a laborer charges a fixed amount
of $100.00 for a day's weeding
contract plus an additional amount
for each acre of land cleared per day.
on a particular day, he was paid
$1500.00 for weeding 5 acres
of land, find.

the amount he received per acre

From the triangle he value of x is given as 13 units

Trigonometrical ratio of angles is a measure used to determine the sign of an angle. It can be calculated by finding the quadrant in which the angle (n ∙ 90° + θ) or (n ∙ 90° - θ) lies

The ratios are given as SOH CAH TOA

Where

S = sine = opposite/Hypothenuse

C = cosine = Adjacent/Hypothenuse

T = Tangent = Opposite/Adjacent

Tan 59 = x/7.7

x = 7.7 * tan59

Finding the value of tan59

x = 7.7 * 1.6643

x = 12.82 units

In conclusion, the value of x = 13 units

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When the pressure is 2.6 g/m² then the depth is 3.9 m.

Given that the pressure varies directly with the depth. When the pressure is 320 g/m² the depth is 480 m.

We need to find the depth if the pressure is 2.6 g/m².

So, here we will use the concept of proportionality,

Let the unknown depth be x,

So,

320 / 480 = 2.6 / x

2 / 3 = 2.6 / x

2x = 7.8

x = 3.9

Hence when the pressure is 2.6 g/m² then the depth is 3.9 m.

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The final value of the investment after 8 years is approximately $2,346.09.

We can use the formula for compound interest to find the final value of the investment:

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

where A is the final amount, P is the initial investment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = 2000, r = 0.02 (2% expressed as a decimal), n = 4 (compounded quarterly), and t = 8.

Plugging in these values, we get:

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

A = 2,000.00(1 + 0.02/4)(4)(8)

A = 2,000.00(1 + 0.005)(32)

A = $2,346.09

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The given problem is concerned with hypothesis testing. The researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The obtained value of the appropriate statistic for testing H0 is t= -2.42.

Given that,

Population mean µ = 115 lbs

Sample mean x = 111 lbs

Sample size n = 41

Standard deviation σ = 12.4 lbs

hypothesis testing

Null hypothesis H0: µ = 115 lbs

Alternate hypothesis H1: µ < 115 lbs

Since the population standard deviation is unknown and the sample size is less than 30, we use a t-distribution to test the hypothesis. The formula for the t-test statistic is,

t= (x- µ)/(s/√n)

Where, x = sample mean, µ = population mean, s = sample standard deviation, and n = sample size

Substituting the given values in the above formula, we get,

t= (111 - 115) / (12.4/ √41)t= -4 / 1.93t= -2.07

The obtained value of the appropriate statistic for testing H0 is t= -2.07.

The calculated t-value is compared with the critical value of t with degrees of freedom (df) = n-1 = 41-1 = 40 at the desired significance level. If the calculated t-value is less than the critical value of t, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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If p and n are positive integers and p > n. 0, 1, 5, 6, 9, and 11 are the remainders when p² - n² is divided by 15.

To find the remainder whilst (p² - n²) is split with the aid of 15, we are able to think of the expression p² - n² the usage of the distinction of squares method.

The distinction of squares formula states that a² - b² can be factored as (a + b)(a - b).

Applying this method to p² - n²;

p² - n² = (p + n)(p - n)

Now, we recognize that p and n are positive integers and p > n. This way that p + n and p - n are both advantageous integers.

To locate the remainder whilst (p^2 - n^2) is split through 15, we will take a look at the remainders of (p + n) and (p - n) when divided with the aid of 15.

Let's don't forget the viable remainders when dividing an integer by means of 15:

zero, 1, 2, 3, 4, five, 6, 7, eight, 9, 10, 11, 12, 13, 14

Since p + n and p - n are both high-quality integers, the feasible remainders when dividing them by way of 15 could be:

zero, 1, 2, three, 4, 5, 6, 7, eight, 9, 10, eleven, 12, thirteen, 14

Now, permits take into account the viable products of (p + n) and (p - n) while the remainder is multiplied:

0 * 0 = 0

1 * 14 = 14

2 * 13 = 26 (that's equal to eleven modulo 15)

3 * 12 = 36 (that's equal to six modulo 15)

4 * eleven = 44 (that's equivalent to fourteen modulo 15)

5 * 10 = 50 (which is equivalent to five modulo 15)

6 * 9 = 54 (that is equivalent to nine modulo 15)

7 * eight = 56 (that's equal to 11 modulo 15)

8 * 7 = 56 (that is equivalent to eleven modulo 15)

9 * 6 = 54 (that's equal to nine modulo 15)

10 * 5 = 50 (which is equivalent to 5 modulo 15)

11 * 4 = 44 (that's equivalent to fourteen modulo 15)

12 * 3 = 36 (that is equal to 6 modulo 15)

13 * 2 = 26 (that's equivalent to 11 modulo 15)

14 * 1 = 14

From the above merchandise, we will see that (p + n)(p - n) will have remainders of zero, 1, five, 6, 9, and eleven when divided via 15.

Therefore, the feasible remainders whilst () is split through 15 are 0, 1, 5, 6, nine, and 11.

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Answer:

The answer is down below

Step-by-step explanation:

y=x²-3x-1

y=mx+c=x²-6x+4-(x²-3x-1)

y=3x+3

where slope=3

y-intercept =3

H0 represents the null hypothesis,

H1 represents the alternative hypothesis,

μ represents the population mean body temperature, and

μ0 represents the claimed mean body temperature.

We are testing the claim that the mean body temperature of a healthy adult is not equal to a certain value. Let's denote the claimed mean body temperature as μ0.

Null Hypothesis (H0):

The mean body temperature of a healthy adult is equal to μ0.

Alternative Hypothesis (H1):

The mean body temperature of a healthy adult is not equal to μ0.

So the null hypothesis states that there is no significant difference between the claimed mean body temperature (μ0) and the actual mean body temperature, while the alternative hypothesis suggests that there is a significant difference.

In symbolic form:

H0: μ = μ0

H1: μ ≠ μ0

The question, the specific value for the claimed mean body temperature was not provided, so we'll refer to it as μ0 without a numerical value.

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The period of the function f(x) = -2 sin⁡x is 2π. So to summarize, the amplitude of the function is -2 and the period is 2π.

The general form of a sinusoidal function is f(x) = A sin(Bx - C) + D, where A is the amplitude, B determines the period, C is the phase shift, and D is the vertical shift.
For the function f(x) = -2 sin⁡x, we can see that the amplitude (A) is -2, since the coefficient of the sin function is -2. The amplitude represents the maximum distance the graph oscillates above and below the midline, so in this case, the graph oscillates between y = -2 and y = 2.
To find the period (B), we can use the formula T = 2π/B, where T is the period and B is the coefficient of x in the sin function. In this case, B = 1, so T = 2π/1 = 2π.

Therefore, the period of the function f(x) = -2 sin⁡x is 2π. So to summarize, the amplitude of the function is -2 and the period is 2π.

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The Shannon index value for an area in which only a single species is present is zero. This is because the Shannon index takes into account both species richness (the number of different species present) and evenness (the relative abundance of each species).

The Shannon Diversity Index (H') is used to measure the diversity of species in a given area and is calculated as H' = -Σ(pi)ln(pi), where pi is the proportion of individuals belonging to the i-th species. In an area where only a single species is present, pi would equal 1, meaning that there is no variation in species and only one species is observed.

Therefore, ln(pi) would be 0, and the entire summation would be equal to 0. As a result, the Shannon Diversity Index for an area with only one species would be 0, indicating no diversity in the community.

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The null hypothesis in a chi-square test for goodness of fit involves frequencies for the entire population, not just proportions or frequencies for the sample. c.

In a chi-square test for goodness of fit, the null hypothesis specifies the expected frequencies or counts for different categories in the entire population being studied.

The test compares the observed frequencies in the sample to the expected frequencies under the null hypothesis to determine if there is a significant difference between the observed and expected distributions.

The chi-square test for goodness of fit assesses whether the observed frequencies in the sample deviate significantly from the expected frequencies specified by the null hypothesis for the entire population. The test evaluates if the observed data supports or contradicts the null hypothesis, which assumes that the observed frequencies follow a specific distribution or proportions.

The null hypothesis in a chi-square test for goodness of fit defines the predicted frequencies or counts for various categories in the total population under investigation.

The test determines if there is a significant discrepancy between the observed and predicted distributions by comparing the observed frequencies in the sample to the anticipated frequencies under the null hypothesis.

The chi-square test for goodness of fit determines if the sample's observed frequencies differ noticeably from the null hypotheses' predicted frequencies for the overall population.

The null hypothesis, which holds that the observed frequencies follow a particular distribution or proportions, is assumed in the test, and it is determined if the observed data supports or refutes it.

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The volume of the cone is 251.20 cubic centimeters if the diameter of the cone is 20 cm and the height of the cone is 24 cm.

The diameter of the cone = 20 cm

The radius of the cone = diameter /2 = 20/2 = 10cm

The height of the cone = 24 cm

The volume of the cone is calculated by using the formula is:

V = (1/3)*π* [tex]r^2[/tex] *h

Substituting the values, we get:

V = (1/3)* π * [tex]r^2[/tex] *h

V = (1/3) * π * [tex](10 cm)^2[/tex] * (24 cm)

V = (1/3) *π * ([tex]100 cm^2[/tex]) * (24 cm)

V = 251.20 cubic centimeters.

Therefore, we can conclude that the volume of the cone is 251.20 cubic centimeters.

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Answer:

The area of the triangle is equal to half the product of its base and height. In this case, the base is 6 дм and the height is 8 дм. Therefore, the area of the triangle is

S = \frac{1}{2}(6)(8) = 24 дм^2

Step-by-step explanation:

Step-by-step explanation:

If t and w are inversely proportional, it means that as one variable increases, the other variable will decrease by the same factor. In this case, we have the equation t = 4/w, which means that if we multiply w by a certain factor, t will be divided by the same factor.

If we multiply w by 6, the new value of w will be 6 times the original value:

w' = 6w

To find the new value of t, we can substitute w' into the equation:

t' = 4/w'

t' = 4/(6w)

t' = 2/3w

So we see that t has been divided by 6/1 = 6. Therefore, the value of t will decrease by a factor of 6 if the value of w is multiplied by 6.

A control chart is a visual representation of the various states in a process. The answer is b. True. Control charts are used in quality control and process improvement to monitor and analyze the performance of a process over time.

b. True. A control chart is a graphical tool used to monitor the performance of a process over time. It is a visual representation of the data collected from the process and helps in identifying any patterns or trends that may occur. The chart typically consists of a central line representing the average or target value, and upper and lower control limits representing the acceptable range of values for the process. The data is plotted on the chart, and any points that fall outside the control limits indicate a process that is out of control and may require further investigation. Control charts are commonly used in industries such as manufacturing, healthcare, and finance to ensure that processes are running smoothly and to identify any potential issues early on. Overall, control charts provide a powerful way to monitor and manage processes in a systematic manner.

They help to identify trends, patterns, and variations that may indicate potential issues, allowing for timely corrective actions to be taken.

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The scale factor is 10.

Given that are two triangles which are similar, we need to find the scale factors,

Scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object.

The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.

For example, a rectangle has a length of 5 units and a width of 2 units. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively.

Hence, we can use the scale factor to get the dimensions of the changed figures.

The scale factor (k) = ratio of the corresponding sides,

So,

k = XY / VU

k = 60 / 6

k = 10

Hence the scale factor is 10.

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The length of C'A' is 10 units.

Triangle ABC is dilated by the rule Dy, 5/4

CA = 8

The length of C'A' will be determined by using the formula of scale factor

Scale factor = Dimensions of new figure/ Dimensions of original figure

So, Scale factor = C'A' / CA

(5/4) x CA = C'A'

C'A' = (5/ 4) x 8

C'A' = 10 units

Thus, the length of C'A' is 10 units.

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Answer:

10

Step-by-step explanation:

Edge 2023

Answer:

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

We need to determine the total number of outcomes and the number of favorable outcomes.

Total outcomes:

Favorable outcomes:

To find the probability, divide the number of favorable outcomes by the total number of outcomes:

The matching choice is C.

The experimental probability of a randomly selected student planning to take auto shop can be found by dividing the number of students.

Who plan to take auto shop (8) by the total number of students surveyed (16):  p(auto shop) = 8/16
Simplifying this fraction, we get: p(auto shop) = 1/2
Therefore, the experimental probability that a randomly selected student plans to take auto shop is 1/2 or 0.5 (as a decimal).

The experimental probability that a randomly selected student plans to take auto shop can be calculated as follows:
P(auto shop) = (number of students planning to take auto shop) / (total number of students surveyed)
P(auto shop) = 8 / 16
By simplifying the fraction, we get: P(auto shop) = 1/2
So, the experimental probability that a randomly selected student plans to take auto shop is 1/2.

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To estimate the chance of getting 12 heads and 13 tails when a coin is tossed 25 times, we can use the binomial probability formula.

The binomial probability formula is given by:

P(x) = (nCx) * p^x * q^(n-x)

Where:

P(x) is the probability of getting x successes,

n is the total number of trials,

x is the number of desired successes,

p is the probability of success on a single trial,

q is the probability of failure on a single trial, which is equal to 1 - p,

and (nCx) is the number of combinations of n items taken x at a time.

In this case, n = 25, x = 12 (number of heads), p = 0.5 (since the coin is fair), and q = 1 - p = 0.5.

Using the binomial probability formula, we can calculate the probability of getting 12 heads and 13 tails as:

P(12 heads) = (25C12) * (0.5^12) * (0.5^13)

Calculating this expression will give us the estimated chance of getting 12 heads and 13 tails when a coin is tossed 25 times.

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Answer:

The answer for radius is 13cm

Step-by-step explanation:

Area of semi circle=1/2pir²

308=1/2×22/7×r²

308=22r²/14

22r²=4312

divide both sides by 22

22r²/22=4312/22

r²=196

take the square root of both sides

√r²=√196

r=14cm

Answer:

b

Step-by-step explanation:

Standford form is highest exponent to lowest

If the tax rate at this restaurant is 9. 5% and some other person’s sales tax is $5. 69 then their subtotal is $65.58

Here, some other person’s sales tax is $5. 69

Consider that for the amount of 'p' dollars, the sales tax is 9. 5% is $5. 69

Here, the tax rate at this restaurant is 9.5%

This means, 9.5 percent of m dollars is $5. 69

Using percentage formula,

m × (9.5 / 100) = 5. 69

m × 9.5 = 5. 69× 100

m × 9.5 = 569

m = 59.89 dollars

So, their subtotal would be,

m + sales tax

= 59.89 + 5. 69

= 65.58 dollars

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The curved surface area of cylinder is,

⇒ 90π m²

We have to given that;

the height of the right cylinder is twice it’s diameter.

Hence, We get;

Diameter = 12 / 2 = 6 m

So, Radius = 6 / 2 = 3 m

So, Lateral surface area of cylinder is,

⇒ 2πrh

⇒ 2π × 3 × 12

⇒ 72π m

And, Curved surface area is,

⇒ 2πr²

⇒ 2π × 3²

⇒ 18π m

Thus, The curved surface area is,

⇒ 72π + 18π

⇒ 90π m²

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a) The exact circumference of the circle is given as follows: 20π yd.

b) The approximate circumference of the circle is given as follows: 62.8 yd.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius for the circle in this problem is given as follows:

r = 10 yd.

Hence the circumference of the circle is given as follows:

C = 2π x 10

C = 20π yd.

For the approximation, we consider π = 3.14, hence:

C = 20 x 3.14

C = 62.8 yd.

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The height of the cylinder whose area is given would be =7.6cm.

To calculate the height of a cylinder, the formula for the area of cylinder should be used and it is given below as follows;

Surface area of cylinder = 2πr²+2πhr

This can also be written as = 2πr(h+r)

surface area = 54cm²

h+r = 9cm

r = ?

54 = 2×2.14×r(9)

54 = 38.52r

r = 54/38.52

r = 1.4

h = 9-1.4 = 7.6cm

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The total surface area of the triangular prism is 636 square meters

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

The triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = 1/2 * 10 * 24 * 2 + 11 * 26 + 10 * 11

Evaluate

Area = 636

Hence, the surface area is 636 square meters

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The expression that correctly calculate the perimeter of the right triangle is:

15 + 15tan42° + 15/cos42°

Trigonometry deals with the relationship between the ratios of the sides of a right triangle with its angles.

The perimeter of the right triangle is the sum of all the sides of the triangle.

We have:

15 units

Let the side opposite angle 42° be x. Thus,

tan 42 = x/15

x = 15 tan 42°

For the hypotenuse side (h):

cos 42° = 15/h

h = 15/cos 42°

Perimeter = 15 + x + h

Perimeter = 15 + 15tan42° + 15/cos42°

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Complete Question

Check the attached image

Mr. Singh had three sheets of stickers. He gave 20 stickers from each sheet to his students and has 12 total stickers. The total number of stickers that there were originally on each sheet is 24.

Let the number of stickers on one sheet be 'a'

So, the number of stickers on three sheets = 3a

Number of stickers given from each sheet = 20

So, total number of stickers given from three sheets = 3 × 20 = 60

Number of stickers left with Mr. Singh = 12

Therefore,

3a - 60 = 12

3a = 12 + 60 = 72

a = 72/3

a = 24

So, the total number of stickers that were there originally on the sheet is 24 and Mr. Singh had three sheets of stickers. He gave 20 stickers from each sheet to his students and has 12 total stickers.

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