Alana only has $56.47 saved for college, brainstorm possible reasons why she has only managed to save this
amount.
ponly has $56.47 saved for college, brainstorm possible reasons why she has only managed to save this

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

\(2x+3y=22\\3x+y=19|\cdot(-3)\\\\2x+3y=22\\\underline{-9x-3y=-57}\\-7x=-35\\x=5\)

The length of the base, AB, can be found to be 12. 49 cm

The base length can be found using the Pythagoras Rule which is:

c ² = a ² + b ²

a = CD which is the height

c = AC

So we can find half od base length when we divide the shape into a right angled triangle :

8 ² = 5 ² + b²

b ² = 64 - 25

b = √ 39

b = 6. 24 cm

Double of this would be:

= 12. 49 cm

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Answer:

Here is the solution solution-

(-15x+6y)-(-10x+7y)

= -15x+6y+10x-7y

= (-15x+10x)+(6y-7y)

= -5x-y

Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

The given quadratic function models the projectile of the object as it is

launched off the top of the building.

The interpretation of the function values are;

The appropriate domain is 0 ≤ x ≤ 7

Reasons:

The given function for the height of the object is f(x) = -16·x² + 16·x + 672

The domain is given by the values of x for which the value of y ≥ 0

Therefore, when -16·x² + 16·x + 672 = 0, we get;

-16·x² + 16·x + 672 = 0

16·(-x² + x + 42) = 0

-x² + x + 42 = 0

x² - x - 42 = 0

(x - 7)·(x + 6) = 0

x = 7, or x = -6

The minimum value of time, x is 0, which is the x-value at the top of the

building, and when x = 7, the object is on the ground.

Therefore;

The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)

Therefore;

We have;

\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)

Which gives;

\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)

The height of the building is given when the time, x = 0, as follows;

Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672

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The rational number that can be used to represent the number of points needed for Abraham to get an A will be 1.5.

It should be noted that a rational number is the number that can be written as a fraction. It can be while numbers and decimals have well.

Therefore, since Abraham needs one-half of a point to get an A– in Math, the rational number that can be used to represent the number of points needed for Abraham to get an A willbe 1.5.

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The instantaneous rate of change of the given function at the given points are h'(-1) = -1, h'(-0.75) = 0, and h'(1) = 7.

Given that:

h(p) = 2p² + 3p

Differentiate it with respect to p.

h'(p) = 4p + 3

Now find the derivative value at the given points.

At p = -1:

h'(-1) = 4(-1) + 3 = -1

At p = -0.75:

h'(-0.75) = 4(-0.75) + 3 = 0

At p = 1:

h'(1) = 4(1) + 3 = 7

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C. the additional amount Liz saves per month

Here, we want to give the meaning of the slope of the equation

As stated, the function models the balance of LIz's savings account after x months

The number of month is represented by x

What this mean is that the additional amount she saves per month is 20 as it is constant throughout the entire savings period. The slope of a linear equation is expected to be constant

The probability of exactly two heads in tossing three fair coins is 3/8.

To find the probability of exactly two heads, we need to count the number of outcomes in the sample space that have exactly two heads and divide that by the total number of outcomes in the sample space.
In the sample space {hhh, hht, hth, htt, thh, tht, tth, ttt}, there are three outcomes that have exactly two heads: hht, hth, and thh.
So the probability of exactly two heads is 3/8.

In mathematical terms, this can be represented as:
P(exactly two heads) = number of outcomes with exactly two heads / total number of outcomes
P(exactly two heads) = 3 / 8

Therefore, the probability of exactly two heads in tossing three fair coins is 3/8.

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Let us consider the ration of two numbers be x

The two numbers are 5x and 3x

Since two numbers differ by 18, we can write the equation

5x – 3x = 18

2x = 18

x= 9

Therefore the two numbers are

5x = 5 x 9 = 45

and

3x = 3 x 9 = 27

∴ The two numbers are 45 and 27.

Jack can jump upto 97.5 inches.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Jack who can long-jump 195% of his height with a running start.

Assume that he can jump a height of [x] inches. So -

x = 195% of 50

x = (195/100) x 50

x = 97.5 inches

Therefore, Jack can jump upto 97.5 inches.

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We are aware that by day 20, the blossom will have covered half of the lake, or 1/2. It doubles the following day to become 1, which equals the entire lake. Knowing that the following day is  21.

Given that:

Each day, the amount of water lilies doubles. after 20 days, there are so many water lilies that the entire lake is covered.

we have something that doubles so 2 times something

after 20days = 20 × 2 = 40

However, we are aware that by day 20, the blossom will have covered half of the lake, or 1/2. It doubles the following day to become 1, which equals the entire lake. Knowing that the following day is  21.

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Answer:

Step-by-step explanation:

A project scope document is a formal agreement that outlines the goals, deliverables, timelines, and responsibilities of a project. It defines what is included and excluded from the project, the boundaries of the project, and the constraints that will impact the project. The document is created at the beginning of the project planning process and serves as a roadmap throughout the project.

It is important to clearly define the project scope for several reasons. Firstly, it helps to ensure that everyone involved in the project has a clear understanding of what is expected of them and what their responsibilities are. This can prevent misunderstandings and conflicts that can arise due to differing expectations.

Secondly, it helps to ensure that the project stays on track and is completed within the agreed upon timeframe. By defining the deliverables and timelines, the team can create a detailed plan for how the project will be executed, monitored, and controlled.

Thirdly, it helps to manage stakeholder expectations. By clearly defining the project scope, stakeholders can understand what will be delivered and when. This can prevent scope creep, where additional requirements are added to the project without proper evaluation of the impact on time, cost, and resources.

Finally, it helps to manage risk by identifying potential challenges and constraints that may impact the project. This allows the team to proactively address these issues and develop contingency plans to minimize their impact.

In summary, a project scope document is essential for the success of any project as it helps to ensure that everyone involved has a clear understanding of the project goals, timelines, and deliverables. It also helps to manage stakeholder expectations, prevent scope creep, and manage risks.

The effective annual rate for 9% compounded daily is approximately 9.34%, for 9% compounded monthly is approximately 9.38%, and for 9% compounded yearly is 9%.

To calculate the effective annual rate, we use the formula: (1 + r/n)^n - 1, where r is the stated annual interest rate and n is the number of compounding periods per year.

For 9% compounded daily, the calculation is (1 + 0.09/365)^365 - 1, resulting in an effective annual rate of approximately 9.34%.

For 9% compounded monthly, the calculation is (1 + 0.09/12)^12 - 1, which gives an effective annual rate of approximately 9.38%. Finally, for 9% compounded yearly, there is no need for calculation as the stated interest rate and the effective annual rate are the same, which is 9%. The effective annual rate takes into account the compounding frequency and represents the total interest earned on an investment over a year. Higher compounding frequencies lead to slightly higher effective annual rates due to more frequent interest accumulation.

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Answer:

ai = 190.0

Step-by-step explanation:

I'll presume the sequence is arithmetic, simply because assuming the series is mathematical, there is more than one solution.

Assuming the series is comprised of numbers in an arithmetic progression, you will have...  (see attachment for better explanation and step by step.)

Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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The code sorts the skill array in ascending order.

It then creates a HashMap to store the number of occurrences of each skill level. The left and right pointers are initialized to point to the first and last elements of the skill array. The result variable is used to store the sum of the effectiveness of all teams that can be created. The code then iterates through the skill array using the left and right pointers. If both pointers point to skills that have more than one occurrence, then two of each skill are used to create the team, and effectiveness is added to the result.

If only one pointer points to a skill with more than one occurrence, then one instance of that skill is paired with one instance of the other skill to form a team. Otherwise, if both pointers point to skills that have only one occurrence, then one instance of each skill is used to create the team. In any case, when a team is created, the HashMap is updated accordingly.

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Answer:

704

Step-by-step explanation:

multiply 32 and 22 and you will get 704

hope this helps

The partial derivative of z with respect to s is :

(3 - 9t) / (v * (9s - 3t)) + (3s/3t-s)^2 * 9 / (v * (3t-s)^2)

The partial derivative of z with respect to t is :

-9 / (v * (9s - 3t)) + (3s/3t-s)^2 * 3 / (v * (3t-s)^2).

To find ∂z/∂s and ∂z/∂t using the chain rule, we can first find the partial derivatives of z with respect to u and v, and then use the chain rule to find the partial derivatives with respect to s and t.

∂z/∂u = sec^2(u/v) * 1/v

∂z/∂v = -sec^2(u/v) * u/v^2

Using the chain rule, we have:

∂z/∂s = (∂z/∂u) * (∂u/∂s) + (∂z/∂v) * (∂v/∂s)

∂z/∂t = (∂z/∂u) * (∂u/∂t) + (∂z/∂v) * (∂v/∂t)

Substituting the expressions for ∂z/∂u and ∂z/∂v, as well as the expressions for u and v in terms of s and t, we get:

∂z/∂s = sec^2(3s/9s-3t) * 1/(9s-3t) * (3 - 9t)

- sec^2(3s/9s-3t) * (3s/9s-3t)^2 * (-9)/(9s-3t)^2

∂z/∂t = sec^2(3s/9s-3t) * 1/(9s-3t) * (-9)

- sec^2(3s/9s-3t) * (3s/9s-3t)^2 * (3)/(9s-3t)^2

Simplifying these expressions, we get:

∂z/∂s = (3 - 9t) / (v * (9s - 3t))

+ (3s/3t-s)^2 * 9 / (v * (3t-s)^2)

∂z/∂t = -9 / (v * (9s - 3t))

+ (3s/3t-s)^2 * 3 / (v * (3t-s)^2)

Therefore, the partial derivative of z with respect to s is (3 - 9t) / (v * (9s - 3t))

+ (3s/3t-s)^2 * 9 / (v * (3t-s)^2), and the partial derivative of z with respect to t is -9 / (v * (9s - 3t))

+ (3s/3t-s)^2 * 3 / (v * (3t-s)^2).

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The number of threads Marvin have left is 13 yards of thread

If  each spool thread is 10.5 yards 2 spools of thread will contain how many yards

= 10.5 * 2

= 21 yards

Marvin used 4 yards from each, hence Marvin used a total of 2 * 4 = 8 yards from the 2 spools of thread

The number of yards remaining is found by subtraction

= 21 - 8

= 13 yards

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Answer:

It is a segment connecting the midpoints of two sides of a triangle. It is always parallel to the third side, and the length of the midsegment is half the length of the third side. As shown in the triangle given below. Therefore the value of x is 15 .

Step-by-step explanation:

Using the Triangle Midsegment Theorem, it is found that x = 14.

The Triangle Midsegmenet Theorem states that the length of the midsegment is half the length of the base.

In this problem:

Thus, applying the theorem:

\(\frac{x}{2} = 7\)

\(x = 14\)

The value is x = 14.

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Answer:

Total width = 5/2 or 2½

Step-by-step explanation:

Since we have 3 beads and each of them have a width of 5/6 inches, thus;

Total width = 3 × (5/6)

Total width = 15/6

Simplifying this since 3 is common multiple to both numerator and denominator, we have;

Total width = (15/3)/(6/3)

Total width = 5/2

Since this is an improper fraction, we need to turn it into a mixed fraction, thus;

Total width = 5/2 = 2½

Those total width is 5/2 or 2½

(i) At t = 0.5 s, the voltage output is approximately 0.1737 volts, and the indicated pressure is approximately 129.18 psi.

(ii) The output reaches 5.0 volts approximately at t = 0.6764 s.

(i) At t = 0.5 s, we need to calculate the voltage output and the indicated pressure.

To find the voltage output, we first need to determine the resistance at t = 0.5 s using the given pressure-resistance relationship. Substituting p = 150 psi into the equation R = (0.15p km) p + 2.5 kΩ, we get R = (0.15 * 150) + 2.5 = 25 + 2.5 = 27.5 kΩ.

Next, we can calculate the voltage output using the voltage-resistance relationship. Substituting R = 27.5 kΩ into V = (0.15p em) R / (R + 10 kΩ), we get V = (0.15 * 150 * e^-27.5) * 27.5 / (27.5 + 10) = 0.1737 volts.

To determine the indicated pressure, we can rearrange the voltage-resistance relationship and solve for p. Substituting V = 0.1737 volts and R = 27.5 kΩ, we get p = -ln[(40 * R * V) / (R + 10 kΩ)] / (0.15 * e^-R) = 129.18 psi.

Therefore, at t = 0.5 s, the voltage output is approximately 0.1737 volts, and the indicated pressure is approximately 129.18 psi.

(ii) To find the time at which the output reaches 5.0 volts, we need to determine the time constant and the corresponding time value.

Given that the sensor time constant is 350 ms, we know that the voltage will reach approximately 63.2% of its final value after one time constant. Therefore, the voltage at the time constant (t = τ) is V(τ) = 0.632 * 5.0 volts = 3.16 volts.

To find the time at which the voltage reaches 3.16 volts, we can solve for t in the voltage equation V = (0.15p em) R / (R + 10 kΩ). Rearranging the equation and substituting V = 3.16 volts, we get t = -ln[(R * V) / (40 * R - V * R - 10 kΩ)] / (0.15 * e^-R).

Calculating the value of R using the given pressure-resistance relationship for p = 150 psi, we get R = 27.5 kΩ. Substituting this value into the equation, we find t ≈ 0.6764 s.

Therefore, the output reaches 5.0 volts approximately at t = 0.6764 s.

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Answer:

step 3

Step-by-step explanation:

it's C on edg

Ernesto made his first error in Step 3 because he failed to apply the distribution property properly. It should be 3y + 21 - 2y = 8 instead of 3y + 7 – 2y = 8.

Using the substitution method, the solution to a system of equations is solved by finding one variable in one of the equations, then substituting it to find the other variable.

Given, the systems of equations as:

Thus, Ernesto made his first error in Step 3 because he failed to apply the distribution property properly. It should be 3y + 21 - 2y = 8 instead of 3y + 7 – 2y = 8.

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Answer:

$121,000

Step-by-step explanation:

30000 + .13(4 * 175000) = Total earnings

30000 + .13(700000)

30000 + .13(700000)

30000 + 91000

121000

The formula to calculate the distance between two points in the cartesian plane is the following:

replacing:

The distance between the two points is 7.94 units

Answer:

x = -24, y = 10

Step-by-step explanation:

Since it's a parallelogram, you know that the opposite sides are equal in length. Thus, you can set the opposite sides equal to each other and isolate the variable.

To find x:

-x + 2 = 26

Subtract 2 from both sides

-x = 24

Divide each side by -1

x = -24

To find y:

6y - 8 = 52

Add 8 to both sides

6y = 60

Divide both sides by 6

y = 10