the question is in the picture. please help

The equations of the line parallel to the z-axis and passing through the midpoint between the two given points are x = -1, y = 0.5, and z = t, where t represents the distance along the z-axis.

Since the line is parallel to the z-axis, its direction vector will be (0, 0, 1). Now, let's find the midpoint between the two given points:

Midpoint = ((0 + (-2))/2, (-2 + 3)/2, (7 + 5)/2)

= (-1, 0.5, 6)

Therefore, the line parallel to the z-axis and passing through the midpoint (-1, 0.5, 6) can be represented by the following set of parametric equations:

x = -1 (remains constant)

y = 0.5 (remains constant)

z = t (where t is a parameter representing the distance along the z-axis)

In Cartesian form, the equation of the line can be written as:

x = -1

y = 0.5

z = t

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Answer:

I think it's 21. .........

Answer:

42 quarts

Step-by-step explanation:

There are 4 quarts in one gallon, so you'd just multiply.

Tori will need to spend $88.00 to buy enough stain for the whole porch. The total area of the porch can be calculated as follows:

Area = length x width

Area = 8 feet x 11 feet

Area = 88 square feet

Since the cost of the stain is $1.00 per square foot, we can calculate the total cost of the stain needed for the porch by multiplying the area of the porch by the cost per square foot of the stain:

Total cost of stain = Area x Cost per square foot

Total cost of stain = 88 square feet x $1.00/square foot

Total cost of stain = $88.00

Therefore, Tori will need to spend $88.00 to buy enough stain for the whole porch.

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Answer:

The value of two numbers if their sum is 12 and their difference is 4 are 8 and 4.

Step-by-step explanation:

I hope this helped

The angle measure of NQL is given as follows:

m < NQL = 80º.

By the Parallelogram Consecutive Angles Theorem, <NQL and <QLM are supplementary.

The Parallelogram Consecutive Angles Theorem states that two consecutive interior angles in a parallelogram are supplementary, that is, the sum of their measures is of 180º.

The consecutive angles for this problem are given as follows:

As the measure of < QLM is of 100º, the measure of angle NQL is given as follows:

m < NQL = 180º - 100º

m < NQL = 80º.

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To solve this equation you: divide both sides of the equation into -5:

a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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The correct answer to the equation result = (h/3) * (y(1) + 4*sum(y(2:2:n)) + 2*sum(y(3:2:n-1)) + y(n+1));

Here's an example MATLAB code that implements the composite trapezoidal rule and the composite Simpson's rule for approximating definite integrals:

% Function to evaluate the relevant function f(x)

function y = evaluateFunction(x)

   % Define the function f(x) here

   y = log(x);  % Example: ln(x)

end

% Composite trapezoidal rule

function result = compositeTrapezoidalRule(a, b, n)

   h = (b - a) / n;

   x = linspace(a, b, n+1);

   y = evaluateFunction(x);

   result = (h/2) * (y(1) + 2*sum(y(2:n)) + y(n+1));

end

% Composite Simpson's rule

function result = compositeSimpsonsRule(a, b, n)

   h = (b - a) / n;

   x = linspace(a, b, n+1);

   y = evaluateFunction(x);

   result = (h/3) * (y(1) + 4*sum(y(2:2:n)) + 2*sum(y(3:2:n-1)) + y(n+1));

end

% Main program

a = 1;  % Lower limit of integration

b = 2;  % Upper limit of integration

n = 100;  % Number of subintervals

% Approximate the integral using the composite trapezoidal rule

approximation_trapezoidal = compositeTrapezoidalRule(a, b, n);

% Approximate the integral using the composite Simpson's rule

approximation_simpsons = compositeSimpsonsRule(a, b, n);

% Display the results

disp("Approximation using the composite trapezoidal rule:");

disp(approximation_trapezoidal);

disp("Approximation using the composite Simpson's rule:");

disp(approximation_simpsons);

To use this code, you need to define the function you want to integrate within the evaluateFunction function. In this example, the function evaluateFunction is defined to compute the natural logarithm of x.

You can change the values of a, b, and n to approximate different integrals. The n value determines the number of subintervals and can be adjusted to control the accuracy of the approximation.

To investigate the behavior of the errors, you can compare the approximations with the exact values of the integrals if known. You can also experiment with different values of n to observe how the errors decrease as the number of subintervals increases.

The choice of which technique is more accurate for a given cost depends on the specific function being integrated and the desired level of accuracy. Generally, the composite Simpson's rule provides a more accurate approximation than the composite trapezoidal rule for the same number of function evaluations, but it may require more computational resources.

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The correct answer is: ∣r(1)∣ is equal to 17.709167734312061, that is the magnitude of vector .

To find the magnitude of vector r(1), we need to integrate the vector function dt/dr(t) from t = 0 to t = 1 and then evaluate it at t = 1.

Given dtdr(t) = ⟨-te^t, 4e^(2t), 8te^(t^2)⟩ and r(0) = ⟨1, 1, 2⟩, we can integrate each component of dtdr(t) separately with respect to t.

Integrating the first component: ∫(-te^t) dt = -te^t + e^t + C1

Integrating the second component: ∫(4e^(2t)) dt = 2e^(2t) + C2

Integrating the third component: ∫(8te^(t^2)) dt is not a straightforward integral and might not have an elementary solution.

To find the constants C1 and C2, we can substitute t = 0 and equate it to r(0). From r(0) = ⟨1, 1, 2⟩, we get the following equations:

-0e^0 + e^0 + C1 = 1 => C1 + 1 = 1 => C1 = 0

2e^(2*0) + C2 = 1 => 2 + C2 = 1 => C2 = -1

With C1 = 0 and C2 = -1, we can determine the vector function r(t) by integrating each component:

r(t) = ⟨\(\int(-te^t) dt + 1, \int (4e^(2t)) dt - 1, \int (8te^(t^2)) dt + 2\)⟩

r(t) = ⟨\(-te^t + e^t + 1, 2e^(2t) - 1, \int (8te^(t^2)) dt + 2\)⟩

To find the magnitude of r(1), we substitute t = 1 into the vector function r(t) and evaluate it:

r(1) = ⟨\(-(1)e^1 + e^1 + 1, 2e^(2*1) - 1, \int(8te^(1^2)) dt + 2\)⟩

r(1) = ⟨-e + e + 1, 2e^2 - 1, ∫(8te) dt + 2⟩

r(1) = ⟨1, 2e^2 - 1, 8∫(te) dt + 2⟩

The first and second components are straightforward, but the third component involves integrating te with respect to t. We can evaluate this integral:

∫(te) dt = t^2e/2 - ∫(t^2e/2) dt

∫(te) dt = t^2e/2 - ∫(t^2/2)e dt

∫(te) dt = t^2e/2 - (1/2)∫(t^2)e dt

∫(te) dt = t^2e/2 - (1/2)(t^3/3)

∫(te) dt = t^2e/2 - t^3/6 + C3

Substituting t = 1 into this expression, we get:

∫(te) dt = (1^2e)/2 - (1^3)/6 + C3

∫(te) dt = e/2 -

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Answer:

It is a little hard to see.  I think that it is 10.

Step-by-step explanation:

They break even where the two lines intersect.  If you look at the bottom of the graph and find 10 and then trace that straight up, I think that is where I see the lines crossing.

Answer:

5600 ×11/100 = 616

616 × 3 = 1848

£5600 + £1848 = £7448

Step-by-step explanation:

Using the sample interest rate, we know that the value of investment after 3 years will be £7,448.

So, the value of the investment after 3 years will be:

Then, calculate as follows:

Total investment value: 5600 + 1848 = £7,448

Therefore, using the sample interest rate, we know that the value of investment after 3 years will be £7,448.

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Danny used half a cup of flour, so Paul Bunyan would need  2 cups of flour for his foot-diameter griddle.

To determine the number of cups of flour Paul Bunyan would need for his circular griddle, we need to compare the surface areas of the two griddles.

We know that Danny Henry's griddle has a diameter of six inches, which means its radius is three inches (since the radius is half the diameter). Thus, the surface area of Danny's griddle can be calculated using the formula for the area of a circle: A = πr², where A represents the area and r represents the radius. In this case, A = π(3²) = 9π square inches.

Now, let's calculate the radius of Paul Bunyan's griddle. We're given that it has a diameter in feet, so if we convert the diameter to inches (since we're using inches as the unit for the smaller griddle), we can determine the radius. Since there are 12 inches in a foot, a foot-diameter griddle would have a radius of six inches.

Using the same formula, the surface area of Paul Bunyan's griddle is A = π(6²) = 36π square inches.

To find the ratio between the surface areas of the two griddles, we divide the surface area of Paul Bunyan's griddle by the surface area of Danny Henry's griddle: (36π square inches) / (9π square inches) = 4.

Since the amount of flour required is directly proportional to the surface area of the griddle, Paul Bunyan would need four times the amount of flour Danny Henry used.

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You are designing a 5 kilometer course for charity run. The design now has been covers 4,908.5 meters, hence, you need to add more 91.5 meters on the course.

The conversion from yard to meter is:

1 yard = 0.9144 meters

The course streets and the distances after converted into meters are:

main street to 6th ave.  781 yards = 714.15 meters

6th ave. to pleasant road 1,250 yards = 1143 meters.

pleasant road to city park 275 yards = 251.46 meters

route through city park 2,337 yards = 2,136.95 meters

city park to main street 725 yards = 662.94 meters

Total course = 714.15 + 1143 + 251.46 +  2,136.95 +  662.94

Total course = 4,908.5 meters

The design is 5 km = 5000 meters. Therefore, you still need to add:

5000 - 4,908.5 = 91.5 meters more course.

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Answer: The area is 6.5

Answer:

The total weight of the pool when it is full of water is 690.2 pounds.

Step-by-step explanation:

We know that total weight of the wading pool (\(m_{T}\)) is the sum of the weight of empty pool (\(m_{pool}\)) and the weight of water (\(m_{w}\)), all measured in pounds, that is:

\(m_{T} = m_{pool} + m_{w}\)

The weight of water can be determined by definition of density, as we know the geometry of the wading pool and density of water:

\(m_{w}=\rho_{w}\cdot (w\cdot h\cdot l)\)

Where:

\(\rho_{w}\) - Density, measured in pounds per cubic foot.

\(w\), \(h\), \(l\) - Width, height and length of the wading pool, measured in feet.

Now, we are noticed that \(\rho_{w} = 6.24\,\frac{pd}{ft^{3}}\), \(w = 7\,ft\), \(h = 6\,ft\), \(l = 2.5\,ft\) and \(m_{pool} = 35\,pd\) and the total weight of the pool when it is full of water is:

\(m_{w} = \left(6.24\,\frac{pd}{ft^{3}} \right)\cdot (7\,ft)\cdot (6\,ft)\cdot (2.5\,ft)\)

\(m_{w} = 655.2\,pd\)

\(m_{T} = 35\,pd + 655.2\,pd\)

\(m_{T} = 690.2\,pd\)

The total weight of the pool when it is full of water is 690.2 pounds.

Answer:

Mallory gets paid $20 for every 1 hour.

Step-by-step explanation:

You take the lowest set of numbers in this table, & divide them to find how much it would be for 1 hour: $40÷2hours= $20

ratio 1 hr./20 dollars

The two ways to write the expression k/3+16 are 1/3k + 16 and (k + 48)/3

From the question, the expression is given as

k/3+16

Start by factoring 1/3 out of the first term

So, we have the following expression

1/3k + 16

The above is one of the ways of rewriting the expression

Another way is by taking the LCM

So,we have

k/3+16 = (k + 48)/3

Hence, the equivalent expressions are 1/3k + 16 and (k + 48)/3

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Answer:

A.

81π

Step-by-step explanation:

PLEASE MAKE IT BRAINLIEST

PLEASE FOLLOW....

I believe the answer would be M= 132 because 48+132=180 and 180 is the degree of a straight line. I hope this makes sense! :)

Answer:

11

Step-by-step explanation:

11

since it asks the absolute value of -11 it

will be 11 because in absolute value-for negatives it always positive.

Answer:

see attached

Step-by-step explanation:

its 2 gallons

4 would be 16

12 would be 48

32 would be 128

Some of the most common symbols used in formulas include (addition), - (subtraction), * (multiplication), and / (division). These are called "operators". The correct option is c) operators.

Operators are symbols that represent a specific operation to be performed on one or more values or variables. In mathematics and programming, operators are used to build expressions that represent calculations. The most common operators include addition (+), subtraction (-), multiplication (*), and division (/), which are used to perform basic arithmetic operations.

Other operators include exponents (^), modulus (%), and comparison operators (>, <, =, etc.), which are used for more complex operations. Understanding operators is an essential part of learning mathematics and programming, as they form the building blocks for more complex calculations and algorithms. The correct option is c) operators.

The complete question is:

Fill in the blank: Some of the most common symbols used in formulas include + (addition), - (subtraction), * (multiplication), and / (division). These are called _____.

a) references

b) domains

c) operators

d) counts

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Answer:

16.6 in

Step-by-step explanation:

Amount of space left = volume of prism - volume of 3 golf balls

volume of prism = base area x height

base area = area of a square  = length² = 2² = 4

volume = 4 x 6 = 24

Volume of a sphere = 4/3 x pi x r^3

r = 1.68/2 = 0.84

4/3 x 3.14 x 0.84^3 = 2.48

volume of 3 balls = 2.48 x 3 =

The congruent segments are the sides of the small triangles, then the congruent segments are: HA, BD and BF.

Therefore the answer are B, E and F.

Duela Dent's income taxes can be calculated using the given tax rates and her taxable income of $189,000. Her average tax rate and marginal tax rate can also be determined.

To calculate Duela Dent's income taxes, we need to determine the tax amount for each tax bracket that her taxable income falls into.

The taxable income of $189,000 falls into the following tax brackets:

$0-$9,950: Not applicable

$9,950-$40,525: ($40,525 - $9,950) * 12% = $3,546

$40,525-$86,375: ($86,375 - $40,525) * 22% = $9,992

$86,375-$164,925: ($164,925 - $86,375) * 24% = $19,110

$164,925-$209,425: ($189,000 - $164,925) * 32% = $7,744

$209,425-$523,600: Not applicable

$525,600 and above: Not applicable

Summing up the tax amounts for each bracket, Duela Dent's income taxes amount to $40,392.

The average tax rate is calculated by dividing the total tax amount ($40,392) by the taxable income ($189,000) and multiplying by 100:

Average Tax Rate = ($40,392 / $189,000) * 100 ≈ 21.37%

The marginal tax rate refers to the tax rate applied to an additional dollar of income. In this case, Duela Dent's marginal tax rate is 32%, which corresponds to the tax rate of the last bracket her taxable income falls into.

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Answer: 2.25

Step-by-step explanation: 2.25 because if u subtract 10.75 - 8.5 = 2.25

The net of a triangular pyramid consist of a total of 4 triangles. it has 4 faces with the base being one of them which is also in the shape of a triangle.

A net of the triangular pyramid is the pattern formed when the surface of it is laid out flat showing each triangular face of the figure, therefore we know that the net of a triangular pyramid consist of a total of 4 triangles.

Triangular pyramid  is a pyramid which has a triangular base. In geometry, vertices are essentially corners. All triangular-based pyramids, either regular or irregular, have four vertices.

It has 6 edges, 4 faces, 4 vertices.

A regular triangular pyramid has equilateral triangles all four faces

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Answer:

1.5 feet of the Bush is still above ground

Step-by-step explanation:

3 2/10= 3.2

3.2-1.7=1.5

Given:

Coordinates of point C are (-3,6).

Point B(0,5.5) is the midpoint of AC.

To find:

The coordinates of A.

Solution:

Let the coordinates of point A are (a,b).

Formula for midpoint:

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

Using the above formula, the midpoint of A(a,b) and C(-3,6) is

\(B=\left(\dfrac{a+(-3)}{2},\dfrac{b+6}{2}\right)\)

\((0,5.5)=\left(\dfrac{a-3}{2},\dfrac{b+6}{2}\right)\)

On comparing both sides, we get

\(\dfrac{a-3}{2}=0\)

\(a-3=0\)

\(a=3\)

and,

\(\dfrac{b+6}{2}=5.5\)

\(b+6=11\)

\(b=11-6\)

\(b=5\)

Therefore, the coordinates of point A are (3,5).