1. Find the derivatives of the following functions: --- (a) f(x) = 2x + sec(x) - cot(x) (b) f(x) = sin(x)(1+ csc x) (c) f(x) = (x + 2)^3

Answer:

function is a special type of relation where every input has a unique output

Step-by-step explanation:

Answer:

The zeros of the function correspond to the x-intercept of the graph.

Step-by-step explanation:

74.95 or 75 I think

Step-by-step explanation:

I put it into a triangle calculator, so it could be wrong.

The measure of the angle S from the given triangle QRS is 65°.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine states that: a² = b² + c² − 2bc·cosA.

Given that, in ΔQRS, q = 99 cm, r = 17 cm and s=96 cm.

96²=99²+17²-2×99×17cosS

9216=9801+289-198cosS

-874=-198cosS

cosS=4.14

∠S=65°

Therefore, the measure of the angle S is 65°.

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hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა

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The roots of the equation are 7 and -4, because 7 - 4 = 3 and 7. - 4 = -28

Step-by-step explanation:

The positive number is equal to 7.

Assuming that the number is equal to "x" we have:

\(\begin{gathered}x^2 = 3x + 28\\\\x^2 - 3x - 28 = 0\\\\a = 1\\\\b = -3\\\\c = -28\\\end{gathered}\)

By the sum and product method, we have:

\(\begin{gathered}S = -b / a\\\\S = -(-3) / 1\\\\S = 3\\\\\end{gathered}\)

\(\begin{gathered}P= c / a\\\\P = 28 / 1\\\\P = 28\\\\\end{gathered}\)

The exact value of the circle is 36π square feet. Option A

The formula used for calculating the area of a given circle is expressed with the equation;

A = π(d/2)^2

A = πr²

Such that the parameters are;

The formula for radius is given as;

radius = diameter/2

divide the values

radius = 6 feet

Substitute the values

Area = 3.14 ×6²

multiply the values

Area = 36π square feet

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Answer: The column that comes down,

Step-by-step explanation: On the left

To multiply two mixed numbers, you can convert them to improper fractions and then multiply the numerators and denominators separately.

2 1/5 can be written as (2 x 5 + 1) / 5 = 11/5

2 2/3 can be written as (2 x 3 + 2) / 3 = 8/3

So the product of 2 1/5 x 2 2/3 is (11/5) * (8/3) = 88/15 which is equivalent to 5 8/15 or 5.533 repeating (if you want to express it as decimal)

You can simplify 88/15 by dividing both numerator and denominator by the greatest common divisor (GCD) which is 1 in this case, so the final result is 88/15.

The Ella works 16 hours after school and 8 hours before school.

What is an mathematical expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that :

Ella works two part-time jobs, one before school and one after school. Before school, she earns $11.25/hour, and after school "a" she earns $11..75/hour and She works twice as many hours after school that is :

a = 2b ......(1)

also, 11.25a + 11.75b = 278....(2)

now, solving for a and b :

11.25a + 11.75b = 278

11.25(2b) + 11.75b = 278

b = 278/34.25

b ≈ 8 hours

Now, the value of a will be 2b = 16 hours

Therefore, the Ella works 16 hours after school and 8 hours before school.

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Answer:

answer is this =8y-2v-8x

Step-by-step explanation:

Answer:

8y - 2v - 8x

Step-by-step explanation:

-2(-3y + v) + 2(-4x + y)

~Distribute

6y - 2v - 8x + 2y

~Combine like terms

8y - 2v - 8x

Best of Luck!

Answer:

The depth is 5.33cm

Step-by-step explanation:

Given

\(D =20cm\) --- diameter at open end

\(d = 12cm\) --- diameter at bottom

\(H=16cm\) -- depth

\(d_c = 28cm\) --- diameter of the cylinder

Required

The depth the bucket will fill the cylinder

First, calculate the radii at the ends of the bucket

\(R=D/2 =20cm/2 = 10cm\)

\(r=d/2 =12cm/2 = 6cm\)

The volume of the bucket (frustum) is:

\(V = \frac{1}{3} \pi H(R^2 + Rr + r^2)\)

\(V = \frac{1}{3} *\pi * 16 * (10^2 + 10*6 + 6^2)\)

\(V = \frac{1}{3} *\pi * 16 * 196\)

\(V = 1045.33\pi cm^3\)

The volume of a cylinder is:

\(V = \pi r_c^2h_c\)

Where:

\(r_c = d_c/2 = 28cm/2 =14cm\)

So, we have:

\(1045.33\pi = \pi * 14^2 * h_c\)

\(1045.33\pi = \pi * 196 * h_c\)

\(1045.33\pi = 196\pi * h_c\)

Make h the subject

\(h_c = \frac{1045.33\pi}{ 196\pi}\)

\(h_c = \frac{1045.33}{ 196}\)

\(h_c = 5.33\)

The link represented by function g multiplies the dependent variable by 9 for every increase of 2 units in the independent variable. The equation that represents g is \(g(x)= 2 \times3^x\),and the function has a value of 2 at 0

Let x be the independent variable, and let g(x) be the dependent variable.

According to the problem, for every 2 units the independent variable increases, the dependent variable is multiplied by 9. This suggests an exponential relationship of the form:

 \(g(x)= a \times b^x\)

where a is the initial value of the dependent variable (when x=0), and b is the growth factor (how much the dependent variable changes for every unit increase in x).

We are given that g(0) = 2, so we can plug in these values and solve for a:

 \(g(0)= a \times b^0\)

a = 2

So now we have:

\(g(x)= 2 \times b^x\)

We still need to find the growth factor b. We are told that the dependent variable is multiplied by 9 for every 2 units the independent variable increases. In other words:

\(g(x+2) = 9 \times g(x)\)

Using our equation for g(x), we can substitute in and simplify:

  \(2 \times b(x+2) = 9 \times 2\times b^x\)

Simplifying, we get:

\(b^2\) = 9

Taking the square root of both sides (we take the positive square root since b must be positive in order for g to be an increasing function), we get:

b = 3

So the final equation for g(x) is:

\(g(x) = 2 \times 3^x\)

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The unit rate of the beef if it cost $14.40 for 4.5 pounds of beef is $3.2 per pound

The unit rate is the cost of each unit of an item at a particular time.

Cost of 4.5 pounds of beef = $14.40

Unit rate of beef = Total cost / Total pounds

= $14.40 / 4.5

= $3.2 per pound

Check:

Cost of 4.5 pounds of beef = unit cost of beef × pounds of beef

= $3.2 × 4.5

= $14.4

In conclusion, the unit rate of beef is given as $3.2 per pound.

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What is the solution to this equation? 7-1^3 √2-x=12

X=5

Answer:

x = 127

Step-by-step explanation:

\(7-\sqrt[3]{2-x} = 12\) , add the cube root to both sides and subtract the 12

\(7-12 = \sqrt[3]{2-x}\), combine like terms

\(-5 = \sqrt[3]{2-x}\), raise both sides to the third power

\((-5)^{3} = (\sqrt[3]{2-x} )^{3}\), simplify

\(-125= 2-x\) , to isolate the variable subtract 2 from both sides

\(-125-2 =-x\), combine like terms

\(-127=-x\), multiply both sides by -1

\(127=x\) Finished!

From the given information, cholesterol level X follows the N(222, 37) distribution.

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:

z = (x - μ) / σ

For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595

For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as

P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406

In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:

z = (x - μ) / σ

Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.

So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.

By using the standard normal distribution table,

we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274

The cholesterol level of 90% of men in this population is at most 274 mg/dl.

The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.

The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.

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a. the direction of the acceleration is approximately 78.4° counterclockwise from the +x-axis. b. the mass of the object is approximately 12.1 kg. c. the initial speed of the object is 0 m/s. d. the velocity components after 21.0 s based solely on the given information.

To solve this problem, we will use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

ΣF = m * a

Given:

F₁ = (-1.85i + 6.75) N

F₂ = (-5.50i - 2.35) N

F₃ = (-43i) N

Acceleration magnitude (a) = 3 m/s²

(a) Direction of the acceleration:

To determine the direction of the acceleration, we need to find the net force acting on the object and then calculate the angle between the net force vector and the positive x-axis.

Net force (ΣF) = F₁ + F₂ + F₃

Net force = (-1.85i + 6.75) + (-5.50i - 2.35) + (-43i)

         = (-1.85i + 6.75 - 5.50i - 2.35 - 43i)

         = (-7.35i - 35.6)

The magnitude of the net force can be calculated using Pythagorean theorem:

|ΣF| = sqrt(Re² + Im²) = sqrt((-7.35)² + (-35.6)²) ≈ 36.3 N

The angle (θ) between the net force vector and the positive x-axis can be found using trigonometry:

θ = atan(Im/Re) = atan((-35.6)/(-7.35)) ≈ 78.4°

Therefore, the direction of the acceleration is approximately 78.4° counterclockwise from the +x-axis.

(b) Mass of the object:

From Newton's second law, we know that ΣF = m * a. Since we have the acceleration magnitude and the net force, we can solve for the mass (m):

|ΣF| = m * a

36.3 = m * 3

m = 36.3 / 3

m ≈ 12.1 kg

Therefore, the mass of the object is approximately 12.1 kg.

(c) Initial speed:

Given that the object is initially at rest (v₀ = 0 m/s), we can use the formula for final velocity (v) in terms of initial velocity (v₀), acceleration (a), and time (t):

v = v₀ + a * t

Since v₀ = 0 m/s and a = 3 m/s², we have:

v = 0 + 3 * 0

v = 0 m/s

Therefore, the initial speed of the object is 0 m/s.

(d) Velocity components after 21.0 s:

The problem does not provide information about the time evolution of the forces acting on the object, so we cannot determine the velocity components after 21.0 s based solely on the given information.

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Amount of interest on loan at Rimrock Bank, using ordinary interest at a rate of 15%, is $48,750 and at rate of 14.5%, is $47,125. In Southside National Bank , interest at a rate of 15%, is $49,500.

To compete with Rimrock Bank's offer, Southside National Bank would need to quote a rate of 14.38% using exact interest.                                    (a) To calculate the amount of interest on the loan at Rimrock Bank, we use the formula I = PRT, where I is the interest, P is the principal amount, R is the interest rate, and T is the time in years. Plugging in the values, we have I = $1,300,000 * 0.15 * (90/365) = $48,750.

(b) The amount of interest on the loan at Southside National Bank using exact interest is calculated the same way as in part (a), resulting in I = $1,300,000 * 0.15 * (90/360) = $49,500.                                                        (c) Similarly, using the same formula, we find the interest on the loan at Rimrock Bank with a rate of 14.5% to be I = $1,300,000 * 0.145 * (90/365) = $47,125.

(d) To determine the rate at which Southside National Bank should quote to compete with Rimrock Bank's last offer, we subtract the given interest difference of $1,125 from the interest calculated in part (b). Solving for R, we have $48,750 - $1,125 = $1,300,000 * R * (90/360). Solving this equation results in R ≈ 0.1438, which is 14.38% rounded to the nearest hundredth of a percent.

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(a) Isla's trading cards are 125% of Lily's trading cards.

(b) Lily's trading cards are 80% of Isla's trading cards.

Given that,

There are 225 trading cards and Lily has 180 trading cards.

To calculate the percentage of Isla's trading cards compared to Lily's,

We can use this formula:

⇒ Isla's trading cards / Lily's trading cards x 100%

Plugging in the values we get:

⇒ (225 / 180) x 100% = 125%

Therefore,

Isla's trading cards are 125% of Lily's trading cards.

b) To calculate the percentage of Lily's trading cards compared to Isla's, we can use the formula:

⇒ Lily's trading cards / Isla's trading cards x 100%

Plugging in the values we get:

(180 / 225) x 100% = 80%

Therefore,

Lily's trading cards are 80% of Isla's trading cards.

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Answer:

A = 3/4

Step-by-step explanation:

alternately could equal 0.75

We know that the probability of selecting players who have experience as a goalie is 1/8.

Probability is a mathematical discipline that deals with numerical representations of the likelihood of an event happening or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 roughly denoting impossibility and 1 denoting certainty.

So, we know that:

There is a total of 16 players.

2 of them are trained o be a goalie.

The probability that the randomly selected players will be the trained goalie:

P(E) = favorable events/total events

P(E) = 2/16

P(E) = 1/8

Therefore, we know that the probability of selecting players who have experience as a goalie is 1/8.

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The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer: 12%

Step-by-step explanation: dont have one lol

Answer:

Long wings: 0

Short wings: 100

Step-by-step explanation:

Genotype of the flies: ww

The cross will yield the genotype ww and the flies will express the recessive phenotype which is short wings.

The probability for long wings will be 0 as there is no dominant allele present. The probability for short wings will be 100 as all the flies will have short wings.

Hope that helps.

The points in a scatter plot cluster closely around the regression line, the correlation can be said to be the proportion of variance in Y that is determined or explained by X.

It is critical to understand that a correlation coefficient of zero indicates that there is no linear courting, but there can also nonetheless be a strong relationship among the 2 variables.

If one point of a scatter diagram is farther from the regression line than a few other factor, then the scatter diagram has as a minimum one outlier. If two or extra points are the identical farthest distance from the regression line not a commonplace prevalence), then every of those points is an outlier.

When the y variable has a tendency to increase because the x variable increases, we say there may be a high-quality correlation between the variables. when the y variable has a tendency to lower as the x variable increases, we are saying there's a bad correlation between the variables.

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The earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

a. The earnings per share for Company XYZ can be calculated by dividing the closing price by the P/E ratio. In this case, the closing price is $100.76 and the P/E ratio is 1525. Therefore, the earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

b. Based on the historical P/E ratio range of 12-14, the stock price of Company XYZ seems overpriced. The P/E ratio indicates the price investors are willing to pay for each dollar of earnings generated by the company. A higher P/E ratio suggests that investors have higher expectations for future earnings growth. In this case, the P/E ratio of 1525 is significantly higher than the historical range of 12-14, indicating that the stock is being valued at a much higher premium relative to its earnings. This suggests that the stock price may be inflated and not in line with the company's historical valuation metrics, indicating an overpriced condition.

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Answer:

2/15

Step-by-step explanation:

slow heart rate and blue eyes (2) over total (15)

2/15 doesn't simplify

Answer:

13/100 is my final answer

Step-by-step explanation:

First, in order to get blue eyes, you need to be part of 40% thats not much but not little either. Then in order to get A fast heart rate out of that, you need to be part of the 26% out of 40% and that leaves you with 13 to 14 %.

I say 13 to 14 because both the 13 and 26 % came from a decimal that went on forever but due to rounding it can be 27 gets fast heart rate with 13 percent gets slow heart rate and blue eyes or 14 gets it and 26 gets faster

Hope this helped.

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1: 48 cubos

2.150 cubos

3.63

4.14

Explicación:

Prácticamente es multiplicar los 3 numeros.

Considering the recursive rule, the explicit rule for the arithmetic sequence is given by:

\(a_n = 14 + 4(n - 1)\)

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

\(a_n = a_1 + (n - 1)d\)

In which \(a_1\) is the first term.

From the recursive sequence, we have that the first term is \(a_1 = 14\), while each term is the previous added to four, hence the common difference is d = 4. Thus, the explicit formula is given by:

\(a_n = 14 + 4(n - 1)\)

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The tolerance and respect are a part of interpersonal wellness.

The goal of working on your interpersonal dimension of wellbeing is to form or join a group. Another crucial feature is the family's 'pursuit of harmony.'

However, interpersonal wellbeing encompasses more than simply friends and family; it also includes a bond with pets and the natural world.

The tolerance and respect are a part of interpersonal wellness.

Accepting and respecting others, even when they hold opposing viewpoints, can go a long way toward bringing us closer together.

Thus, the tolerance and respect are a part of interpersonal wellness.

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Answer:

This relationship is not a function because more than one amount of plant food remains each day.

Step-by-step explanation:

i hope this is correct but sorry if im wrong

Answer:

3.47 and 3.21

Step-by-step explanation:

Let us assume the nails length be X

\(X \sim N(3.34,0.07^2)\)

Value let separated the top 3% is T and for bottom it would be B

\(P(X < T)= 0.97\)

Now converting, we get

\(P(Z < \frac{T-3.34}{0.07})= 0.97\)

Based on the normal standard tables, we get

\(P(Z < 1.881)= 0.97\)

Now compare these two above equations

\(\frac{T-3.34}{0.07} = 1.881 \\\\ T = 1.881 \times 0.07 + 3.34 \\\\ = 3.47\)

So for top 3% it is 3.47

Now for bottom we applied the same method as shown above

\(P(Z < \frac{B-3.34}{0.07})= 0.03\)

Based on the normal standard tables, we get

\(P(Z < -1.881)= 0.03\)

Now compare these two above equations

\(\frac{B-3.34}{0.07} = -1.881\)

\(= -1.881 \times 0.07 + 3.34 \\\\ = 3.21\)

hence, for bottom it would be 3.21