Calculus(Question in picture)

Answer:

[tex]\sin(\theta) = -\dfrac{\sqrt2}{2}[/tex]

[tex]\cos(\theta) = -\dfrac{\sqrt2}{2}[/tex]

Step-by-step explanation:

The sine of any given angle on the unit circle is the y-coordinate of the point on the circle at the given angle.

The cosine of any given angle on the unit circle is the x-coordinate of the point on the circle at the given angle.

See the attached image for a labeled unit circle.

The point on the unit circle that is at angle 5π/4 is:

[tex]\left(-\dfrac{\sqrt2}{2},-\dfrac{\sqrt2}{2}\right)[/tex]

This means that:

[tex]\sin\left(\dfrac{5\pi}{4}\right) = \cos\left(\dfrac{5\pi}{4}\right) = \boxed{-\dfrac{\sqrt2}{2}}[/tex]

Answer:

To subtract two fractions, you need to have a common denominator. The common denominator for 8 and 3 is 24.

-5/8 = -15/24 (multiply both the numerator and denominator by 3)

-4/3 = -32/24 (multiply both the numerator and denominator by 8)

Now, we can subtract the two fractions by subtracting their numerators while keeping the common denominator.

-15/24 - (-32/24) = -15/24 + 32/24 = 17/24

Therefore, -5/8 - -4/3 = 17/24 in its simplest form.

Carter is a salesperson who sells computers at an electronics store.

He gets paid a base pay amount each day and a commission for every computer sale he makes.

Carter's total pay on a day depends on the number of computers he sells, represented by x.

The relationship between x and Carter's total pay, represented by P, is linear.

linear means the graph is a straight line, not a curve

A table with select values of x and P is given.

The task is to determine Carter's base pay regardless of computer sales.

Table of select values of x and P:

x P

0 30

1 40

2 50

3 60

4 70

5 80

To determine Carter's base pay, we need to identify the amount he earns when he doesn't sell any computers, represented by x = 0. Looking at the table, we see that when x = 0, Carter's total pay is $30. Therefore, his base pay is $30.

ChatGPT

Answer:

The maximum height occurs at the vertex of the parabolic equation, which is given by the formula:

t = -b/2a

where a = -16 and b = 20. Substituting these values, we get:

t = -20 / (2 * -16) = 0.625 seconds

To find the maximum height, we can substitute this value of t back into the original equation:

h = -16(0.625)^2 + 20(0.625) + 19

h = -6.25 + 12.5 + 19

h = 25.25 feet

Therefore, the maximum height the ball reaches is 25.25 feet.

Answer:

h=16(t+5/8)^2+51/4

h=25.25

The hiker's altitude after 4.5 hours is 448 feet.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given: A hiker is climbing a local peak. After 1.5 hours of hiking, he is at an altitude of 220 feet. After 4 hours, he is at an altitude of 410 feet.

We have to find the hiker's altitude after 4.5 hours.

We have height as a function of time:

x = time, y = height

Our two points are (1.5, 220), (4, 410), and (4.5,x)

(4-1.5) = (410-220)

2.5 = 190

1 = 190/2.5

1 hours = 76 feet

0.5 hours = 38 feet

4.5 hours = 410 + 38 feet = 448 feet

Hence,  the hiker's altitude after 4.5 hours is 448 feet.

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Answer:

False

Step-by-step explanation:

[tex](x+y)^{2} = x^{2} +2xy +y^{2}[/tex]

This means that they are not equal. For this reason, the statement is false.

The radian measure of an angle is directly proportional to the length of the arc intercepted by that angle on the unit circle.

Proportional is a mathematical concept that describes the relationship between two or more values that have a constant ratio. It is commonly used to describe the relationship between two or more variables, such as the size of an object in relation to another or the amount of a certain item in relation to the total amount. In proportionality, the ratio of the amounts remains consistent, no matter what the size of the values.

This means that as the angle increases, so does the length of the arc. This is because the length of an arc is determined by the angle measure of the central angle created by the arc, and the radian measure of an angle is the ratio of the arc length to the radius of the circle. Therefore, if the angle measure increases, so does the arc length.

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Answer: 86.5

Step-by-step explanation:  

(83.5 + x )/2= 85

2(85)= 83.5 + x

170-83.5 =x

x= 86.5

In the above prompt involving a trajectory calculation, the correct option is: "The kick is not successful. The ball is approximately 5 feet too low." (Option A)

x component of trajectory =   73 cos 34   f/s  

   Now how long will it take to travel 49 yards (= 147 feet) ?

         147 / (73 cos 34) = 2.43 seconds

Initial y component of trajectory = 73 sin 34 f/s = 40.82 f/s  

    but this velocity is acted upon by gravity

       y = y0 + vot - 1/2 a t^2      

                         y0 = 0        

Now we need to know the y value at 2.43 seconds to see if it will clear the uprights.

y = 40.82 (2.43)  - 1/2 (32.174)(2.43)2  

= 4.2 Feet      
Thus, it is correct to state that the "The kick is not successful. The ball is approximately 5 feet too low."

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The quadratic equation has no real roots for c > 1, two roots of the same sign for c ≥ 1,  one root equal to zero & one negative root for 0 < c < 1, and two roots of opposite signs, c < 1.

What is a quadratic equation?

A quadratic equation is a polynomial equation of degree 2, which means that the highest exponent of the variable in the equation is 2. It has the general form:

[tex]ax^2 + bx + c = 0[/tex]

The quadratic equation [tex]x^2 - 2x + c = 0[/tex] has roots given by the quadratic formula:

x = (-b ±[tex]\sqrt{b^2 - 4ac}[/tex]) / (2a)

where a = 1, b = -2, and c is the unknown constant.

1) To have no real roots, the discriminant [tex]b^2 - 4ac[/tex] must be negative. So, we need:

[tex]b^2 - 4ac[/tex] < 0

[tex](-2)^2 - 4(1)(c)[/tex] < 0

4 - 4c < 0

4 < 4c

1 < c

Therefore, the quadratic equation has no real roots for c > 1.

2) To have two roots of the same sign, the discriminant [tex]b^2 - 4ac[/tex] must be negative or zero.

[tex]b^2 - 4ac[/tex] = [tex](-2)^2 - 4(1)(c)[/tex] = 4 - 4c

For two roots of the same sign, the discriminant must be negative or zero, so

4 - 4c ≤ 0

Simplifying the inequality, we get:

c ≥ 1

Therefore, for the quadratic equation, [tex]x^2 - 2x + c = 0[/tex] to have two roots of the same sign, c must be greater than or equal to 1.

3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:

x = 0 or x < 0

Setting x = 0 in the quadratic equation, we get:

c = 0

So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:

[tex](-2)^2 - 4(1)(c)[/tex] > 0

4 - 4c > 0

1 > c

Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.

4) To have two roots of opposite signs, the discriminant [tex]b^2 - 4ac[/tex] must be positive.

So we need:

[tex]b^2 - 4ac[/tex] > 0

[tex](-2)^2 - 4(1)(c)[/tex] > 0

4 - 4c > 0

Simplifying the inequality, we get:

c < 1

Therefore, for the quadratic equation to have two roots of opposite signs, c must be less than 1.

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For c > 1, the quadratic equation has no real roots; for c ≥1, it has two roots of the same sign; for c<1, it has one root that is equal to zero and one root that is negative; and for 0 <c <1, it has two roots of the opposite signs.

The largest exponent of the variable in a quadratic equation, which is a polynomial equation of degree 2, is 2. The formula is: ax² + bx + c.

The quadratic equation x² - 2x + c has roots given by the quadratic formula:

x = (-b ±√[b²-4ac]) / (2a)

where a = 1, b = -2, and c is the unknown constant.

1) To have no real roots, the discriminant b² - 4ac must be negative.

So, we need:

b² - 4ac < 0

(-2) ² - 4(1) < 0

4- 4c < 0

1 < c

Therefore, the quadratic equation has no real roots for c > 1.

2) To have two roots of the same sign, the discriminant b² - 4ac must be negative or zero.

b² - 4ac = (-2) ² - 4(1)c = 4 - 4c

For two roots of the same sign, the discriminant must be negative or zero, so

4 - 4c ≤ 0

Simplifying the inequality, we get:

c ≥ 1

Therefore, for the quadratic equation, x² - 2x + c   to have two roots of the same sign, c must be greater than or equal to 1.

3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:

x = 0 or x < 0

Setting x = 0 in the quadratic equation, we get:

c = 0

So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:

(-2) ² - 4(1)c > 0

4 - 4c > 0

1 > c

Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.

4) To have two roots of opposite signs, the discriminant b² - 4ac must be positive.

So, we need:

b² - 4ac > 0

(-2) ² - 4(1)c > 0

4 - 4c > 0

Simplifying the inequality, we get:

c < 1

Hence, c must be lower than 1 in order for the quadratic equation to have two roots with opposing signs.

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Answer:

C: y=2x-4

Step-by-step explanation:

pls mark brainliest

Therefore, the value of x is -4 if A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9.

An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.

Here,

Since A = B, we know that AB = B². So, we can rewrite the equation AB = 3x - 5 as B² = 3x - 5.

Similarly, we can rewrite BC = 5x - 6 as B² = 5x - 6, and AC = 2x - 9 as A² - B² = (2x - 9) - (B^2).

Since we know that A = B, we can substitute B for A in the last equation to get:

B² - B² = (2x - 9) - (B²)

Simplifying this equation, we get:

0 = 2x - 9 - B²

Now we can substitute the equation B² = 3x - 5 into the above equation to get:

0 = 2x - 9 - (3x - 5)

Simplifying this equation, we get:

0 = -x - 4

Solving for x, we get:

x = -4

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Answer:

a) To find the percentage of years with an annual rainfall of less than 44 inches, we need to find the area under the normal curve to the left of 44. Using a standard normal distribution table or a calculator, we find the z-score corresponding to 44 inches:

z = (44 - 40.9) / 5.3 = 0.585

The area to the left of z = 0.585 is approximately 0.7202. Therefore, about 72.0% of years will have an annual rainfall of less than 44 inches.

b) To find the percentage of years with an annual rainfall of more than 38 inches, we need to find the area under the normal curve to the right of 38. Using a standard normal distribution table or a calculator, we find the z-score corresponding to 38 inches:

z = (38 - 40.9) / 5.3 = -0.717

The area to the right of z = -0.717 is approximately 0.4713. Therefore, about 47.1% of years will have an annual rainfall of more than 38 inches.

c) To find the percentage of years with an annual rainfall between 37 inches and 43 inches, we need to find the area under the normal curve between the corresponding z-scores:

z1 = (37 - 40.9) / 5.3 = -0.736

z2 = (43 - 40.9) / 5.3 = 0.396

Using a standard normal distribution table or a calculator, we find the area between z = -0.736 and z = 0.396 is approximately 0.6181. Therefore, about 61.8% of years will have an annual rainfall between 37 inches and 43 inches.

Step-by-step explanation:

Step-by-step explanation:

a) To find the percentage of years with an annual rainfall of less than 44 inches, we need to find the area under the normal distribution curve to the left of 44 inches.

Using a standard normal distribution table or calculator, we can find the z-score:

z = (44 - 40.9) / 5.3 = 0.585

The area to the left of this z-score is approximately 0.72, or 72%.

Therefore, approximately 72% of years will have an annual rainfall of less than 44 inches.

b) To find the percentage of years with an annual rainfall of more than 38 inches, we need to find the area under the normal distribution curve to the right of 38 inches.

Using a standard normal distribution table or calculator, we can find the z-score:

z = (38 - 40.9) / 5.3 = -0.736

The area to the right of this z-score is approximately 0.77, or 77%.

Therefore, approximately 77% of years will have an annual rainfall of more than 38 inches.

c) To find the percentage of years with an annual rainfall between 37 inches and 43 inches, we need to find the area under the normal distribution curve between the z-scores for 37 inches and 43 inches.

Using a standard normal distribution table or calculator, we can find the z-scores:

z1 = (37 - 40.9) / 5.3 = -0.736

z2 = (43 - 40.9) / 5.3 = 0.394

The area between these z-scores is approximately 0.53, or 53%.

Therefore, approximately 53% of years will have an annual rainfall between 37 inches and 43 inches.

The vertex form is:y(x-3)2-4

:) Good luck

Use the method of completing the square to express in vertex form.

Given

[tex]y = x^2 - 6x + 11[/tex]

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 6x

[tex]y = x^2 + 2(- 3)x + 9 - 9 + 11[/tex], then

[tex]y = (x - 3)^2 + 2[/tex]

Answer: the answer is C $912.

Step-by-step explanation: The interest on the loan is calculated as follows:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the length of the loan in years. Substituting the given values, we get:

Interest = $800 x 0.14 x 1

Interest = $112

Therefore, the total amount to be repaid is the sum of the principal and the interest, which is:

Total amount = Principal + Interest

Total amount = $800 + $112

Total amount = $912

For the given situation the probability event can be denoted mathematically as P(V|W).

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The event we are interested in is "a randomly chosen person has varicose veins" (V), given that "the person drinks sixty-four ounces of water per day" (W).

So, we can write this as -

P(V|W)

which is the conditional probability of event V given event W.

Therefore, the event can be denoted as P(V|W).

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Answer:

$0.81

Step-by-step explanation:

We know

A grocery store sells a bag of 3 oranges for $2.43.

What is the unit cost?​

We take

2.43 / 3 = $0.81

So, the answer is $0.81

Answer:

7/9

Step-by-step explanation:

Find the reciprocal of the divisor

Reciprocal of 3/4 : 4/3

Now multiply it with the dividend..

so, 7/12 ÷ 3/4 = 7/12 × 4/3

=7/12×4/3 = 28/36

And after reducing the fraction, the answer is 7/9

Therefore , the solution of the given problem of volume comes out to be a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are these marks for cubic measurements. To compute an object's measurements, you must, however, comprehend its volume. Converting an object's weight into mass units including grams and kilograms is a common procedure.

Here,

The formula: can be used to determine the capacity of a hemisphere with a radius of 2 inches.

=> V = (2/3) * π * r³

where "π" is a mathematical constant that is roughly equivalent to 3.14159 and "r" is the hemisphere's radius.

When we substitute the radius's value, we obtain:

=> V = (2/3) * π * 2³

=> (2/3) * π* 8

=>  V = 16.755 cubic inches. (approx)

Therefore, a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.

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Nate made 18 loaves of bread and gave an equal number to each of his 9 neighbors, resulting in each neighbor receiving 2 loaves of bread.

The problem provides us with some information about Nate's bread-making and bread-giving activities. We know that he made 8 loaves of bread on Monday and 10 more on Tuesday, for a total of 18 loaves. We also know that he gave an equal number of loaves to each of his 9 neighbors.

To find out how many loaves each neighbor received, we need to divide the total number of loaves (18) by the number of neighbors (9). This gives us:

18 loaves / 9 neighbors = 2 loaves per neighbor.

This means that each neighbor received 2 loaves of bread from Nate. We can check this by multiplying 2 (the number of loaves per neighbor) by 9 (the number of neighbors):

2 loaves/neighbor x 9 neighbors = 18 loaves

So, we can see that the math checks out and each neighbor received 2 loaves of bread from Nate.

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Answer:

Step-by-step explanation:

Let's call the average yearly salary of an architect "A" and the average yearly salary of a lawyer "L".

From the first sentence, we know that:

L = 2A - 25

From the second sentence, we know that:

A + L = 209

We can substitute the first equation into the second equation:

A + (2A - 25) = 209

Simplifying:

3A - 25 = 209

Adding 25 to both sides:

3A = 234

Dividing both sides by 3:

A = 78

Now we can use the first equation to find L:

L = 2A - 25 = 2(78) - 25 = 131

Therefore, the average yearly salary of an architect is $78,000 and the average yearly salary of a lawyer is $131,000.

Answer: W = 357.2

Step-by-step explanation:

x/38 * 940/100

100x * 35,720

x=357.2

Answer: (1/10, 9/10)

Step-by-step explanation:

The given function does not satisfy the condition for an odd function (f(-x) = -f(x)), we can conclude that -6.66 is not an odd function

Hi there! An odd function is a mathematical function that satisfies the condition f(-x) = -f(x) for all values of x in its domain. In simpler terms, an odd function exhibits symmetry with respect to the origin in a coordinate plane.

Now, let's analyze the given function: -6.66. This function represents a constant function since it has no variables (e.g., x or y). Constant functions have a graph that appears as a horizontal line on the coordinate plane.

For constant functions, f(-x) will always equal f(x) because the function's value doesn't change regardless of the input.

In this specific case, the function value is -6.66,

so f(-x) = f(x) = -6.66 for all x.

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Answer: Budgeting for electricity is important because it allows you to plan and allocate your financial resources in a way that ensures that you can pay your electricity bills on time and avoid late payment fees, disconnection, or debt accumulation. Electricity bills can fluctuate significantly from month to month, depending on factors such as the weather, the number of people living in your home, your electricity usage patterns, and changes in electricity rates.

To create a plan to adjust your monthly budget as bills fluctuate month by month, you can take the following steps:

- Review your past electricity bills to identify patterns and trends in your usage and costs. Look for any changes that may have occurred, such as the addition of new appliances, a change in occupancy, or a change in electricity rates.

- Use this information to estimate your average monthly electricity costs. This will be your baseline budget.

- Consider setting aside a buffer amount, such as 10-15%, to account for unexpected changes or fluctuations in your electricity bills.

- Monitor your electricity bills closely each month to compare your actual costs with your budgeted amount. If your bills are consistently higher or lower than your budgeted amount, adjust your budget accordingly for the following month.

- Look for ways to reduce your electricity usage and costs, such as turning off lights and appliances when not in use, using energy-efficient light bulbs and appliances, and adjusting your thermostat settings.

- Consider enrolling in a budget billing or level payment plan offered by your electricity provider, which allows you to pay the same amount each month based on your estimated annual usage.

By budgeting for electricity and adjusting your budget as bills fluctuate month by month, you can better manage your finances, avoid surprises, and ensure that you can pay your bills on time.

Step-by-step explanation:

The largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5) is 8.5 (if x is οdd) οr 5.5 (if x is even)

The median is the middle value in a set οf numbers arranged in οrder. It is the value that separates the higher half frοm the lοwer half.

Tο find the largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5), we need tο cοnsider the different cases when x is an integer.

First, let's arrange the numbers in οrder:

{2, 3, 2x, 5, x}

Tο find the median, we need tο determine the middle number in the set. If the set has an οdd number οf elements, the median is the middle number. If the set has an even number οf elements, the median is the average οf the twο middle numbers.

Case 1: x is even

If x is even, then 2x is even and x < 2x. Therefοre, the middle numbers are 2x and 3, and the median is (2x + 3) / 2.

Case 2: x is οdd

If x is οdd, then 2x is even and 2 < 2x. Therefοre, the middle numbers are 2 and 2x, and the median is (2 + 2x) / 2.

Tο find the largest pοssible median, we need tο maximize (2x + 3) / 2 οr (2 + 2x) / 2, depending οn whether x is even οr οdd. This οccurs when x is the largest pοssible integer, which is:

x = 4 (if x is even)

x = 7 (if x is οdd)

Therefοre, the largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5) is:

(2x + 3) / 2 = (2(7) + 3) / 2 = 8.5 (if x is οdd)

οr

(2x + 3) / 2 = (2(4) + 3) / 2 = 5.5 (if x is even)

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The probabilities are given as follows:

a) All 10: 0.0163 = 1.63%.

b) Exactly eight: 0.3483 = 34.83%.

c) At least nine: 0.1518 = 15.18%.

The mass probability formula, giving the probability of x successes, is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

N = 20, k = 15, n = 10.

Hence the probability of answering all 10 is given as follows:

[tex]P(X = 10) = h(10,20,10,15) = \frac{C_{15,10}C_{5,0}}{C_{20,10}} = 0.0163[/tex]

The probability of exactly 8 is given as follows:

[tex]P(X = 8) = h(8,20,10,15) = \frac{C_{15,8}C_{5,2}}{C_{20,10}} = 0.3483[/tex]

The probability of nine successes is of:

[tex]P(X = 9) = h(9,20,10,15) = \frac{C_{15,9}C_{5,1}}{C_{20,10}} = 0.1355[/tex]

Hence the probability of at least nine successes is of:

P(X >= 9) = P(X = 9) + P(X = 10) = 0.1355 + 0.0163 = 0.1518 = 15.18%.

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The average absolute deviation, which tells you how much the values in the data set vary from the mean on average.

Deviation is a statistical measure that indicates how much a set of data varies from its average or expected value. It is calculated by finding the difference between each data point and the mean value of the data set.

Absolute deviation is a measure of how far apart a set of numbers is from their average, or mean, value. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences.

Here are the basic steps to find the absolute deviation:

1) Find the mean of the data set by adding up all the numbers and dividing by the total number of values.

2) For each value in the data set, subtract the mean from the value to find the difference.

3) Take the absolute value of each difference (ignore the positive or negative sign) by simply dropping the minus sign if there is one.

4) Add up all the absolute differences found in step 3.

5) Subtract the total number of values in the data set from the sum of the absolute differences.

The result is the average absolute deviation, which tells you how much the values in the data set vary from the mean on average.

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