Find the cost to asphalt a circular racetrack if asphalt costs $90 per 100 f2. (Use 3.14 for it. Round to the nearest dollar.) r = 80 ft R = 145 ft
Small circle in a large circle
r= 80 ft
R=145 ft
Y
R
(Use 3.1 4 for a.)

Answer:

\(P(x\geq 3)=0.3233\)

Step-by-step explanation:

If the number of defects in poured metal follows a Poisson distribution, the probability that x defects occurs is:

\(P(x)=\frac{e^{-m}*(m)^{x}}{x!}\)

Where x is bigger or equal to zero and m is the average. So replacing m by 2, we get that the probability is equal to:

\(P(x)=\frac{e^{-2}*(2)^{x}}{x!}\)

Finally, the probability that there will be at least three defects in a randomly selected cubic millimeter of this metal is equal to:

\(P(x\geq 3)=1-p(x\leq 2)\\\)

Where \(P(x\leq 2)=P(0)+P(1)+P(2)\)

So, P(0), P(1) and P(2) are equal to:

\(P(0)=\frac{e^{-2}*(2)^{0}}{0!}=0.1353\\P(1)=\frac{e^{-2}*(2)^{1}}{1!}=0.2707\\P(2)=\frac{e^{-2}*(2)^{2}}{2!}=0.2707\)

Finally, \(P(x\leq2)\) and \(P(x\geq3)\) are equal to:

\(P(x\leq 2)=0.1353+0.2707+0.2707=0.6767\\P(x\geq 3)=1-0.6767=0.3233\)

Answer:

✅\( R = 4c \)

Step-by-step explanation:

The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as \( y = mx + b \).

Where,

y = R (amount of cake sold in dollars)

x = c (cakes sold)

m = slope

b = y-intercept.

The equation would look like:

\( R = mc + b \)

We need to find the value of m and b, to get an equation to represent the situation.

The first point we have from the information given is (15, 60) => 15 cakes sold for $60.

The second point is (22, 88) => 22 cakes sold for $88.

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{88 - 60}{22 - 15} = \frac{28}{7} = 4 \)

To find b, substitute c = 15, R = 60 and m = 4, into \( R = mc + b \).

\( 60 = 4(15) + b \)

\( 60 = 60 + b \)

\( 0 = b \)

Since b = 0, this means there is a proportional relationship between R and c.

Substitute m = 4 and b = 0 into \( R = mc + b \) to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.

\( R = 4c + 0 \)

✅\( R = 4c \)

Answer:

The total amount that the consumer had to pay for both products was $ 94.50.

Step-by-step explanation:

Given that Mal sold a large photo for $ 50 and a large frame for $ 40, and that the sales tax for these products is 5%, to determine the total amount that the consumer had to pay to purchase these products arises from the following calculation:

(50 + 40) x 1.05 = X

90 x 1.05 = X

94.5 = X

Therefore, the total amount that the consumer had to pay for both products was $ 94.50.

Answer:

1. Evaluate the expression: $4.50

2. Expand the expression: 2.5 + 2 = 4.5 (4.50)

3. Total tax is 4.50. yes, both the evaluating and expanding got me the same answer.

4. Expanded Expression

Step-by-step explanation:

1.  0.05(50 + 40) evaluated is 4.50

2. I broke apart 4.50 into different numbers and got 2.5 + 2

3. pretty self explanatory

4. again, pretty self explanatory

Solution,

CP for rajan=180 rs

Sp for rajan=(20%+1)×180

=216

Cp for niranjan=216

And, Sp=.8×216

=172.8

Cp for niranjan=172.8

For 5% profit,

Sp for Niranjan=(5%+1)×172.8

=181.44

Hence, for Niranjan to gain 5% profit, he must sell it for 181.44 rs

Answer - 181.44

Explanation - For Rajan,

Cost Price = Rs 180

Profit Percent = 20%

Profit Percent = (S.P - C.P/C.P)*100

20 = (S.P - 180/180) *100

S.P = Rs 216

For Sajan,

C.P = Rs 216

Loss Percent= 20%

Loss = (C.P - S.P/C.P)*100

20 = (216-S.P/216)*100

S.P = Rs 172.8

For Niranjan to Sell Book and get 5% profit,

C.P = Rs 172.8

Profit Percent = (S.P - C.P/C.P)*100

5 = (S.P-172.8/172.8)*100

S.P = 181.44

Answer:

g=34 trust me i learned it the hard way

Step-by-step explanation: i took test

Answer:

34

Step-by-step explanation:

The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.

In the confidence interval formula p ± z, the circled portion represents the Margin of Error.

The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.

It indicates the range within which the true population parameter is likely to fall based on the sample data.

The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.

The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.

The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.

It reflects the trade-off between the desired level of confidence and the width of the interval.

A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.

Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.

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Answer:

It would be C

Step-by-step explanation:

I have done this before!

Answer:

to you in 1980 is the lol in lol1234in lol to you in the kids in the lero girl

The components of v are -2 and 1.

The components of a vector in two dimension coordinate system are usually considered to be x-component and y-component. It can be represented as, V = (\(v_x, v_y\)), where V is the vector.

As, Vector v have an initial point at (6, -7) and a terminal point at (4, -6).

If initial point of vector \((x_1,y_1)\) and terminal point is \((x_2,y_2)\), then components of vector is

v= (\(x_2-x_1, y_2-y_1\))

Initial point= (6,-7) and terminal point=(4,-6)

Then,

v= (4-6, -6-(-7))

v=(-2, 1)

Thus, the vector v=(-2, 1) have two components -2 and 1.

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Answer:

y = 20x + 200

Step-by-step explanation:

The 200 is the constant.  It is only added once, but the monthly deposits are added at 20 every month.  

After 1 month:

y = 20x + 200

y = 20(1) + 200

y = 20 + 200

y =220       money deposited.

After 2 months:

y = 20x + 200

y = 20(2) + 200

y = 40 + 200

y =240 money deposited.

After 3 months:

y = 20x + 200

y = 20(3) + 200

y = 60 + 200

y = 260  money deposited

And so on, and so on, and so on...

Answer:

113.04ft^2

Step-by-step explanation:

Like before \(A=\pi r^2\\=\pi 6^2\\=113.04ft^2\)

=======================================================

Explanation:

1 balloon = 0.7 ft^3 of helium

200 balloons = 200*0.7 = 140 ft^3 of helium

Katerina needs 140 cubic feet of helium to fill all 200 balloons.

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

1m^3 = 35ft^3 which is approximate

0.2 m^3 = 0.2*35 = 7 ft^3

Each canister holds approximately 7 cubic feet of helium.

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

To summarize so far.

Let x be the number of canisters. Because of fact 2 mentioned above, 7x represents the total amount of helium from all of the x number of canisters.

Set this equal to the amount she needs (140) and solve for x.

7x = 140

x = 140/7

x = 20

Katerina needs 20 canisters.

Answer:

4

Step-by-step explanation:

The difference between the numbers 7 and 3 is 4.

We have,

The given expression is solved by using subtraction.

The expression can be written as:

= 7 - 3

The difference between 7 and 3 is calculated by subtracting the smaller number (3) from the larger number (7):

= 7 - 3

= 4

Therefore,

The difference between the numbers 7 and 3 is 4.

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Answer:

\(\frac{25\pi}{2}\approx39.27\text{ units}^2\)

Step-by-step explanation:

I assume your problem is \(\displaystyle \int\limits^{5}_{-5} {\sqrt{5^2-x^2}} \, dx\). Recognize that \(\sqrt{5^2-x^2}=\sqrt{25-x^2}\) is a semi-circle directly above the x-axis with a radius of 5. The bounds cover the whole area of the semicircle, so its area is just half the area of a circle with a radius of 5. You probably know that the area of a circle is \(A=\pi r^2\), so the area of a semicircle would be \(A=\frac{\pi r^2}{2}\). Thus, the area using geometry is \(A=\frac{\pi (5)^2}{2}=\frac{25\pi}{2}\approx39.27\text{ units}^2\).

Answer:

Step-by-step explanation:

Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.

The unadjusted cost of goods sold for the year is calculated by subtracting the ending inventory from the sum of beginning inventory and purchases. The formula is as follows:

Unadjusted Cost of Goods Sold = Beginning Inventory + Purchases - Ending Inventory

Without knowing the values for beginning inventory, purchases, and ending inventory, we cannot compute the unadjusted cost of goods sold for the year.

5. Given that the $70,000 ending balance in Work in Process includes $24,000 of direct materials, we can calculate the missing information as follows:

Direct Labor = Total Work in Process - Direct Materials - Overhead
Direct Labor = $70,000 - $24,000 - Overhead

Without knowing the value for overhead, we cannot compute the direct labor cost. However, we can rearrange the formula to solve for overhead:

Overhead = Total Work in Process - Direct Materials - Direct Labor
Overhead = $70,000 - $24,000 - Direct Labor

Without knowing the value for direct labor, we cannot compute the overhead cost.

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Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

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The equation represents the relationship between the x and y values is y = 2.75x

The first point = (0,0)

The second point = (4,11)

The slope of the line m = \(\frac{y_2-y_1}{x_2-x_1}\)

Where m is the slope of the line

\((x_1,y_1)\) is the coordinates of the first point

\((x_2,y_2)\) is the coordinates of the second point

Substitute the values in the equation

The slope of the line m = (11-0) / (4-0)

= 11 / 4

= 2.75

The slope intercept form is

y = mx + b

m is the slope of the line

b is the y intercept

The equation will be

y = 2.75x

Hence, the equation represents the relationship between the x and y values is y = 2.75x

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The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

5x+30

Step-by-step explanation:

we just open the bracket and multiply

The area of triangle ADE is,

⇒ A = 48 square units

We have to given that,

In the diagram , DE is a midsegment of triangle ABC.

And, The area of triangle ABC is 96 square units

Now, We know that,

Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.

Hence, the area of triangle ADE is half the area of triangle ABC,

That is,

A = 96 / 2

A = 48 square units

Thus, The area of triangle ADE is,

⇒ A = 48 square units

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Answer: +5

Step-by-step explanation:

-6 + 5 = -1

-1 + 5 = 4

4 + 5 = 9

9 + 5 = 14

The exact value of sin(5π/12) is (√6 + √2)/4

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

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

El ingeniero civil es aquella persona que dedica o aplica sus ... usan muy seguido el Teorema de Pitágoras, cuando construyen rampas. ... En las curvas se aplican cierto grado de ángulos, para evitar que el ... ...conocer y aprender más sobre los ángulos y triángulos, que es una parte muy importante

Step-by-step explanation:

The length of the arc is equivalent to 5.024 miles.

The formula to calculate the arc length is -

L{arc} = (θ/360°) x 2πr

Given is that an arc that subtends a central angle of 12° in a circle of radius 24 miles.

We can write the length as -

L{arc} = (θ/360°) x 2πr

L{arc} = (12/360°) x 2 x 3.14 x 24

L{arc} = 1/30 x 2 x 3.14 x 24

L{arc} = 5.024 miles.

Therefore, the length of the arc is equivalent to 5.024 miles.

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The surface area of the cube is 1536 ft².

We have,

The cube can be seen as 6 square areas in the net.

So,

The surface area of the cube.

= 6 x area of one square surface.

Now,

Side = 16 ft

Area of one square surface.

= side²

= 16²

= 256 ft²

Now,

The surface area of the cube.

= 6 x area of one square surface.

= 6 x 256

= 1536 ft²

Thus,

The surface area of the cube is 1536 ft².

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Using the z-distribution, the 95% confidence interval for the proportion is given as follows:

(0.4576, 0.5824).

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The other parameters for the interval are given as follows:

\(n = 246, \pi = 0.52\).

The lower and upper bound of the interval, respectively, are given by:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576\)

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824\)

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Answer:

2

Step-by-step explanation:

1+1=2