transformation that would linearize the data for volume and time is ln(Seconds), ln(cm3).

The correct option is (D)

To determine which transformation will linearize the data, we can look at the form of the relationship between volume and time in the scatterplot. Since the pattern is curved, it suggests that the relationship may be exponential. Therefore, we can try taking the logarithm of the volume or the time or both and see which transformation produces a linear relationship.

A) Seconds, cm3: This transformation does not involve taking the logarithm of either variable, so it is unlikely to linearize the relationship.

B) ln(Seconds), cm3: This transformation takes the natural logarithm of the time variable. It may help to linearize the relationship if the relationship is exponential with respect to time.

C) Seconds, ln(cm3): This transformation takes the natural logarithm of the volume variable. It is unlikely to linearize the relationship because it does not address the potential exponential relationship with respect to time.

D) ln(Seconds), ln(cm3): This transformation takes the natural logarithm of both variables. It is a good choice because it can linearize an exponential relationship between the two variables.

Therefore, the transformation that would linearize the data for volume and time is D) ln(Seconds), ln(cm3).

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The correct slope of the tangent line to y = f(t)g(2) at the point where r = 3 is 21, not 14 as Adam entered.

To find the slope of the tangent line to the function y = f(t)g(2) at the point where r = 3, we can use the product rule of differentiation. Let's analyze Adam's approach and identify the mistake(s).

Adam's mistake is in assuming that the slope of the tangent line to y = f(x)g(x) at the point where x = 3 is simply the product of the slopes of the individual tangent lines to f(x) and g(x) at x = 3. This assumption is incorrect because the product rule accounts for the interaction between the two functions.

To find the slope of the tangent line to y = f(t)g(2) at the point where r = 3, we need to apply the product rule:

(dy/dt) = (f'(t) * g(2)) + (f(t) * g'(2))

Given the information provided, we know:

f(3) = 5

f'(3) = 2

g(3) = -7

g'(3) = 7

Now, let's substitute these values into the product rule equation:

(dy/dt) = (f'(t) * g(2)) + (f(t) * g'(2))

(dy/dt) = (2 * g(2)) + (f(t) * 7)

(dy/dt) = (2 * g(2)) + (5 * 7)

(dy/dt) = (2 * g(2)) + 35

Since we are interested in the slope at the point where r = 3, we substitute r = 3 into the equation:

(dy/dt) = (2 * g(2)) + 35

(dy/dt) = (2 * (-7)) + 35

(dy/dt) = -14 + 35

(dy/dt) = 21

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Answer:

30°

Step-by-step explanation:

All angles add up to 180°

x + 4x + 30 = 180

Combine like terms

5x + 30 = 180

Isolate the x ( subtract 30 from both sides)

5x = 150

Divide both sides by 5

x = 30°

Answer:

4x=>-74

Step-by-step explanation:

x+23=>18

4(x+23)=>18

4x+92=>18

collect like terms

4x=>18-92

4x=>-74

Answer is 4 (x + 23 ) ≥ 18

Step by step

4 times the sum of a number and 23

4(x + 23)

Is at least 18

≥ 18

Your inequality

4 (x + 23 ) ≥ 18

to solve, distribute

4x + 92 ≥ 18

subtract 92 from both sides

4x + 92 - 92 ≥ 18 - 92

simplify

4x ≥ -74

divide both sides by 4 to solve for x

4/4 x ≥ -74/4

x ≥ 18.5

18.5 is equal to or greater than 18 so problem solved

** We used ≥ in this inequality which means at least (equal to) this number or greater

The equation of a straight line is written as

y = mx + c

Where

m represents slope

c represents y intercept

The given equation is expressed as

3x + y = 3

y = 3 - 3x

y = - 3x + 3

Comparing the above equation with the slope intercept equation,

y intercept = 3

The x intercept is the value of x when y = 0

Putting y = 0 in the equation, it becomes

0 = - 3x + 3

3x = 3

x = 3x/3

x = 1

x intercept = 1

To create a relative frequency table showing the distribution of pet ownership, we divide each frequency by the total number of people in the group.

This will give us the proportion or percentage of people who have each kind of pet relative to the total.

Let's assume the group consists of 100 people. The frequency table shows the number of people who have dogs, cats, or birds as pets. We can calculate the relative frequency by dividing each frequency by the total number of people (100).

For example, if 30 people have dogs, the relative frequency of dog ownership is 30/100 = 0.3 or 30%. Similarly, if 40 people have cats, the relative frequency of cat ownership is 40/100 = 0.4 or 40%. Finally, if 20 people have birds, the relative frequency of bird ownership is 20/100 = 0.2 or 20%.

The completed relative frequency table would look like this:

Pets    | Frequency | Relative Frequency

----------------------------------------

Dogs    | 30        | 0.3 or 30%

Cats    | 40        | 0.4 or 40%

Birds   | 20        | 0.2 or 20%

This table provides a distribution of pet ownership within the group, expressed as proportions or percentages relative to the total number of people.

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Answer:

Static

Step-by-step explanation:

By process of elimination, static is the only one that would work.

Answer:

static.

Step-by-step explanation:

\(\\ \leq \int\limits^a_b {x} \, dx x^{2} \sqrt{x} \sqrt[n]{x} \leq \geq \neq \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx \left \{ {{y=2} \atop {x=2}} \right.\)