Raj is making korma for a party. He puts 25 g of curry powder

The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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Answer:

b is the vertical line while y is the horizontal

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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The equation representing the ball's movement is given as follows;

To determine the value of t (that is, time), we shall now make the equation become;

This is because when the height is zero, then the ball has actually touched the ground. So making h equal to zero, we now have a quadratic equation and we shall solve it using the quadratic equation formula as follows;

The variables are,

We now have;

The quadratic equation now has two solutions.

Note however, that the question requires us to determine the time taken and we know this cannot be a negative value.

Therefore, we shall take t = 3.1896, and rounded to the nearest hundredth this becomes;

Answer:

.67

Step-by-step explanation:

There are three friends and two pies. You are splitting the pies not the people so you divide 2 by 3 to get 0.66666667. Meaning each girl got .67 or around 6/10 of a pie.

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

To find the equation of a parabola that passes through two points and a third point, we need to write a system of three equations in three variables (a, b, and c) using the standard form of the parabolic equation, and then solve for the variables.

To find the equation of a parabola that passes through two points, we can use the standard form of a parabolic equation: y = ax^2 + bx + c. Since we have two points, (x1,y1) and (x2,y2), we can write two equations:
y1 = ax1^2 + bx1 + c
y2 = ax2^2 + bx2 + c
We need to solve for a, b, and c. One way to do this is to eliminate c by subtracting the second equation from the first:
y1 - y2 = a(x1^2 - x2^2) + b(x1 - x2)
Now we can use the fact that the parabola passes through a third point, (x3,y3), to write another equation:
y3 = ax3^2 + bx3 + c
We can substitute c from the first equation into this equation:
y3 = ax3^2 + bx3 + y1 - a(x1^2 - x2^2) - b(x1 - x2)
Now we have three equations and three unknowns (a, b, and c), which we can solve using algebra or matrix methods. Once we have the values of a, b, and c, we can plug them into the standard form of the parabolic equation to get the equation of the parabola that passes through the three points.
The resulting equation will be the equation of the parabola that passes through the given points.

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The calculated z-value, rounded to the nearest hundredth, is -11.88 ,  there is enough evidence to reject the insurance company's claim

The automobile insurance company claims that it offers an average savings of $470 for teenage drivers compared to another company. To test this claim, we'll use the given data from the random sample of 30 customers with an average savings of $405 per year and a standard deviation of $30 per year.
To calculate the z-value, we'll use the formula:
z = (sample mean - population mean) / (standard deviation ÷ √sample size)
Here, the sample mean is $405, the population mean is $470, the standard deviation is $30, and the sample size is 30.
z = ($405 - $470) ÷ ($30 / √30)
z = (-$65) ÷ ($30 ÷ √30)
z = -65 ÷ (30 ÷ 5.48)
z = -65 ÷ 5.47
z ≈ -11.88
To determine whether there is enough evidence to reject the company's claim, we'll compare the z-value with the critical value, usually a 95% confidence interval (z = ±1.96). Since -11.88 is far outside this range.

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Algebraic expressions are mathematical statements made up of variables, constants, and operations, which can be simplified to -17x²+4x+5.

Given expression: -10x²+4x-7x²+5.A mathematical statement made up of variables, constants, and mathematical operations is known as an algebraic expression. It stands for a mixture of numbers and letters, where the letters are called variables and they can have various values. In algebra, relationships are represented and calculations are done using algebraic expressions.

The given expression can be simplified as:

Adding the like terms together,

we get,-10x²-7x²+4x+5

= -17x²+4x+5

Thus, the simplified expression is -17x²+4x+5.

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Answer:

y=-4/5 x + 7

Step-by-step explanation:

Subtract 8 x by 8 x. Do not put 8 x under 10 y or 70.

Then divide 10 by all of the terms.

Then you have: y= 7  - 8/10 x

But then you have to flip 7 and - 8/10 x

And get y= -8/10 x + 7

Simplified is y= 4/5 x + 7

REMEMBER: y=m x + b

M= Slope

B= y-intercept

Answer:

60

Step-by-step explanation:

Plug in 4 for y

3(4)² + (4) + 8

3(16) + 4 + 8

48 + 12

60

Using 3 different methods, we can find that YZ = 25m

Method 1:

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations -

sin(θ) = (opposite side)/Hypotenuse

cos(θ) = (adjacent side)/Hypotenuse

tan(θ) = (opposite side)/(adjacent side)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent side

YZ = opposite side.

We want to find YZ, so with the known things, we can use the first relation:

sin(30°) = YZ/50m

YZ = sin(30°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 2:

We know that the sum of the measure of all the internal angles of a triangle is always equal to 180°.

In a right-angled triangle, we have an angle equal to 90°.

Then we can write -

Z + 90° + 30° = 180°

Z = 180° - 90° - 30°

Z = 60°

From this angle, the side YZ is the adjacent side, then we can use the second trigonometric relation:

cos (60°) = YZ/50m

YZ = cos(60°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 3:

With the same angle of 60° we could find side XY, the opposite side as follows:

sin(60°) = XY/50m

XY = sin(60°) * 50m

XY = √3/2 *50m

XY = 25m

Now that we know one of the sides, we can use the last trigonometric relation-

tan(60°) = XY/YZ

tan(60°) = 43.3m/YZ

YZ =  43.3m/tan(60°)

YZ = 25m

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The complete question is -

Describe three ways to determine the measure of segment YZ.

Triangle XYZ is shown. Angle XYZ is a right angle and angle ZXY is 30 degrees. The length of hypotenuse XZ is 50 meters.

A firm has the short-run total cost function c(y) = 4y^2 + 100; its marginal cost is mc(y) = 8y. At the A: 5 quantity of output the short-run average cost is minimized.

AC=c/y,   where y is the output produced

AC= c/y= (4y^2 + 100)/y

            = 4y+100/y

To minimize AC, the first derivative of the AC function is determined

dAC/dy= 4 -100/y^2

4 -100/y^2=0

4 = 100/y^2

y^2 = 100 /4

y^2 = 25

y = 5

At y=5 we find the second derivative of the AC function to ascertain if AC is minimized.

d(dAC/dy)= -200/y^3

-200/(5)^3= 1.6,   revealing that AC is minimized at y=5.

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Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Solve the problem?

Given that a card is selected from a 52-card deck that has been thoroughly shuffled without being replaced, the following card is drawn.

A: The top card is a 4, and B: The next card is an ace.

Probability =A∩B

After this first card is pulled, if 10is drawn, we have 51 cards left with 4 aces in them. This is the probability we need to discover for

P(A). =  10/52  

P(B) = number of aces in 51 cards divided by 51, thus = 4/51

Hence A∩B =10/52×10/51

=   100/2652

(From this, we can see that, after changing the card count, A and B are independent.

Additionally, we multiply the probability for both.)

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Answer: \(\boxed{\left(c-\frac{5}{2}-\frac{i\sqrt{11}}{2} \right)\left(c-\frac{5}{2}+\frac{i\sqrt{11}}{2} \right)}\)

Step-by-step explanation:

Using the quadratic formula to find the roots of the equation,

\(c=\frac{-(-5) \pm \sqrt{(-5)^2 -4(1)(9)}}{2(1)}\\\\c=\frac{5}{2} \pm \frac{i\sqrt{11}}{2}\)

So,

\(c^2 -5c+9=\boxed{\left(c-\frac{5}{2}-\frac{i\sqrt{11}}{2} \right)\left(c-\frac{5}{2}+\frac{i\sqrt{11}}{2} \right)}\)

Answer:

x = 4\(\sqrt{6}\) , y = 8\(\sqrt{2}\)

Step-by-step explanation:

Using the sine ratio in the right triangle on the left and the exact value

sin45° = \(\frac{\sqrt{2} }{2}\)

let the altitude of the outer triangle be h ( common to both right triangles )

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{h}{8}\) = \(\frac{\sqrt{2} }{2}\) ( cross- multiply )

2h = 8\(\sqrt{2}\) ( divide both sides by 2 )

h = 4\(\sqrt{2}\)

----------------------------------------------------------------

Using the tangent ratio in the right triangle on the right and the exact value

tan30° = \(\frac{1}{\sqrt{3} }\) , then

tan30° = \(\frac{opposite}{adjacent}\) = \(\frac{h}{x}\) = \(\frac{4\sqrt{2} }{x}\) = \(\frac{1}{\sqrt{3} }\) ( cross- multiply )

x = 4\(\sqrt{6}\)

--------------------------------------------------------------------

Using the sine ratio in the right triangle on the right and the exact value

sin30° = \(\frac{1}{2}\) , then

sin30° = \(\frac{h}{y}\) = \(\frac{4\sqrt{2} }{y}\) = \(\frac{1}{2}\) ( cross- multiply )

y =8\(\sqrt{2}\)

Answer:

Step-by-step explanation:

are the what???

If 100 students participate in the fundraiser, each student needs to raise $137.50.If 25 students participate in the fundraiser, each student needs to raise amount $550.

Amount = (Total Amount Needed) ÷ (Number of Students)

For 60 students:

Amount = $275 ÷ 60 = $4.58

For 75 students:

Amount = $275 ÷ 75 = $3.67

For 40 students:

Amount = $275 ÷ 40 = $6.88

To solve this problem, we need to use a simple equation: Amount = (Total Amount Needed) ÷ (Number of Students). We can then plug in the given information to calculate the amount each student needs to raise. For example, if 50 students participate in the fundraiser, we can calculate that each student needs to raise $275 ÷ 50 = $5.50. We can then use this equation to calculate the amount that each student needs to raise if there are different numbers of students participating in the fundraiser. For example, if there are 100 students participating in the fundraiser, each student needs to raise $275 ÷ 100 = $2.75. Similarly, if there are 25 students participating in the fundraiser, each student needs to raise $275 ÷ 25 = $11.00.

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Answer:

A

Step-by-step explanation:

The y intercept = (0,0) since the c value = 0.

Since the numerical coefficient of x^2 is > 0, the graph opens upward.

a = 1

b = 7

c = 0

The Table describing all the conditions is A

y =-1/2x+7 is the equation of the line that is parallel to 2x+4y=6 and passes through the point (6, 4).

Parallel to 2x+4y=6 and passing through(6,4) 2 x 4y = 6

Find the slope of this line and make y the subject 4y=-2x 6

By Dividing the equation by 4 we get:

y=-1/2 x + 3/2

Compare this equation with y=mx+b

slope m=-1/2

The slope of a line parallel to the above line will be the same

The slope of the required line will be - 1/2

m=-1/2,  at the point (6,4)

Finding b by plugging the values of m & the point in y=mx+b

4=-3+b

b= 7

m=-1/2

Plug value of the slope and b in y = mx +b

The required equation is y=-1/2x+7

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Using the given approximations, logb(1/42) can be simplified to -1 * (logb(6) + logb(7)). Substituting the given values, the logarithm of logb(1/42) is approximately -3.738.

To find the logarithm of logb(1/42), we can use logarithmic properties to simplify the expression.

First, let's rewrite 1/42 as 42^(-1) to make it easier to work with:

logb(1/42) = logb(42^(-1))

Next, we can use the power rule of logarithms, which states that logb(a^k) = k * logb(a). Applying this rule, we can bring the exponent -1 down as a coefficient:

logb(42^(-1)) = -1 * logb(42)

Now, we can express logb(42) using the given logarithmic approximations:

logb(42) = logb(6 * 7)

Using the properties of logarithms, we can break this expression into two parts:

logb(42) = logb(6) + logb(7)

Substituting the given approximations:

logb(42) ≈ 1.792 + 1.946

Now, we can substitute this value back into our previous expression:

logb(1/42) ≈ -1 * (1.792 + 1.946)

logb(1/42) ≈ -1 * 3.738

Therefore, the logarithm of logb(1/42) is approximately -3.738.

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Answer:

d. $34.94

Step-by-step explanation:

the monthly finance charge = (24 * 145.59) /100 = $34.94

Answer:

2x - 31 = -2x - 31

I hope this helps!

By drawing the green section within a right triangle inside the rectangle, we are able to determine its area using the known dimensions of the rectangle. This method ensures that the green section's area is accurately calculated.

To determine the area of the green section inside a rectangle, by drawing it within a right triangle:

1. First, draw the rectangle and identify its length and width.

2. Next, draw a right triangle inside the rectangle, making sure that the green section is completely contained within this triangle.

One side of the triangle should be parallel to the rectangle's length, and the other side should be parallel to the rectangle's width. The hypotenuse will connect the opposite corners of the rectangle.

3. Now, we can determine the lengths of the right triangle's legs using the length and width of the rectangle.

For example, if the rectangle's length is 10 units and its width is 6 units, the right triangle's legs would have lengths of 10 and 6 units.

4. Since we know the lengths of the right triangle's legs, we can use these measurements to find the area of the green section inside the rectangle.

By drawing the green section within a right triangle inside the rectangle, we are able to determine its area using the known dimensions of the rectangle.

This method ensures that the green section's area is accurately calculated.

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The equation of the line that a slope of 6 and a y-intercept of -9 will be y = 6x - 9.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation of the line that a slope of 6 and a y-intercept of -9 will be

The equation of the line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

Then we have

m = 6 and c = - 9

Then the equation of the line will be

y = 6x - 9

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The total Cost of the equipment is $2,27,700. In which the following included, excluded and expensed as incurred are

Invoicing costs - included in the price

Electrical work required for installation - Included in the price

Delivery costs - included in the price

Sales tax - included in the price

Repair costs - not included or excluded

A machine used by a company to produce products and services is known as a machine tool. It is a vital long-term asset as it speeds up the production process such as transportation, computers and other equipment. These costs will include the costs that were necessary to start opening the plant property. There are equipment costs.

We have given the following details ,

Total Cost DR Machinary DR Expense

Invoice cost $190,000 $190,000

electric work

and $20,000 $20,000

installation cost

delivery cost। $4,000 $4,000

sales tax $13,700 $13,700

repair cost $1,850 $1,850

total $22,9550 $22,7700 $ 1,850

Accordingly, all the mentioned costs except for the repair of the part will be included in the cost of the machinery.

Included in price Excluded

invoice repair cost

electric and installation

delivery

sales tax

Hence , the total equipment cost is $22,7700.

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The predicted population of Glandian rats in 2031 will be approximately 33,290.

In the case of Gland, the population of rats is growing at a rate proportional to its size. This means that the growth can be modeled using an exponential function. Given the data from 2019 (9,325 rats) and 2022 (12,140 rats), we can find the growth rate (r) and use it to predict the population in 2031.
Let's denote the initial population as P0, the population after t years as Pt, the growth rate as r, and the time elapsed in years as t.
1. Calculate the annual growth rate:
Pt = P0 * (1 + r)^t
12,140 = 9,325 * (1 + r)^(2022-2019)
12,140 = 9,325 * (1 + r)^3
2. Solve for r:
(1 + r)^3 = 12,140 / 9,325
(1 + r)^3 ≈ 1.301
1 + r ≈ 1.091
r ≈ 0.091 or 9.1%
3. Predict the population in 2031:
P2031 = P0 * (1 + r)^(2031-2019)
P2031 = 9,325 * (1.091)^(2031-2019)
P2031 = 9,325 * (1.091)^12
P2031 ≈ 33,290 rats
So, the predicted population of Glandian rats in 2031 will be approximately 33,290.

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Given the function h(x) = x² - 7x - 8. The extremum of the function is the minimum one and its value is h(x) = -32.5

The relation between symmetry of the graph and the extremum point is:

Suppose x = p is the line equation of the graph's symmetry, then f(p) is the extremum value.

The given function is:

h(x) = x² - 7x - 8

Find the x-intercepts:

h(x) = 0

x² - 7x - 8 = 0

(x + 1) (x - 8) = 0

x = -1 or x = 8

The symmetry lies in the middle of x-intercepts. Hence, the symmetry occurs at:

x = (-1 + 8) / 2

x = 3.5

The extremum point is:

h(3.5) = 3.5² - 7 x 3.5 - 8 = -32.5

Since the quadratic term x²  has a positive coefficient, the graph is open downward, hence the extremum point is the minimum one.

Complete question:

Find the extremum of each function using the symmetry of its graph. classify the extremum of the function as a maximum or a minimum and state the value of x at which it occurs. h(x) = x² - 7x - 8

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