How much money will you have after 8 years if you invest $4300 at an interest rate of 2% compounded continuously?

Using the theory  of the Fundamental Theorem of Calculus, the derivative of the function given in the question as calculated is f'(x) = -(7 + sec (4t).

The given question is incomplete , I am answering it as my general knowledge.

The differential of g(x); g'(x) = f(x).

As a result , the function f'(x)'s derivative is '

f' ( x ) = - √(7 + sec(4t) .

The derivative of a function means the rate of change of function as per the given limits .

It tells us about the sensitivity of the function's value (output value) to changes in its argument .

Derivations are an important part of calculus . The velocity of an item, for instance, is the derivative of its position with respect to time, it tells us how quickly the object's position varies as time passes.

When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable. The function closest to that input value is best approximated linearly by the tangent line.

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Answer:

1586 cm³

Step-by-step explanation:

bottom big one v= wlh = 22* 13 * 5 =1430

top little one v= wlh= 6*2*13 =156

total = 1586

A quadratic function is a second-degree polynomial function that forms a symmetric parabolic curve, has a vertex, axis of symmetry, roots, and a constant leading coefficient.

A quadratic function is a type of function that can be represented by a quadratic equation of the form\(f(x) = ax^2 + bx + c,\)

where a, b, and c are constants.

Here are five characteristics of quadratic functions:

Degree: Quadratic functions have a degree of 2.

This means that the highest power of the independent variable, x, in the equation is 2.

Shape: The graph of a quadratic function is a parabola.

The shape of the parabola depends on the sign of the coefficient a.

If a > 0, the parabola opens upward, and if a < 0, the parabola opens downward.

Vertex: The vertex of the parabola represents the minimum or maximum point of the quadratic function.

The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate can be calculated by substituting the x-coordinate into the quadratic equation.

Axis of Symmetry: The axis of symmetry is a vertical line that divides the parabola into two equal halves.

It passes through the vertex of the parabola and is represented by the equation x = -b / (2a).

Roots or Zeros: Quadratic functions can have zero, one, or two real roots. The roots are the x-values where the quadratic function intersects the x-axis.

The number of roots depends on the discriminant, which is given by the expression b^2 - 4ac.

If the discriminant is greater than zero, there are two distinct real roots. If the discriminant is equal to zero, there is one real root (the parabola touches the x-axis at a single point).

If the discriminant is less than zero, there are no real roots (the parabola does not intersect the x-axis).

These characteristics help define and understand the behavior of quadratic functions and their corresponding graphs.

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Answer:

I would say 7, because if you think about you would know that your answer is 7

The complete proof is:

Statement                                                   Reason

∠WZX ≅ ∠WZV                                          Given

∠WZX and ∠WZV are a linear pair           Definition of a linear pair

m ∠WZX + m ∠WZV = 180°                        Linear pairs theorem

m ∠WZX + m ∠WZX = 180°                        Substitution

m ∠WZX = 90°                                            Subtraction property of equality

WY ⊥ VX                                                     Definition of perpendicular lines

From the question, we are to complete the proof by dragging the word choices to supply the missing statements and reasons

Studying the given diagram and applying the proper theorems,

The complete proof is:

Statement                                                   Reason

∠WZX ≅ ∠WZV                                          Given

∠WZX and ∠WZV are a linear pair           Definition of a linear pair

m ∠WZX + m ∠WZV = 180°                        Linear pairs theorem

m ∠WZX + m ∠WZX = 180°                        Substitution

m ∠WZX = 90°                                            Subtraction property of equality

WY ⊥ VX                                                     Definition of perpendicular lines

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Answer:

0.000032 and 0.0000064

The probability that 4 students arrive during a randomly selected office hour is 0.134, or about 13.4%.

To find the probability that 4 students arrive during a randomly selected office hour, we need to use the Poisson distribution formula.

The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space.

The formula for the Poisson distribution is:

P(X = x) = (e^-λ * λ^x) / x!

Where X is the number of events, λ is the average number of events per interval, and e is the mathematical constant e.

In this case, λ = 2.5, since the average number of students who arrive during an office hour is 2.5. So, we can plug in λ and x = 4 into the formula:

P(X = 4) = (e^-2.5 * 2.5^4) / 4!

P(X = 4) = (0.082 * 39.0625) / 24

P(X = 4) = 0.134

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Answer:

£2.50+5b>21

Step-by-step explanation:

this is because a bag is b and they cost £5 so therefore it's 5b then they have to be under 21 pounds so you use the less than symbol.

Answer:

1.5 pounds of beans are in each nag

The square root of open paren x negative 3 close paren squared =

3 negative x​  negative x times the absolute value of x is greater than 0.

Let the equation be: |x−3|=3−x|x−3|=3−x

When x>3x>3, then RHS is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.

When x≤3x≤3, then LHS=|x−3|=−x+3=3−x=RHSLHS=|x−3|=−x+3=3−x=RHS

x≠3x≠3

Thus,

−x|x|>0−x|x|>0, this inequality implies that x<0x<0, hence x<3x<3.

Hence option b becomes the correct option i.e, negative x times the absolute value of x is greater than 0.

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.

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Answer:

45%

Step-by-step explanation:

In a class of 20 students, 5 have a brother and 11 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who does not have a brother has a sister?

P (no bro / yes sis) = P(no bro) - P(sis and bro)

       = 12/20 - 3/20

       = 9/20

       or 45%

Answer: 100+100/70-6*4= 77 3/7 (Mixed number form) or 542/7 (Improper fraction form)

A 20 year old has height below 3.7 feet and above 7.9 feet then 20 year old be considered abnormal.

The average height means that the given population determined by the interaction between the environment in which it lives and the resources it commands.

Abnormal means diffrent from what is normal or usual, in a way that worries you or that is unplesant.

We have given that average height is 5.8 feet.

And abnormal height a 20 year old must be 2.1 feet below average height or 2.1 feet above average height.

Therefore 5.8 - 2.1 = 3.7 feet

                 5.8 + 2.1 = 7.9 feet

Hence height below 3.7 feet abd above 7.9 feet is considered to be abnormal.

That means [-∞ , 3.7] and [7.9,∞] is considered to be abnormal height for 20 year old man.

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Answer: 6

Step-by-step explanation:

Given: Amount of sugar he has = \(\dfrac34\) pounds

Amount of sugar is required for each batch = \(\dfrac18\) pounds

Now, the  greatest number of batches of cookies the baker can make with the \(\dfrac34\) pounds of sugar = \(\dfrac{\dfrac{3}{4}}{\dfrac{1}{8}}=\dfrac{3}{4}\times\dfrac{8}{1}\)

\(=3\times2=6\)

Hence, the greatest number of batches of cookies the baker can make = 6

Answer:

55

Step-by-step explanation:

the value of the expression 5y² + 4x when x = 2.5 and y = 3 will be 55.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 5y² + 4x

To calculate the value of expression at x = 2.5 and y = 3

Substitute the value of x and y in the expression:

=> 5y² + 4x

=> 5* 9 + 4 * 2.5

=> 45 + 10

=> 55

therefore, 55 is the value of the expression 5y² + 4x when x = 2.5 and y = 3.

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Answer:

Solution given:

length of arc LM={angle}/360*2*π*r

=here π=180 for angle and π for length

=(3π/4)/360*2*π *6

=(3*180/4)/360*2*π*6

=9/2π

option C

9/2π is a required answer.

We need to determine the vectors that are orthogonal to every vector in S. To find a basis for the orthogonal complement of subspace S, denoted as S⊥. The subspace S is spanned by the vectors x1 = [1, 2, 3, 1]ᵀ, x2 = [0, -1, 1, 0]ᵀ, and x3 = [3, -1, -1, 2]ᵀ. The basis for S⊥ consists of vectors that are orthogonal to each of these vectors.

To find a basis for S⊥, we need to find vectors that satisfy the condition of orthogonality with respect to every vector in S. This can be achieved by finding the nullspace of the matrix formed by stacking the vectors x1, x2, and x3 as its columns.

Constructing the augmented matrix [x1 | x2 | x3] and performing row reduction, we obtain the row-echelon form:

[1 0 3 | 0]

[0 -1 -1 | 0]

[0 0 0 | 0]

[0 0 0 | 0]

From the row-echelon form, we can see that the third and fourth columns are the free variables. Therefore, we can express the basis for S⊥ in terms of these free variables.

Choosing the values of the free variables as t and s respectively, we obtain the following vectors:

v1 = [-3s, s, 1, 0]

v2 = [0, 1, 0, -2s]

The vectors v1 and v2 form a basis for S⊥, as they are orthogonal to each vector in S.

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K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.

Therefore, the coordinate of the image of point K is K’(-2, 1).

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The formula used for given problem is y = mx+ b.

Slope-intercept form: A line with m as the slope and m and c as the y-intercept makes up the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

This relationship is linear. Let y be the boiling point and let x be the altitude in feet.

We need the equation y = mx+ b for a linear one.

This is a linear relationship.  Let x = the altitude in feet and y be the boiling point

 For a linear equation, we want y = mx+ b

From the description m = -1.72/1000 and when x = 0, y = 212, so b = 212

  y = -1.72/1000 + 212

B)  When y = 190

    190 = -1.72/1000x + 212

    1.72x/1000 = 22

 x = 22000/1.72 ≈ 12791 feet

  When the boiling point is 190°​F, the elevation is about 12791 ft.

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The symmetrical interval that includes 93% of the sample means is (3.2455 gallons per month, 3.5545 gallons per month) assuming the population follows a normal distribution.

To calculate the probabilities and identify the symmetrical interval, we'll use the provided information:

Given:

Population mean (μ) = 3.4 gallons per month

Population standard deviation (σ) = 0.85 gallons per month

Sample size (n) = 100

a. Probability that the sample mean will be less than 3.3 gallons per month: To calculate this probability, we need to use the sampling distribution of the sample mean, assuming the population follows a normal distribution. Since the sample size (n) is large (n > 30), we can approximate the sampling distribution as a normal distribution using the Central Limit Theorem. The mean of the sampling distribution is equal to the population mean (μ), which is 3.4 gallons per month. The standard deviation of the sampling distribution, also known as the standard error (SE), can be calculated as σ / √n:

SE = σ / √n

= 0.85 / √100

= 0.085 gallons per month

Now, we can calculate the z-score using the formula:

z = (x - μ) / SE

Substituting the values:

z = (3.3 - 3.4) / 0.085

= -0.1 / 0.085

= -1.1765

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -1.1765. The probability that the sample mean will be less than 3.3 gallons per month is approximately 0.1190. Therefore, the probability is 0.1190.

b. Probability that the sample mean will be more than 3.6 gallons per month:

Similarly, we can calculate the z-score for this case:

z = (x - μ) / SE

= (3.6 - 3.4) / 0.085

= 0.2 / 0.085

= 2.3529

Using a standard normal distribution table or calculator, we find the probability corresponding to a z-score of 2.3529. The probability that the sample mean will be more than 3.6 gallons per month is approximately 0.0096.

Therefore, the probability is 0.0096.

c. Identifying the symmetrical interval that includes 93% of the sample means:

To find the symmetrical interval, we need to determine the z-scores corresponding to the tails of 93% of the sample means.

Since the distribution is symmetrical, we can divide the remaining probability (100% - 93% = 7%) equally between the two tails.

Using a standard normal distribution table or calculator, we find the z-score corresponding to a tail probability of 0.035 on each side. The z-score is approximately 1.8125.

The symmetrical interval is then given by:

=μ ± z * SE

=3.4 ± 1.8125 * 0.085

=(3.4 - 1.8125 * 0.085, 3.4 + 1.8125 * 0.085)

=(3.4 - 0.1545, 3.4 + 0.1545)

=(3.2455, 3.5545)

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(hope this helps) :)

Answer:

1.false. 2.true 3.false 4.true

Answer:

\( 28\: ft^2\)

Step-by-step explanation:

Area of the triangle

\( = \frac{1}{ \cancel2} \times 7 \times \cancel 8 \\ \\ = 7 \times 4 \\ \\ = 28 \: {ft}^{2} \)

Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

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Answer:

$138

Step-by-step explanation:

$120 going up 15% = $138

Answer:

please what is equaling to

Answer:

3-1/6

Step-by-step explanation:

1-2/3 *4 = 20/3 = 6-2/3

Now subtract 3-1/2 from that and you will now get 19/6 or 3-1/6

Then your new answer it 3-1/6