The fence requires a post every 3 ft, and the fence is to be 30 feet long, how many posts are needed?

Answer:

(a)123 km/hr

(b)39 degrees

Step-by-step explanation:

Plane X with an average speed of 50km/hr travels for 2 hours from P (Kano Airport) to point Q in the diagram.

Distance = Speed X Time

Therefore: PQ =50km/hr X 2 hr =100 km

It moves from Point Q at 9.00 am and arrives at the airstrip A by 11.30am.

Distance, QA=50km/hr X 2.5 hr =125 km

Using alternate angles in the diagram:

\(\angle Q=110^\circ\)

(a)First, we calculate the distance traveled, PA by plane Y.

Using Cosine rule

\(q^2=p^2+a^2-2pa\cos Q\\q^2=100^2+125^2-2(100)(125)\cos 110^\circ\\q^2=34175.50\\q=184.87$ km\)

SInce aeroplane Y leaves kano airport at 10.00am and arrives at 11.30am

Time taken =1.5 hour

Therefore:

Average Speed of Y

\(=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)\)

(b)Flight Direction of Y

Using Law of Sines

\(\dfrac{p}{\sin P} =\dfrac{q}{\sin Q}\\\dfrac{125}{\sin P} =\dfrac{184.87}{\sin 110}\\123 \times \sin P=125 \times \sin 110\\\sin P=(125 \times \sin 110) \div 184.87\\P=\arcsin [(125 \times \sin 110) \div 184.87]\\P=39^\circ $ (to the nearest degree)\)

The direction of flight Y to the nearest degree is 39 degrees.

Answer:

Slope: \(\frac{1}{2}\)

Y-intercept: (0,4)

Step-by-step explanation:

Put the equation into y = mx + b form, which is y = \(\frac{1}{2}\) +4. Then create a table.

X: -2, -1, 0, 1, 2

Y: 3, \(\frac{7}{2}\), 4, \(\frac{9}{2}\), 5

After solving the given equation, the values obtained will be equal to 210° and 330°. Hence, option B is correct.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

2 sin x + 1 = 0

2 sin x = -1

sin x = -1/2

So, the coordinates will be \((\frac{-\sqrt{3} }{2},\frac{-1}{2} )\) and \((\frac{\sqrt{3} }{2},\frac{-1}{2} )\) Have y values of -1/2.

So, The coordinates have the following radian correspondents (7 π)/6 and (11π)/6.

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Answer:

21

Step-by-step explanation:

There are 4 cubes of size 1/4 foot would fill the inside of the prism.

We have to given that;

Height of cuboid = 3 feet

Length of cuboid = 3/4 feet

Width of cuboid = 1/2 feet

We know that;

Volume of cuboid = Length x width x height

Hence,

V = 3/4 x 3 x 1/2

V = 9/8

Thus, Number of 1/4-foot cubes which would fill the inside of the prism is,

= (9/8) ÷ (1/4)

= (9/8) x 4

= 9/2

= 4.5

Thus, There are 4 cubes of size 1/4 foot would fill the inside of the prism.

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Tom sold 27 raffle tickets and Steve sold 98 raffle tickets.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

Together, Steve and Tom sold 125 raffle tickets for their school.

Steve sold 17 more than three times as many raffle tickets as Tom.

Let s be the number of raffle tickets sold by Steve and t be the raffle tickets sold by Tom.

So,

3t + 17 + t = 125

4t = 108

t = 27

And s = 98

Therefore, Steve sold 98 and Tom sold 27 tickets.

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Answer:

.

Step-by-step explanation:

.

The required residual for Dianna's iguana is $0.05.

To find the residual for Dianna's iguana, we need to first calculate the predicted value of weekly food cost for the iguana using the given regression equation:

\($\hat{y} = 0.4 + 0.15x$\)

where x is the weight of the iguana in pounds.

Substituting x = 11 into the equation, we get:

\($\hat{y} = 0.4 + 0.15(11) = 2.05$\)

So the predicted weekly feed cost for Dianna's iguana is $2.05.

To find the residual, we subtract the predicted value from the actual value:

\($residual = actual\ value - predicted\ value = 2.10 - 2.05 = 0.05$\)

Therefore, the residual for Dianna's iguana is $0.05.

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Answer:

2

a) 6.37%

b) 6.25%

3

a) 0.60 %

b) 0.59 %

Step-by-step explanation:

2 )

a) With replacement

Probability of extracting a club is 13/52

Probability of extracting a spade is 13/51

13/52 * 13/51

= 6.37 %

b) Without replacement

13/52 * 13/52

= 6.25 %

3) With replacement

Probability of extracting a ace is 4/52

Probability of extracting a queen is 4/51

4/52 * 4/51

= 0.60 %

b) Without replacement

4/52 * 4/52

= 0.59 %

Answer:

None

Step-by-step explanation:

Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.

Answer:

One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.

Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.

One way to construct a confidence interval for a proportion is to use the formula:

p ± z * sqrt(p * (1 - p) / n)

where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:

0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)

which simplifies to:

0.6 ± 0.22

or:

(0.38, 0.82)

This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.

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Answer:

I think it’s is into fifths if I’m correct

Step-by-step explanation:

The radius of the circle, marked p on the diagram, is approximately 5.8 cm.

Radius is a term used in geometry to describe the distance from the center of a circle to any point on the circumference. It is a line segment that has its two endpoints at the center of the circle and at any point on the circumference.

The area of a sector is equal to the fraction of the circle's area that the sector occupies multiplied by the area of the entire circle.
Therefore, the area of the sector is equal to (θ/360) × πr^2.
Since the area of the sector is given as 85 cm^2, we can rearrange the equation to get:
85 = (θ/360) × πr^2
Rearranging further, we get:
r^2 = (85 × 360)/(πθ)
Taking the square root of both sides, we get:
r = √((85 × 360)/(πθ))
Since the angle θ is not given, we cannot solve for r. However, we can approximate the angle θ to be equal to 360° since the sector occupies the entire circle.
Therefore, the radius of the circle is equal to:
r = √((85 × 360)/(π × 360))
r = √(85/π)
r ≈ 5.8 cm
Therefore, the radius of the circle, marked p on the diagram, is approximately 5.8 cm.

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By taking a subtraction, we will see that the change that Kate receives is $1.08

The change will be given by the difference between what Kate has, and the cost of all the items she buys.

She has $20.00, and the costs are: $6.99, $3.98, and $7.95.

Then the change will be:

C = $20.00 - $6.99 -  $3.98 - $7.95 = $1.08

We conclude that the change is $1.08

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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Answer:

(x−5) and (x−4)

Step-by-step explanation:

The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.

To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.

The formula for calculating compound interest is as follows:

A = P(1 + r/n) ^nt,

where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.

The table is given below:
\(\begin{array}{|c|c|c|} \hline \text{n} &

\text{A = P(1 + r/n) }^{nt} &

\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &

\text{3100(1 + 0.04/1)}^{1*10} &

\text{\$4788.03} \\ \hline \text{2} &

\text{3100(1 + 0.04/2)}^{2*10} &

\text{\$4798.76} \\ \hline \text{4} &

\text{3100(1 + 0.04/4)}^{4*10} &

\text{\$4817.46} \\ \hline \text{12} &

\text{3100(1 + 0.04/12)}^{12*10} &

\text{\$4861.94} \\ \hline \end{array}\)

The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.

In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.

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Ending Inventory Cost and Cost of Goods Sold using different inventory methods:

FIFO Method:

Ending Inventory Cost: $11,920

Cost of Goods Sold: $15,068

LIFO Method:

Ending Inventory Cost: $11,996

Cost of Goods Sold: $15,123

Weighted Average Cost Method:

Ending Inventory Cost: $11,974

Cost of Goods Sold: $15,087

Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.

This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.

Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.

This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.

Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.

Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.

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Step-by-step explanation:

we are to first collect like terms here I mean all numbers that look alike are to be out on the same side so we are now going to have.

\(2 - 8x > 34\)

\( - 8x > 34 - 2\)

\( - 8x > 32\)

now we are to divide both sides with the coefficient of x and we are to get

\( - 8x \div - 8 < 32 \div - 8 = x < 4\)

Answer: 18.774 or rounded off 18.8 percent of her weight is fat.

Answer: 18.125 lbs

Explanation: The baby weighed 18.125 pounds at the end of eight months.

The baby weighed 7.25 lbs at birth. Eight months later, he weighed 2.5 or 2½ times its birth weight. Multiply 7.25 by 2.5  (which equals 18.125).

So now eight months later, he's 18.125 pounds.

Answer:

area of polygons

Step-by-step explanation:

you've been given the radius

find the central angle 360/8

highlight a triangle for consideration

draw an altitude

this is your apothem

use sine to find the opposite side

double that, that is 1 side, multiply by 8, that is your perimeter

use cosine to find the apothem length

use 1/2aP to find the area.

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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Let, the points be A (8, −4) and B (1, −5). The slope of line AB exists 1/7.

Utilize the slope formula to estimate the slope of a line provided the coordinates of two points on the line.

The slope formula exists \($m = (y_{2} -y_{1})/(x_{2} - x_{1} )\), or the difference in the y values over the difference in the x values. The coordinates of the first point symbolize \($x_{1}\)and \($y_{1}\). The coordinates of the second points exist \($x_{2} , y_{2} .\)

The slope of the line exists the ratio of the rise to the run, or rise separated by the run.

\($m = (y_{2} -y_{1})/(x_{2} - x_{1} )\)

The Line, AB contains points A (8, −4) and B (1, −5).

Substitute the value of points in the equation then we get

\($m = (y_{2} -y_{1})/(x_{2} - x_{1} )\)

m = (-5-(-4))/(1 - 8)

Simplifying the above equation, we get

m = (-5+4)/(1 - 8)

m = (-1)/(-7)

m = 1/7

Therefore, the slope of line AB exists 1/7.

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