The total cost after tax to repair Susan’s dishwasher is represented by 0.07(35h) + 35h, where h represents the number of hours it takes to repair Susan’s dishwasher. Choose a coefficient or term in the expression and explain what it means in context of the problem.

The quadratic equation that has a discriminant of 0 is x^2 - 4x + 4 = 0.

The discriminant of a quadratic equation is calculated using the formula b^2 - 4ac, where 'a', 'b', and 'c' are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

For the quadratic equation x^2 - 12x + 38 = 0, the coefficients are: a = 1, b = -12, and c = 38. Calculating the discriminant, we have:

Discriminant = (-12)^2 - 4(1)(38) = 144 - 152 = -8

Since the discriminant is -8, it is not equal to 0.

However, for the quadratic equation x^2 - 4x + 4 = 0, the coefficients are: a = 1, b = -4, and c = 4. Calculating the discriminant, we have:

Discriminant = (-4)^2 - 4(1)(4) = 16 - 16 = 0

Since the discriminant is 0, this is the quadratic equation with a discriminant of 0.

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The range of the parabola will be y ≥ 6.

Given is that a graph of a parabola opens up and the minimum point is located at (-3, 6).

Therefore, the range of the parabola will be y ≥ 6.

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Answer:

$180 in total!

Step-by-step explanation:

10 + 30 + 30 + 100 + 10 = 180

the uncle and aunt gave their money together, it didn't specify that they each gave 100

Answer:

The total amount of money i have is $180.

Step-by-step explanation:

Given information:

The money i have = $10

Mom gives = $30

Dad gives = $30

Aunt and uncle gives = $100

Now i had another $10

The total amount of money (x) i have is the sum of all money i receive.

x = 10+30+30+100+10

x = 180

Hence , the total amount of money i have is $180.

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The group who has the largest percentage of people who prefer to travel by automobile is given as follows:

Adult.

A bar graph, also known as a bar chart, is a type of graph used to represent and compare data. It consists of rectangular bars of equal width and varying heights, where the height of each bar represents the value of the data being graphed.

Automobiles are represented by the green bars, hence we must observe the input for which the green bar has the largest value, which is for adults, hence adults compose the largest percentage of people who prefer to travel by automobile.

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sequent depth in the spillway = 3.54 m.

The sequent depth d2 in a spillway can be determined using the following equation:

d2 = d1 * (1 + 8 * F1 * cos(phi) - 1)^(1/2)

where:

d1 is the initial depth

F1 is the Froude number at the initial depth

phi is the angle of the spillway

The initial depth can be calculated using the following equation:

d1 = (Q * 2g) / (n * b * R^2)

where:

Q is the discharge

g is the acceleration due to gravity

n is the Manning's roughness coefficient

b is the channel width

R is the hydraulic radius

The Froude number can be calculated using the following equation:

F1 = V1 / (sqrt(g * d1))

where:

V1 is the initial velocity

The angle of the spillway can be determined by considering the geometry of the spillway.

In this case, the initial depth is 8.6 m, the discharge is 8.0 m3/s, the Manning's roughness coefficient is 0.015, the channel width is 4.0 m, the hydraulic radius is 2.0 m, the head loss is 0.5 m, and the angle of the spillway is 45 degrees.

The Froude number at the initial depth is:

F1 = V1 / (sqrt(g * d1)) = V1 / (sqrt(9.81 * 8.6)) = 1.43

The sequent depth d2 is:

d2 = d1 * (1 + 8 * F1 * cos(phi) - 1)^(1/2) = 8.6 * (1 + 8 * 1.43 * cos(45) - 1)^(1/2) = 3.54 m

Therefore, the sequent depth in the spillway is 3.54 m.

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Answer:

hence the value of x is 6

Step-by-step explanation:

\( {4}^{4x} = {64}^{x + 2} \\ {4}^{4x} ={ 4}^{3(x + 2)} \\ 4x = 3x + 6 \\ 4x - 3x = 6 \\ x = 6\)

The value of x in the expression given is -94/7

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between

Given is an expression 3/4(x+2) = 6(x+12), we need to find the value of x,

3/4(x+2) = 6(x+12)

Multiply by 4 in the expression [multiplication property of equality]

3(x+2) = 24(x+12)

Divide by 3 in the expression [Division property of equality]

x+2 = 8(x+12)

Open brackets and multiply by 8 in the RHS  of the expression [distributive property]

x+2 = 8x+96

Subtract x from both sides [subtraction property of equality]

x-x+2 = 8x-x+96

2 = 7x+96

Subtract 96 from both sides [subtraction property of equality]

2-96 = 7x+96-96

-94 = 7x

Divide by 7 in the expression [Division property of equality]

-94/7 = x

x = -94/7

Hence, the value of x in the expression given is -94/7

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To evaluate the double integral ∬r(5x^8y)^2 da, we need to determine the limits of integration for both x and y within the region R.

(a) The triangle R has vertices at (-1, 0), (0, 1), and (1, 0). To set up the iterated integral, we can integrate over x first, then y. The limits of integration for x will depend on the y-value within the triangle.

Considering the left side of the triangle, the limits of integration for x are -1 to 0. For the right side of the triangle, the limits of integration for x are 0 to 1. As for y, it ranges from the bottom of the triangle (y = 0) to the top (y = 1 - x).

Therefore, the iterated integral can be expressed as:

∬r(5x^8y)^2 da = ∫[-1,0]∫[0,1-x] (5x^8y)^2 dy dx.

We first integrate with respect to y, from 0 to 1 - x, and then integrate the resulting expression with respect to x, from -1 to 0.

In the first integration, we obtain the expression (5x^8y)^2 evaluated from y = 0 to 1 - x. This simplifies to (5x^8(1 - x))^2.

In the second integration, we evaluate the expression (5x^8(1 - x))^2 with respect to x from -1 to 0. This will give us the final value of the double integral.

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All five of the triple integrals are over the same region of space, they should produce the same result so the one that produces a different result must be over a different region.

a. The triple integral for F(x, y, z) over the region D with order of integration dy dz dx is x=0 to 1, y=0 to x and z=0 to 1-x-y.

b. The triple integral for F(x, y, z) over the region D with order of integration dx dy dz is z=0 to 1, y=0 to 1-z and x=y to 1-z.

c. The triple integral for F(x, y, z) over is 0 ≤ z ≤ 1 - x - y, 0 ≤ x ≤ y and 0 ≤ y ≤ 1.

To evaluate the function F(x, y, z) over the region D, we need to set up the appropriate triple integral. Since the order of integration is given, we can use that to determine the limits of integration.

(a) dy dz dx:

In this order of integration, we integrate with respect to y first, then z, then x.

The limits of integration for x are from 0 to 1.

For y, the limits of integration depend on the value of x. When x is between 0 and y, the limits of y are from 0 to 1. When x is between y and 1, the limits of y are from 0 to x.

For z, the limits of integration depend on the value of y and x. When x is between 0 and y, and y is between 0 and 1, the limits of z are from 0 to 1 - x - y. When x is between y and 1, and y is between 0 and x, the limits of z are from 0 to 1 - x - y.

Therefore, the triple integral for F(x, y, z) over the region D with order of integration dy dz dx is:

∫∫∫ F(x, y, z) dy dz dx

x=0 to 1

y=0 to x

z=0 to 1-x-y

(b) dx dy dz:

In this order of integration, we integrate with respect to x first, then y, then z.

The limits of integration for z are from 0 to 1.

For y, the limits of integration depend on the value of z. When z is between 0 and 1 - x - y, the limits of y are from 0 to 1 - x - z. When z is between 1 - x - y and 1 - x, the limits of y are from 0 to x + y - 1.

For x, the limits of integration depend on the value of y and z. When z is between 0 and 1 - x - y, and y is between 0 and 1 - x - z, the limits of x are from 0 to 1 - z. When z is between 1 - x - y and 1 - x, and y is between 0 and x + y - 1, the limits of x are from y to 1 - z.

Therefore, the triple integral for F(x, y, z) over the region D with order of integration dx dy dz is:

∫∫∫ F(x, y, z) dx dy dz

z=0 to 1

y=0 to 1-z

x=y to 1-z

(c) dz dx dy:

In this order of integration, we integrate with respect to z first, then x, then y.

The limits of integration for y are from 0 to 1.

For x, the limits of integration depend on the value of y. When y is between 0 and x, the limits of x are from 0 to y. When y is between x and 1, the limits of x are from 0 to 1 - y.

For z, the limits of integration depend on the value of x and y. When y is between 0 and x, and x is between 0 and 1, the limits of z are from 0 to 1 - x - y. When y is between x and 1, and x is between 0 and 1, the limits of z are from 0 to 1 - y.

Therefore, the triple integral for F(x, y, z) over the region D in the order of integration dz dx dy is:

∫∫∫ F(x, y, z) dz dx dy

where the limits of integration are:

0 ≤ z ≤ 1 - x - y

0 ≤ x ≤ y

0 ≤ y ≤ 1

So, we can write:

∫∫∫ F(x, y, z) dz dx dy = ∫₀¹ ∫₀¹-y ∫₀¹-x-y F(x, y, z) dz dx dy

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The question is -

Evaluate the function, F ( x, y, z ) over the region D, a tetrahedron with vertices ( 0, 0, 0 ), ( 1, 1, 0 ), ( 0, 1, 0 ), and ( 0, 1, 1 ). Set up the appropriate triple integral if the order of integration is, (a) dy dz dx. (b) dx dy dz. (c) dz dx dy. Which one is different?

Answer:

False

Step-by-step explanation:

In the confidence interval, the population parameter is unknown and the interval is a random variable.

The  |120-x| simplifies to 120-x when x is less than 120.

S If x is less than 120, then the expression |120-x| simplifies to 120-x. This is because the absolute value bars mean that the result must be positive,

so if x is already less than 120, then subtracting x from 120 will give a positive result.

For example, if x is 115, then |120-x| would equal |120-115|, which simplifies to |5|, which equals 5.  

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Answer:

2,075 = 5 × 5 × 83

√2,075 = 5√83 = about 45.55

Absolute change is the numerical difference between two values and relative change is the proportional difference between two values expressed as a percentage.

Absolute change is the numerical difference between two values and is typically expressed as a positive number. It tells us the amount by which a value has increased or decreased.

For example, if the temperature increases from 20 degrees Celsius to 25 degrees Celsius, the absolute change in temperature is 5 degrees Celsius.

Relative change, on the other hand, is the proportional difference between two values and is typically expressed as a percentage. It tells us the amount by which a value has increased or decreased relative to its original value.

For example, if the price of a product increases from $10 to $15, the relative change in price is 50%, because the increase of $5 is 50% of the original price of $10.

In summary, absolute change is the numerical difference between two values and relative change is the proportional difference between two values expressed as a percentage.

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Answer: 40%

Step-by-step explanation:

There are four red marbles and six blue marbles, so there is a total of 10 marbles. Since four of those marbles are red, there is a 4 in 10 chance to select a red marble, or 4/10. 4/10 equals 0.4 which in terms of percentage is 40% (multiply by 100).

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

3a=4.5

Step-by-step explanation:

it says that "a is equal to 3 times b", which translates to a=3b

We can substitute a as 3b in 2a+4b=5

2(3b)+4b=5

multiply

6b+4b=5

add

10b=5

divide by 10

b=1/2

since it's given that a=3b, we can multiply 1/2 by 3

a=3/2

3a is 3 times a, so we can mutiply 3(3/2)=9/2=4.5

Hope this helps!

Answer:

Point form:

(4,-1)

x=4,y=-1

Step-by-step explanation:

Graph:

Answer:

x = 4 , y = -1

Step-by-step explanation:

Note that both equations equal y. Set the two equations equal to each other.

x - 5 = y = -x + 3

x - 5 = -x + 3

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

First, add x and 5 to both sides of the equations:

x (+x) - 5 (+5) = -x (+x) + 3 (+5)

x + x = 3 + 5

2x = 8

Next, divide 2 from both sides of the equation:

(2x)/2 = (8)/2

x = 8/2

x = 4

Plug in 4 for x in the given equations and solve:

y = x - 5

y = (4) - 5

y = -1

y = -x + 3

y = -(4) + 3

y = -1

x = 4 , y = -1 are your answers.

~

~

Answer:

Linear

Step-by-step explanation:

We can see if it is by graphing. See attached. The function is linear because it is a straight line and is a one-to-one function.

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

To display formulas, one way is to press the key combination [Ctrl]+[] (grave accent).

The key combination [Ctrl]+[] is used to display formulas.

This is a useful feature for checking and editing formulas without altering the calculated values.

By pressing [Ctrl]+[], users can easily view the underlying formulas and ensure their accuracy.

This key combination provides a convenient way to switch between the formula view and the results view, enabling efficient editing and troubleshooting of complex calculations.

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Answer:

18 sides

Step-by-step explanation:

(N x 180) - 360 = 160N

180N -360 = 160N

20N = 360

N = 18

Proof:

(18 x 180) -360 = 2880 total degrees

2880/18 sides = 160°

Answer:

Step-by-step explanation:

In my opinion yes I think so

Answer: 86 mph

Step-by-step explanation:

Given

Ms. Dos has driven 94.6 miles

Time is taken 1.1 hours

Average speed is given by the ratio of total distance and total time taken

\(\Rightarrow \text{Average speed v=}\dfrac{94.6}{1.1}\\\\\Rightarrow v=86\ mph\)

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

y=-1/3x-1 I believe

Step-by-step explanation:

The Y intercept is where the line meets the Y line, which crosses at -1 and for slope, find a point and do rise/run. This question goes down 1 and to the right 3 so -1/3

The solution to the system of inequalities is (-1, 4).

To graph the system of inequalities and identify the point that represents a solution, we will plot the lines corresponding to the inequalities and shade the regions that satisfy the given conditions.

The first inequality is x > -2, which represents a vertical line passing through x = -2 but does not include the line itself since it's "greater than." Therefore, we draw a dashed vertical line at x = -2.

The second inequality is y ≤ 2x + 7, which represents a line with a slope of 2 and a y-intercept of 7.

To graph this line, we can plot two points and draw a solid line through them.

Now let's plot the points (-1, 6), (1, 11), (-1, 4), and (-3, -1) to see which one lies within the shaded region and satisfies both inequalities.

The graph is attached.

The dashed vertical line represents x > -2, and the solid line represents y ≤ 2x + 7. The shaded region below the solid line and to the right of the dashed line satisfies both inequalities.

By observing the graph, we can see that the point (-1, 4) lies within the shaded region and satisfies both inequalities.

Therefore, the solution to the system of inequalities is (-1, 4).

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Answer:

What are you solving for?

Step-by-step explanation:

Answer:

(7.5,4.1)

Step-by-step explanation:

Given

3x_7y =_40

3x_2y=_4

sol

3x_7y=_40..... equation 1

3x_2y=_4 ..... eq 2

here

eq 2 multi 3 eq 1 multiply 3

9x_21y=_120

9x_6y=_12

_ + = +

__________

0x+ 15y =108

y=108÷15

y=7.5

the y value putting the eq 1

3x_7y=_40

3x_7×7.5=_40

3x_52.5=_40

3x=52.5_40

3x=12.5

x=12.5÷3

x=4.1