Conrad Savings Bank has a $50 overdraft fee. On Friday, Mr. McQuire deposited his paycheck of $382 for a total
account balance of $793. The next morning, his wife wrote a check for $1,233.34 for a new refrigerator and stove.
The check cleared the bank by the end of the day. What is the current balance in the McQuire's account?

Answer:

3/8

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 45 and 120 is 15

Divide both the numerator and denominator by the GCD

45 ÷ 15

120 ÷ 15

Reduced fraction:

3

8

Therefore, 45/120 simplified to lowest terms is 3/8.

The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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Answer:

A = 153.86

Step-by-step explanation:

A = πr^2

A = 3.14 (7)^2

A = 3.14 (49)

A = 153.86

Answer:

B. x = 14

Step-by-step explanation:

1. Add 9 to both sides of the equation

x - 9+9 = 5+9

x = 14

hope this helps :)

The values of k and m for which the given system has infinitely many solutions are k = 6 and m = -7

To find the values of k and m for which the given system has infinitely many solutions, we can analyze the coefficients of the variables and the constant terms.

Given system:

\(\[\begin{align*}\\3a + 2b &= 2, \\6a + 2b &= k - 3a - mb.\end{align*}\]\)

To determine when this occurs, we can compare the constant terms. The constant term on the right side of the second equation is k, while the constant term on the left side is\(\(-3a - mb\)\). For the lines to coincide, the constant terms should be equal.

So, we have\(\(k = -3a - mb\).\)

Now, we can substitute the values of \(\(a\)\) and \(\(b\)\) from the first equation into this equation to eliminate \(\(a\)\) and \(\(b\)\)

\(\[-3a - mb = -3(2b - 2) - mb = -6b + 6 - mb = -6b - mb + 6.\]\)

Comparing this expression with k, we get -6b - mb + 6 = k

Simplifying further, we have -7b - mb = k - 6

Now, we can equate the coefficients of b on both sides:

-7 - m = 0

This gives us m = -7

Substituting this value of m back into the equation -7b - mb = k - 6, we get -7b + 7b = k - 6, which simplifies to 0 = k - 6

Thus, k = 6

Therefore, the values of k and m for which the given system has infinitely many solutions are k = 6 and m = -7

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Answer: 455

Step-by-step explanation:

Answer:

455

Step-by-step explanation:

hope you find this helpfull

The solution to the equation 3x = 8 - 2x is x = 1.6.

To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:

Express the equation in the form of y = f(x). Rearrange the equation:

3x + 2x = 8

5x = 8

x = 8/5 or 1.6

Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.

Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.

The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).

Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.

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Answer:

Step-by-step explanation:

a

The values of all the required angles are; m∠5 = 42°; m∠8 = 138°; m∠10 = 138° and m∠11 = 42°

Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines.

Now, we are given that; m∠1 = 42°

By corresponding angles, we can say that;

m∠1 = m∠5

Thus; m∠5 = 42°

Now, we know that sum of angles on a straight line is equal to 180° i.e. they are supplementary angles.

Now, from the diagram, we can see that m∠5 and m∠8 are supplementary angles and as such;

m∠5 + m∠8 = 180°

42 + m∠8 = 180

m∠8 = 180° - 42°

m∠8 = 138°

Now, m∠9 is a corresponding angle to both m∠1 and m∠5. Thus, we can say that; m∠9 = 42°. However, m∠9 is supplementary to m∠10. Thus;

m∠10 = 180 - 42

m∠10 = 138°

Lastly, m∠10 and m∠11 are supplementary angles and as such;

m∠10 + m∠11 = 180°

138 + m∠11 = 180

m∠11 = 180° - 38°

m∠11 = 42°

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The Probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

To find the probability that a randomly selected senior is both in the band and on the honor roll, we need to divide the number of seniors who are in both categories by the total number of seniors.

Given:

Total number of seniors = 200

Number of seniors in the band = 32

Number of seniors in the band or on the honor roll = 64

Let's calculate the probability using these values:

Probability = Number of seniors in both categories / Total number of seniors

Probability = 64 / 200

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:

Probability = (64 ÷ 8) / (200 ÷ 8)

Probability = 8 / 25

Therefore, the probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

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The required probability is 0.970 (approx.) or 97/100 (in fraction).

Given that 69% of people in a large population have been vaccinated. We are required to determine the probability of at least one person being vaccinated if three people are randomly selected. Let's solve it using the complement rule.

The complement rule states that the probability of an event occurring is equal to 1 minus the probability of that event not occurring. That is, if A is an event, then P(A) = 1 - P(A').

We can solve the given problem using the complement rule as follows: Let P(A) be the probability of at least one person being vaccinated.

Then, the probability of no one being vaccinated is P(A') = (100 - 69) = 31%.

To find the probability of at least one person being vaccinated, we can subtract the probability of none of them being vaccinated from 1. That is, P(A) = 1 - P(A') = 1 - 0.31 × 0.31 × 0.31 = 1 - 0.029791 = 0.97021.

Hence, the probability of at least one person being vaccinated if three people are randomly selected is 0.97021 (rounded to 3 decimal places).

Therefore, the required probability is 0.970 (approx.) or 97/100 (in fraction).

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The solution of y" + 4y sec(2z) by variation of parameters involves finding the homogeneous solution and integrating to find particular solutions.

a. The associated homogeneous differential equation is y'' + 4y = 0. The characteristic equation is r^2 + 4 = 0, which has roots r = ±2i. Thus, the general solution to the associated homogeneous equation is y_h = c1 cos(2z) + c2 sin(2z).

b. To find a particular solution to the nonhomogeneous equation, we assume a solution of the form y_p = u1(z) cos(2z) + u2(z) sin(2z), where u1(z) and u2(z) are unknown functions to be determined. Taking the first and second derivatives of y_p, we have:

y_p' = u1' cos(2z) + u2' sin(2z) - 2u1 sin(2z) + 2u2 cos(2z)

y_p'' = u1'' cos(2z) + u2'' sin(2z) - 4u1 sin(2z) - 4u2 cos(2z) - 4u1' sin(2z) + 4u2' cos(2z)

Substituting these expressions into the nonhomogeneous differential equation, we have:

u1'' cos(2z) + u2'' sin(2z) - 4u1 sin(2z) - 4u2 cos(2z) - 4u1' sin(2z) + 4u2' cos(2z) + 4u1 sec(2z) cos(2z) + 4u2 sec(2z) sin(2z) = 0

Equating the coefficients of cos(2z) and sin(2z), we get the following system of equations:

u1'' - 4u2' + 4u1 sec(2z) = 0

u2'' + 4u1' + 4u2 sec(2z) = 0

To solve for u1(z) and u2(z), we integrate each equation twice. The first equation gives:

u1' - 2u2 tan(2z) + 2u1 sec(2z) tan(2z) = C1

where C1 is an arbitrary constant of integration. Integrating once more, we have:

u1 = C1 integral of sec(2z) dz + C2

where C2 is another arbitrary constant of integration. Using the identity sec(2z) = 1/cos(2z), we can evaluate the integral to get:

u1 = C1/2 ln|cos(2z)| + C2

Similarly, the second equation gives:

u2' + 2u1 tan(2z) + 2u2 sec(2z) tan(2z) = C3

where C3 is another arbitrary constant of integration.

Integrating once more, we have:

u2 = C3 integral of sec(2z) dz + C4

where C4 is another arbitrary constant of integration. Using the same identity as before, we get:

u2 = C3/2 ln|cos(2z)| + C4

Therefore, the particular solution to the nonhomogeneous differential equation is:

y_p = (C1/2 ln|cos(2z)| + C2) cos(2z) + (C3/2 ln|cos(2z)| + C4) sin(2z)

c. The most general solution to the original nonhomogeneous differential equation is the sum of the general solution to the associated homogeneous equation

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The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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Let's use an equation to solve this problem.

Since they are consecutive integers, if we say that the first number is \(x\), then the next two numbers (three dimensions in a rectangular prism) are \(x+1\) and \(x+2\) respectively.

\(x*(x+1)*(x+2)=4896\)

\(x*(x+1)=x^2+x\)

\((x^2+x)*(x+2)=x^3+2x^2+2x\)

\(x^3+3x^2+2x=4896\)

\(x^3+3x^2+2x-4896=0\)

\(x=16\)

B is the correct answer.

y = 1/3x - 21 is the equation of the line in slope-intercept form.

What is a slope?

Slope is a measure of the steepness or incline of a line. It describes how much the dependent variable (usually y) changes for a given change in the independent variable (usually x).

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the slope is 1/3 and that the line passes through the point (3, -20). We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes, and m is the slope. Plugging in the values we have:

y - (-20) = 1/3(x - 3)

Simplifying this equation:

y + 20 = 1/3x - 1

Subtracting 20 from both sides:

y = 1/3x - 21

This is the equation of the line in slope-intercept form.

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Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

There is a 29.27% probability that the flight is overbooked. This is not an unusually low probability. So it does seem too high so that changes must be made to make it lower.

Step-by-step explanation:

For each passenger, there are only two outcomes possible. Either they show up for the flight, or they do not show up. This means that we can solve this problem using binomial distribution probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which  is the number of different combinations of x objects from a set of n elements, given by the following formula.

And  is the probability of X happening.

A probability is said to be unusually low if it is lower than 5%.

For this problem, we have that:

There are 200 reservations, so .

A passenger consists in a passenger not showing up. There is a .0995 probability that a passenger with a reservation will not show up for the flight. So .

Find the probability that when 200 reservations are accepted for United Flight 15, there are more passengers showing up than there are seats available.

X is the number of passengers that do not show up. It needs to be at least 18 for the flight not being overbooked. So we want to find , with . We can use a binomial probability calculator, and we find that:

There is a 29.27% probability that the flight is overbooked. This is not an unusually low probability. So it does seem too high so that changes must be made to make it lower.

Answer:

10

Step-by-step explanation:

22+22=44

64-44=20

20/2=10

Answer:

x=4.47213

I hope it's helps you

The size of the velocity of the ball in the direction of the wind is 2 units

To find the size of the velocity of the ball in the direction of the wind, we can take the dot product of the ball's velocity vector and the wind velocity vector.

The dot product is defined as:

v1 • v2 = (x1 × x2) + (y1 × y2)

Substituting the coordinates of the ball's velocity vector and the wind velocity vector, we get:

(2, 1) • (3, -4) = (2 ×3) + (1 × (-4))

= 6 - 4

= 2

Therefore, the size of the velocity of the ball in the direction of the wind is 2. This represents the component of the ball's velocity that is aligned with the wind.

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Answer:

[(2*8) + 3] *4 = 76

[2*(8 - 3)]*4 = 40

Step-by-step explanation:

Los paréntesis ( ), corchetes [ ] y llaves {} son símbolos de agrupación que indican el orden de las cuatro operaciones aritméticas básicas (suma, resta, multiplicación y división). Las reglas del orden de operaciones establece que se debe realizar primero el cálculo dentro de los símbolos de agrupación.

En otras palabras, la jerarquía de operaciones es el orden en el que hay que realizar las distintas operaciones, ya que unas tienen prioridad frente a otras. Y establece primero debes empezar por resolver los paréntesis, luego los corchetes y finalmente las llaves. Es decir, cuando haya símbolos de agrupación dentro de símbolos de agrupación, calcula de adentro hacia afuera. Esto es, empieza simplificando los símbolos de agrupación en el centro.

Para obtener 76, se pueden realizar la siguiente operación combinada:

[(2*8) + 3] *4

Aplicando lo anteriormente mencionado de la jerarquía de operaciones, comienzas por resolver el paréntesis:

[16 + 3]*4

Ahora, resolviendo el corchete:

19*4

Finalmente, resolviendo la multiplicación:

19*4= 76

Entonces [(2*8) + 3] *4 =76

Para obtener 40, se pueden realizar la siguiente operación combinada:

[2*(8 - 3)]*4

Comenzando a resolver el paréntesis:

[2*5]*4

Ahora, resolviendo el corchete:

10*4

Finalmente, resolviendo la multiplicación:

10*4= 40

Entonces [2*(8 - 3)]*4 = 40

Proving  X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e".

Given :

If I can prove that X is c.e. and ω∖X is c.e. then I can prove that X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e". But I'm not able to proceed on how should I do this.

Take a computable surjection :

f : ω → W.

Defined  G = { f ( x ) ∣ x ∈ ω and ∀y < x ( f ( y ) < f ( x ) ) }.

here clearly, G ⊆ W .

And G is infinite. For if f ( x ) ∈ G, take the smallest y such that f ( y ) > f ( x ); then f ( y ) ∈ V.

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The markup amount of the purchase is $1114

From the question, we have the following parameters that can be used in our computation:

Discount = 30%

Selling price = $780

The markup amount is calculated using the following equation

Selling price = Markup amount * (1 - discount)

Make the markup the subject

Markup = Selling price/(1 - discount)

Substitute the known values in the above equation, so, we have the following representation

Markup = 780/(1 - 30%)

Evaluate

Markup = 1114

Hence, the markup is $1114

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Answer:

a) -73°C, -15°C, -12°C, 0°C, 16°C, 37°C, 96°C

a) 96°C, 37°C, 16°C, 0°C, -12°C, -15°C, -73°C

b) -36°C, -15°C, -7°C, -1°C, 0°C, 20°C, 23°C

b) 23°C, 20°C, 0°C, -1°C, -7°C, -15°C, -36°C

The triangles that have an area of 10 square units are triangles A and B

The area of a triangle is calculated using

Area = 0.5 * Base * Height

Triangle 1

Base = 5

Height = 4

So, we have

Area = 0.5 * 5 * 4

Area = 10

Triangle 2

Base = 4

Height = 5

So, we have

Area = 0.5 * 5 * 4

Area = 10

Triangle 3

Base = 5

Height = 5

So, we have

Area = 0.5 * 5 * 5

Area = 12.5

Hence, the triangles that have an area of 10 square units are triangles A and B

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Answer:

S(4) = 2

Step-by-step explanation:

S(n) = n(n - 3) / 2

S(4) = 4(4 - 3) / 2

= 4 x 1 / 2

= 4/2

= 2

Answer:

C

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Small bag

95p / 250 g * 12/12 to get to 3 kg = 1140 p / 3000g =11.40£s/ 3 kgs

Medium bag

1.8£  / 500 g * 6/6 to get to 3 kg = 10.8£ / 3000g =10.80£/ 3 kgs

Large bag

3.7£  / 3 kg *