Find the value of the expression.

-7 + 11 - 6 + 8

Group of answer choices

6

32

20

It is about 6.13 miles shorter to cut across the diagonal route.

The Pythagorean theorem is a fundamental theorem in geometry that relates to the sides of a right triangle.

We can use the Pythagorean theorem to calculate the distance of the diagonal route:

\(d = sqrt(10^2 + 11^2) = sqrt(221)\)\(=14.87 miles\)

The distance of driving around the perimeter of the town is 10 + 11 = 21 miles.

So, cutting across the diagonal saves:

21 - 14.87 ≈ 6.13 miles

Therefore, it is about 6.13 miles shorter to cut across the diagonal route.

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Answer:

f(x)=ax2+bx+c

Step-by-step explanation:

Let me Know if I helped alot and also Let me know if you need my help again ill be here

Answer:

Step-by-step explanation:

Commission = 2% of 2,50,000

                     \(= \frac{2}{100}*250000\\\\= 2 * 2500\\\)

                     = Rs. 5000

Answer:

the answer is 3.19

Step-by-step explanation:

multiply 3.19x5 then add the 2.95

To predict the cost of driving 1800 miles per month, substitute 1800 in the given function C(d) = 0.2d + 280C(1800) = 0.2 (1800) + 280= $640 per month. Therefore, the cost of driving 1800 miles per month is $640.

(b) Graph is shown below:(c)The slope of the graph represents the rate of change of the cost of driving a car per mile. The slope is given by 0.2, which means that for every mile Lynn drives, the cost increases by $0.2.The y-intercept of the graph represents the fixed cost (amount she pays even if she does not drive).

The y-intercept is given by 280, which means that even if Lynn does not drive the car, she has to pay $280 per month.The linear function gives a suitable model in this situation because the monthly cost increases as the number of miles driven increases.

This is shown by the positive slope of the graph. The fixed cost is also included in the function, which is represented by the y-intercept. Therefore, a linear function is a suitable model in this situation.

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Answer:

b i took the test

Step-by-step explanation:

Her new salary after an 8% increase will be £40,500. To calculate the new salary, we need to determine the amount of increase first. The 8% increase on the current salary of £37,500 can be calculated by multiplying the salary by 0.08 (8% expressed as a decimal). Thus, 0.08 * £37,500 = £3,000.

Next, we add the increase to the current salary to obtain the new salary. £37,500 + £3,000 = £40,500. Therefore, her new salary will be £40,500.

This means that after the 8% increase, the employee's salary will rise by £3,000, resulting in a total new salary of £40,500. The percentage increase represents the fraction of the current salary that is added to it, and by applying this percentage to the original salary, we can determine the specific amount of the increase. Adding that amount to the original salary gives us the final new salary.

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Answer:

85.5m

Step-by-step explanation:

No: of sides in a decagon = 10

Length of each side = 855m ÷ 10 = 85.5m

According to the general equation for conditional probability, the conditional probability of event A given event B is calculated as

P(A|B) = 24/49

Given that P(A∩B) = 3/7 and P(B) = 7/8, we can substitute these values into the equation:

P(A|B) = (3/7) / (7/8)

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:

P(A|B) = (3/7) * (8/7)

Simplifying the expression, we have:

P(A|B) = 24/49

Therefore, the probability of event A given event B is 24/49.

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Since the culture is observed to double every 6 hours, we know that the growth rate is constant at r = ln(2)/6 per hour.

To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value. The most frequent time intervals for growth rates are annually, quarterly, monthly, and weekly.

We can use the formula for exponential growth to model the number of bacteria in the culture after t hours:

n(t) = n0e^(rt)where n0 is the initial number of bacteria.

Substituting in the values given in the problem, we get:

n(t) = 25e^[(ln(2)/6)t]Simplifying this expression using the properties of logarithms, we can rewrite it in the form:

n(t) = 25(2)^(t/6)This is the exponential model for the number of bacteria in the culture after t hours.

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The exponential model for population of bacteria, \(n(t) = n_0{2}^{\frac{t}{a} }\) can be written \(n(t) = 25 \times {2}^{\frac{t}{6} }\) for the number of bacteria in the culture after t hours. The estimate number of bacteria after 13 hours is equals to the 112. In 92 hours, the bacteria count will reach to 1 million.

We have a certain culture of the bacterium Rhodobacter.

Initial population, n₀ = 25

The population become doubles in every 6 months. The exponential model

\(n(t) = n_0{2}^{\frac{t}{a} }\) for the number of bacteria in the culture after t hours. Now, the population become double in 6 hours, so a = 6 , then exponential equation is \(n(t) = 25 \times {2}^{\frac{t}{6} }\).

We have to estimate the number of bacteria after 13 hours. That is t = 13 hours, \(n( t) = 25( 2)^{\frac{t}{6}}\)

Substitute t = 13 hours

\( = 25( 2)^{\frac{13}{6}}\)

\(= 25( 2)^{2.16}\)

= 111.728713807 ~ 112

So, n(13) = 112

We have to determine the value of t in hours for n(t) = 1 million = 1000000, using the above equation, \(1000000 = 25( 2)^{\frac{t}{6}}\)

\(40000 = ( 2)^{\frac{t}{6}}\)

Taking natural logarithm both sides

=>\( ln( 40000) = ln(( 2)^{\frac{t}{6}})\)

=> \(ln(40000) = \frac{t}{6} ln(2)\)

=> \(t = \frac{6 ln( 40000)}{ ln(2)}\)

= 91.7262742773 ~ 92

Hence, required value is 92 hours..

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An inequality for the graph above is y ≤ -3x + 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-3 - 6)/(3 - 0)

Slope (m) = -9/3

Slope (m) = -3

At data point (0, 6) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = -3(x - 0)  

y = -3x + 6

y ≤ -3x + 6 (since the solid line is shaded below).

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The digit in the blank space in the ones place is 5 as it is the last digit that has not been used yet.The final number we get is 4782. Hence, 4 x 2 7 8 = 9 5 2 2. This makes the given equation true. Therefore, the solution is 4 x 27.8 = 952.2.

The equation 4 x 2 _. 8 = 9 _. 2 true, we need to fill in the blanks with the digits from 0-9, using each digit only once.Solution:To make the equation 4 x 2 _. 8 = 9 _. 2 true, we need to fill in the blanks with the digits from 0-9, using each digit only once.Therefore, the solution is:4 x 2 7 8 = 9 5 2 2.The multiplication of 4 and 2 will give 8. The digit 7 in the tens place will give the result of the multiplication of 2 and 7 which is 14, so 4 will be carried over to the hundreds place. Therefore, the number in the blank space in the tens place is 7.To get the digit in the thousands place, we will do multiplication of 4 and 2 which gives 8. Adding the carry from the hundreds place, we have 9 in the thousands place, therefore the digit in the blank space in the thousands place is 9.The digit in the blank space in the ones place is 5 as it is the last digit that has not been used yet.The final number we get is 4782. Hence, 4 x 2 7 8 = 9 5 2 2. This makes the given equation true. Therefore, the solution is 4 x 27.8 = 952.2.

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Answer:

Before that: SOH is a mnemonic for S(ine)= O(pposite)/H(ypotenuse). CAH (not coh!) is a mnemonic for C(osine)= A(djacent)/H(ypotenuse). TOA is a mnemonic for - you guessed it! - T(angent) = O(pposite)/A(djacent).

At this point, you just have to grab a calculator to find the values of the various functions and do simple multiplications.

5:\(tan 49 = \frac{14}x \rightarrow x= \frac{14}{tan49} \approx 12.17\)

6: \(sin 51 =\frac{14}x \rightarrow x = \frac{14}{sin51} \approx 18.01\\\)

7: \(sin 63= \frac{16}x \rightarrow x= \frac{16}{sin63} \approx 17.96\)

8: \(sin 15 = \frac{16}x \rightarrow x= \frac{16}{sin15} \approx61.82\)

No, the three angles can not form a triangle because their sum is not 180°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. For any type of triangle the sum of its angle must be equal to 180°.

from the question ;

angle B= ½ of angle A

C = 2B - 1 and

A+2B = 114°

substituting B = ½A in A+2B = 114°

A +2(½A) = 114

A+ A = 114

2A = 114

A = 114/2 = 57°

substitute 57 for A I. B = ½A

B = ½× 57

B = 28.5°

from C = 2B - 1

C = 2× 28.5-1

C = 57-1

C = 56

Therefore the three angles can not form a triangle because A+B + C is not 180. i.e 57+56+28.5 is not 180°

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We will use Green's theorem, which states that for a vector field F = (F1, F2) with continuous partial derivatives on a simply connected region R bounded by a piecewise smooth, simple, closed curve C, we have:

∮C F · dr = ∬R (∂F2/∂x - ∂F1/∂y) dA

where dr is a differential element of arc length on C, and dA is a differential element of area in R.

In this case, we have F = (−g, f) = (−7y^2, 12x^2), and C consists of two pieces: the upper half of the unit circle, denoted by C1, and the line segment from (−1,0) to (1,0), denoted by C2.

We can parameterize C1 by x = cos(t), y = sin(t) for t in [0,π], and C2 by x = t, y = 0 for t in [−1,1]. Using these parameterizations, we can write the line integral as:

∮C F · dr = ∫C1 F · dr + ∫C2 F · dr

For the first integral, we have:

∫C1 F · dr = ∫0π (−7sin^2(t), 12cos^2(t)) · (−sin(t), cos(t)) dt

= ∫0π 7sin^3(t) - 12cos^3(t) dt

We can evaluate this integral using trigonometric identities to get:

∫C1 F · dr = 7/3 - 12/3 = -5/3

For the second antiderivative,  we have:

∫C2 F · dr = ∫−1^1 (−7(0)^2, 12t^2) · (1, 0) dt

= 0

Therefore, the line integral over C is:

∮C F · dr = ∫C1 F · dr + ∫C2 F · dr = -5/3 + 0 = -5/3

So the value of the line integral is -5/3.

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The object is to get everything except for "h" on one side of the equation. The equation says that everything on the right side is being multiplied by 1/2. What do we have to multiply times 1/2 to get 1?  The answer is 2. So multiply both sides by 2 to get rid of the fraction. 2A = (a+b)h Now we are multiplying h times (a+b) so to get rid of (a+b) we have to divide both sides by that term. (a+b)/(a+b)  is 1 So you are left with:  2A/(a+b) = h

The world population in 2030 will be of 9.0062 billion.

The exponential formula for population growth is given below:

P(t) = P (0)e^rt

Here, P(t) is the population in t years from now P (0) is the population in the current year and r(decimal) is the growth rate, e=2.7 is the Eular number.

If the world population is 7.0 billion in 2012.

2012 is the initial year, P (0) =7

P(t) will be measured in billions of people.

The growth rate is constant at 1 .4%.

So that, r = 0.014

Now, the population in 2030 will be :

2030-2012=18 years after 2012, so this is P(18).

P(t)= 7e^rt

P(18) = 7e^0.0014*18

       = 9.0062

So, the world population in 2030 will be of 9.0062 billion.

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The world population will be 9.0062 billion in 2030.

The population growth exponential formula is as follows:

P(0)ert = P(t)

P(t) denotes the population in t years. P (0) is the current year's population, r(decimal) is the growth rate, and e=2.7 is the Euler number.

If the world population in 2012 is 7.0 billion.

The first year is 2012, and P (0) = 7.

The magnitude of P(t) will be measured in billions of people.

The rate of growth remains constant at 1.4%.

As a result, r = 0.014.

Now, in 2030, the population will be:

2030-2012 = 18 years after 2012, so P (18).

P(t)= 7e^rt

P(18) = 7e^0.0014*18

= 9.0062

As a result, the world population in 2030 will be 9.0062 billion people.

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The standard deviation of the sampling distribution of the sample mean would be approximately 2.8284

To determine the standard deviation of the sampling distribution of the sample mean, we will use the formula;

σ_mean = σ / √n

where σ is the standard deviation of the population that is 20 and n is the sample size (n = 50).

So,

σ_mean = 20 / √50 = 20 / 7.07

σ_mean  = 2.8284

The standard deviation of the sampling distribution of the sample mean is approximately 2.8284 it refers to that the sample mean would typically deviate from the population mean by about 2.8284, assuming that the sample is selected randomly from the population.

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The complete question is;

Another application of the sampling distribution of the sample mean Suppose that, out of a total of 559 full-service restaurants in Delaware, the number of seats per restaurant is normally distributed with mean mu = 99.2 and standard deviation sigma = 20. The Delaware tourism board selects a simple random sample of 50 full-service restaurants located within the state and determines the mean number of seats per restaurant for the sample. The standard deviation of the sampling distribution of the sample mean is Use the tool below to answer the question that follows. There is a.25 probability that the sample mean is less than

When rolling two dice the possible outcomes are:

Probability is calculated as follows:

There is a total of 6x6 = 36 possible outcomes. From the table, we can see that 5 of them are a 6 and 3 of them are a 10. Then, the number of favorable outcomes is 5 + 3 = 8. Therefore, the probability of winning on your next turn is:

Answer:

24/182 = 12/91

Step-by-step explanation:

The probability that the sample mean exceeds 135.4 millimeters is approximately 0.1446.  

You can use the central limit theorem to approximate the sample distribution of the sample mean.

The mean of the sample distribution is a rise to the population mean (135 mm)

 the standard deviation of the test distribution is a rise to the population standard deviation isolated by the square root of the test measure, which is \(5/√42\) ≈ 0.7689 mm.

To find the probability that the sample mean is greater than 135.4 millimeters, use the sample distribution to standardize the sample mean and use the standard normal distribution. That is,

\(z = (x - μ) / (σ / √n) = (135.4 - 135) / (5 / √42) ≒ 1.0607\)

where x = sample mean, μ = population mean, σ =population standard deviation, n=sample size, and z =standard value.

The probability that the sample mean exceeds 135.4 millimeters can be found by using a standard normal distribution table or calculator,

to find the area to the right of the Z value of 1.0607. This range is approximately 0.1446 or 14.46%.

Therefore, the probability that the sample mean exceeds 135.4 millimeters is approximately 0.1446.

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Answer:

-8≤k≤1

Step-by-step explanation:

k²+7k-8≤0

(k+8)x(k-1)≤0

k1= -8

k2= 1

-8≤k≤1

The fixed cost for this item is $800.

The cost of making 25 items is $1050.

The domain of the cost function C(x) is x ≤ 250.

The range of the cost function C(x) is C(x) ≥ $800.

We have,

a.

The fixed cost is determined when zero items are produced. In this case, x = 0.

Plugging x = 0 into the cost function C(x) = 10x + 800:

C(0) = 10(0) + 800

C(0) = 0 + 800

C(0) = 800

b.

To find the cost of making 25 items, plug x = 25 into the cost function C(x) = 10x + 800:

C(25) = 10(25) + 800

C(25) = 250 + 800

C(25) = 1050

c.

Suppose the maximum cost allowed is $3300.

To determine the domain and range of the cost function C(x), we need to find the values of x for which C(x) does not exceed $3300.

Setting C(x) ≤ $3300:

10x + 800 ≤ 3300

10x ≤ 3300 - 800

10x ≤ 2500

x ≤ 2500/10

x ≤ 250

As for the range, the cost function C(x) can take on any value greater than or equal to the fixed cost, which is $800.

Thus,

The fixed cost for this item is $800.

The cost of making 25 items is $1050.

The domain of the cost function C(x) is x ≤ 250.

The range of the cost function C(x) is C(x) ≥ $800.

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Answer:

Step-by-step explanation:

A: +2

B: +2

C: -25

D: x3

Answer:

5:1

Step-by-step explanation:

10 divided by 2 is 5

2 divided by 2 is one.

Hope you get a good Grade!

Answer:

5:1

Hope this helps!

Answer:

A (2) =4*2 +882

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The cone has a height of h = \(\frac{3V}{\pi r^{2} }\)

A geometric object with a three-dimensional shape is called a cone. It features two distinct surfaces, referred to as flat and curved surfaces. A cone is created by connecting the two surfaces. One-third of the area of the base B times the height h equals the volume V of a cone with radius r. The volume of an oblique cone may be calculated using the same formula as a right cone. The volumes of a pyramid and a prism are connected, just as the volumes of a cone and a cylinder are related.

The answer to the question is the provided expression, which represents the cone's volume;

It is spelled as follows:

Volume (V) = \(\frac{1}{3}\pi r^{2}h\)

Now, the formula for calculating height 'h' is displayed below:

h = \(\frac{3V}{\pi r^{2} }\)

As a result, h = \(\frac{3V}{\pi r^{2} }\) is the cone's height.

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Consider that the area of a sector of a circle is given by:

where θ is the angle of the sector and r is the radius.

For θ=40 and r = 8cm, you obtain:

The area of the small sector is about 22.34 cm^2.

Now, for θ=320 and r = 8cm, you obtain:

The area of the small sector is about 178.72 cm^2.

The blanks in the  question has same value and it is equal to 9

Given data

6x​ + ____ =7x-​____ ​, solution is 18

let the missing number be in the left hand side of the equation be equal to  the missing number at the right hand side of the equation and both be represented by y.

if the solution is x which is 18 we substitute for y as follows

6x + y = 7x - y

y + y = 7x + 6x

plugging in the values of x

y + y = 7 * 18 - 6 * 18

2y = 126 - 108

2y = 18

y = 9

testing y = 9 in both equations

6x + y = 6 * 18 + 9 = 108 + 9 = 117

7x + y = 7 * 18 - 9 = 126 - 9 = 117

Hence we can say that the blanks in the  question has same value and it is equal to 9

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