A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 4 reproductions and the population
standard deviation is known to be 1.9. If a sample of 283 was used for the study, construct the 95% confidence interval for the true mean number of reproductions
per hour for the bacteria. Round your answers to one decimal place.

The value of x and y in the diagram are 26° and 9° respectively.

Two adjacent angles formed a linear pair.

The linear pair property:

The sum of the angle measure of both the angles is 180°.

Given:

Using linear pair theorem,

(5x - 17)° + (3x - 11)° = 180°.

8x - 28°= 180°

8x = 180° + 28°

8x = 208°

x = 208/8

x = 26°

The value of x is 26°.

Now,

3x - 11° = 3×26°-11°

           = 67°

Linear pair theorem,

67° + 90° + (2y+5)° = 180°

157°+2y+5° = 180°

2y + 162° = 180°

2y = 180° - 162°

2y = 18°

y = 9°

The value of y is 9°.

Therefore, the value of x is 26° and y is 9°.

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The complete question is given in the attached image.

If it cost them $125 to rent a booth at the farmers market, then their profit will be $2816 - $125 = $2691.

Top Choice Ponce farm wants to set up a booth at a farmers market next weekend, they promise to sell their pistachios at 20% cheaper than the next cheapest farm. They plan to sell 3520 ounces of pistachios at $0.8 per ounce.

The booth rent cost them $125. To calculate the profit, they will subtract the booth cost from the total revenue of pistachios which is $2816. Therefore, their profit will be $2691. They will make this profit after paying for the Farmers Market booth.

If Top Choice Farm's pistachios are 20% cheaper than the next cheapest farm, and the next cheapest farm's pistachios cost $1 per ounce, then Top Choice Farm's pistachios will cost $1 - $1 × 20% = $0.80 per ounce.

If they sell 3520 ounces of pistachios at $0.80 per ounce, then their total revenue from pistachios will be 3520 × 0.8 = $2816

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Answer:

x ≥ 2

Step-by-step explanation:

the solid circle at 2 indicates that x can equal 2

the arrow points to the right indicating values of x greater than 2 , then the inequality being represented by the number line is

x ≥ 2

Using Heron's formula the area of the triangle is 15.78cm²

Heron's formula is a formula for calculating the area of a triangle when the lengths of all three sides are known. It is named after the Greek mathematician and engineer Heron of Alexandria (c. 10–70 AD). The formula is:

Area = √s(s-a)(s-b)(s-c)

Where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter, or half the perimeter, of the triangle, given by:

s = (a + b + c)/2

Let's define the variables as;

s = (5.1 + 7.8 + 6.2) / 2

s = 9.55cm

The area can be calculated as;

A = √s(s - a)(s - b)(s - c)

A = √9.55(9.55 - 5.1)(9.55 - 7.8)(9.55 - 6.2)

A = 15.78cm²

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The slope and the y-intercept of the given data table will be option A) Slope= -0.0018, y-intercept = 212

The y-intercept of any linear equation is the point at which the line or the curve intersects the vertical i.e the Y- axis.

To find this intercept, the value of x is taken to be 0 in the model, since on the Y-axis, the value of x is 0.

Here from the given table, we need to check the boiling point or the value of Y for which the value of the altitude or the x value is 0

Hence we get the y-intercept as 212° F.

Now, the formula for slope

= change in y/ change in x

here we will take any two data rows and divide the difference in boiling points by the difference in altitudes.

Taking the first 2 rows gives us

Slope = -0.9/500

= -0.0018

Hence we choose option A) Slope = -0.0018, y-intercept = 212

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Complete Question

The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit. What are the slope and y-intercept of the line that models this situation?

A. Slope= -0.0018, y-intercept = 212

B. Slope= 0.0018, y-intercept =-212

C. Slope =212, y- intercept= 0.0018

D. Slope=-212, y-intercept = 0.0018

The length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.

We know that the length of the arc of a circle = Radius of the circle × angle subtended by the arc (in radians)

Here radius of the circle is 27 m

The angle subtended is 120°

Hence we will first convert the angle into radians

Angle in radians = Angle in degree X π/180

= 120 X π/180

= 2π/3

Therefore, the length of the arc = 27 X 2π/3

= 18π m

Therefore, the length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.

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Answer:

23; 11 + 2t

Step-by-step explanation:

So let's start with the equation and then plug in the 6 hours:

Because we start with 11 dollars just to enter, our equation would start like this:

11 +

Also, 2 dollars for every hour. One hour could be represented as 1t, or just t:

11 + 2t (2 dollars for every t, every hour)

So now the equation is 11 dollars starting entry plus 2 dollars every hour

Now all we have to do is replace t with the number of hours:

11 + 2(6) = answer

11 + 12 = answer

23 = answer

Actual length is 5.5m and percentage error is 20%.We can find by using percentage error formula.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words the percent error is the relative error multiplied by 100.

Subtract the actual value from the estimated value.And then divide the results with the real value. Multiply the results by 100 to find the total percentage.The formula represent it as a percentage of the exact value.Percent error = |Approximate value – Exact Value|/Exact value * 100.

Now we find

wall is measured 5m to the nearest so

approximate value= 4.5

actual value     =5.5

putting value in the formula

Percentage error  = 5.5- 4.5/5 *100

                              = 20%

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1)correct option is b) true

2)Which of the following expressions always evaluates to true?

 correct option is d)(x > 0) && (x == 0)

given that

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Many authors make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects.

x = 5 and y = 7

Choose the value of the following expression: (x != 7) && (x <= y)

a. false

b. true

c. 0

d. null

(5! = 7) && (5<=7)

5 ≠ 7

correct option is b) true

Suppose that x is an int variable.

Which of the following expressions always evaluates to true?

a. (x > 0) || ( x <= 0)

b. (x > 0) && ( x <= 0)

c. (x >= 0) 11 (x == 0)

d. (x > 0) && (x == 0)

a) x = 1,2,3.... || x =0,-1,-2,-3......

b)x = 1,2,3.... && x = 0,-1,-2,-3,.....

c) x = 0,1,2,3..... 11 x = 0

d) x = 1,2,3.... && x = 0

correct option is d)(x > 0) && (x == 0)

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The temperature of the city of Puerto Rico in Fahrenheit will be 104 Fahrenheit.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

A temperature C, in degrees Celsius, is the same as a temperature of (9/5)C + 32, in degrees Fahrenheit.

The hottest temperature ever recorded in Puerto Rico was 40 degrees Celsius.

Convert the temperature from Celcius to Fahrenheit. Then we have

⇒ (9/5)C + 32

⇒ (9/5) x 40 + 32

⇒ 9 x 8 + 32

⇒ 72 + 32

⇒ 104 F

The temperature of the city of Puerto Rico in Fahrenheit will be 104 Fahrenheit.

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Answer:

Step-by-step explanation:

divide them both by 2

which is 3/ 9

divide them both by 3

whic is 2/6

and finally divide them both by 6

which is 1/3

you can multiply them both by an number as well

take care

Answer:

1.

(a) 4y

(b) 5w

(c) 6a

(d) 3s

(e) 2n

(f) 3g

(g) 2y

(h) 0

2.

(a) -2u

(b) -w

(c) -3a

(d) -7y

3.

(a) 7a+3b

(b) 12y+4h

(c) 2g+10a

(d) 15m+10p

(e) 10e+4

(f) 12+5a

Step-by-step explanation:

Don't be intimidated by the "letter" variables. It is really just simple addition and subtraction. Examples:

For Q1=

y + y + y + y = 4y because there are 4 y's, and since we don't know the values of the y, this is the farthest we can simplify it.

For Q2=

4u - 6u = -2u. Since these two numbers have the same variable, this is just a simple subtraction problem. 4 - 6 = -2.

For Q3=

3a + 2b + 4a + b = 7a + 3b.

Look for the numbers with the same variable. 3a and 4a both have a's, so we add the two and get 7a. 2b and b (b is the same thing as 1b) both have b's, so we add them and would get 3b.

Therefore, the answer is 7a + 3b.

I hope this helped! Good luck with future endeavors!!

Step-by-step explanation:

attached the answers below, hope that helps...

It divides by three. According to the law of divisibility for three, a number is fully divisible by three if its digit sum is likewise divisible by three.

The divisibility rule is a clear and useful method for determining if an integer is divisible by a given set of divisors without actually doing division, sometimes simply looking at the integer's digits. The divisibility test allows you to rapidly determine if a given integer can be divided by a specified divisor without actually doing the division process. The quotient must be an integer and the remainder must be zero when dividing two numbers precisely.

here  

add all the numbers,

326 = 3+2+6 = 11

so it is not divisible by 3

327 = 3+ 2 + 7 = 12

so it is divisible by 3

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On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735

The average of the absolute deviations from the center point within a dataset is called the mean absolute deviation. This statistic summarizes the statistical spread or variability. Each data point's average distance from the mean is known as the dataset's mean absolute deviation. This gives a sense of the dataset's variability. To determine the absolute value, take the mean from each integer in the dataset and then subtraction. Take the total of the absolute values next. Subtract the aforementioned sum from the total number of items in the dataset to obtain the mean absolute deviation.

12,12,12,22,23,32,43

Mean Absolute Deviation (MAD): 8.8979591836735

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Answer:

On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735

Step-by-step explanation:

The answer to linear expression is 233.

A linear expression is defined as an algebraic statement where each term is either a constant or a variable raised to the first power.

We have to Simplify linear expressions in the process of writing linear expressions in their way and simplest forms such that the value of the original expression is maintained.

There are a few steps to follow when we want to simplify expressions

Given equation is C= 240-7

C= 240-7=233

The answer to the given expression is 233.

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The coefficient is -1

Answer:

No triangle

Step-by-step explanation:

Since [tex]4+4=8[/tex], the side lengths fail to satisfy the triangle inequality theorem. Thus, no such triangle exists.

The length of the chord of the larger circle can be found by taking the square root  [tex](5r)^2 - (2r)^2[/tex] which is equal to r√21, where r is the radius of the smaller circle.

The given problem states that there are two concentric circles with radii in the ratio of 3:5. This means that the radius of the smaller circle is 3r and the radius of the larger circle is 5r. The distance between the center of these two circles is 2r.

Also, it is given that the length of the chord of the larger circle that is tangent to the smaller circle is 40 cm. Using this information, we can find the length of the chord of the larger circle by using the Pythagorean theorem.

The length of the chord of the larger circle is found by taking the square root of [tex](the radius of the larger circle)^2[/tex] - [tex](the distance between the two centers)^2[/tex] which is √21[tex]r^2[/tex]= r√21.

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The real roots of the equation x^(2/3) + x^(1/3) - 2 = 0 are 1 and -8.

The equation x^(2/3) + x^(1/3) - 2 = 0 does not have any real roots. Since the exponents are not integers, x^(2/3) and x^(1/3) are not defined for negative values of x, and so the equation has no solutions for real values of x.

But,

Let y = x^(1/3)

The equation x^(2/3) + x^(1/3) - 2 = 0 will become y² + y - 2 = 0.

Solving for the roots of this equation,

y² + y - 2 = 0

(y + 2)(y - 1) = 0

y = -2   ;   y = 1

Substitute the value of y and solve for x.

y = x^(1/3)

-2 = x^(1/3)   ;   1 = x^(1/3)

x = -8   ;   x = 1

Therefore, the real roots of the equation is 1 and -8.

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Answer:

20%

$18.84

Step-by-step explanation:

3.14 is what percent of 15.70?

Use the percent-to-dollar conversion (100: 15.70) :

3.14 * 100% / 15.70 =

3.14 / 15.70 * 100% =

1/5 * 100% =

100% / 5 = 20% ==> percent tip

$15.70 + $3.14 = $18.84  ==> Total cost

Answer: 80 degrees

Step-by-step explanation:

Answer:

the remaining angle of triangle is 80° by the sum of triangle is 180.

To find the x-intercept and y-intercept of a function, one can set the x or y value equal to zero and solve for the other variable.

The x-intercept of a function is the point where the graph of the function crosses the x-axis. To find the x-intercept, one can set the y-value equal to zero and solve for the x-value. For example, if the function is y = 2x + 3, the x-intercept can be found by setting y equal to zero and solving for x. In this case, 0 = 2x + 3, which means x = -3/2. So the x-intercept of this function is (-3/2,0).

The y-intercept of a function is the point where the graph of the function crosses the y-axis. To find the y-intercept, one can set the x-value equal to zero and solve for the y-value. For example, if the function is y = 2x + 3, the y-intercept can be found by setting x equal to zero and solving for y. In this case, y = 2(0) + 3 = 3, so the y-intercept of this function is (0,3).

Knowing the x and y intercepts of a function gives an idea of where the graph will start and the behavior of the function in the x and y-axis.

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Answer:

Yes

Step-by-step explanation:

The side lengths are a Pythagorean triple.

Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

One would earn more if one apprenticed for Sara as a professional artist as evident judging from the current sales ratio and commission rates.

As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.

Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.

Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.

Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.

Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.

Ultimately, one would earn more if one apprenticed for Sara.

Complete question; Sara's pieces of art sell for $25 each your commission is 60%.

Ravi's pieces of art sell for $2000 each and your commission is 25%.

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Total interest earned = 68

Total amount collected = 1268

Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.

Since nothiong mentioned the interest is considered simple

Total amount = 1200 (principal)

Time = 1 year 5 month = [tex]1\frac{5}{12} = \frac{17}{12}[/tex]

rate = 4 %

Total interest earned = [tex]\frac{1200 * 4 * \frac{17}{12} }{100}[/tex] = 68

Total amount generated = 1200 + 68 = 1268.

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Therefore , the solution of the given problem of tractable problem comes out to be  the halting problem is undecidable for Turing machines.

a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.

Here,

Alan Turing proved in 1936 that a general algorithm running on a Turing

machine that solves the halting problem for all possible program-input

pairs necessarily cannot exist.

the halting problem is undecidable for Turing machines.

Therefore , the solution of the given problem of probability comes out to be  the halting problem is undecidable for Turing machines.

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Katie is correct. Any number with 4 as a factor will also have 8 as a factor; therefore, any number with 8 as a factor will have 4 as a factor.

Katie is correct. Any number that is a multiple of 8 will also be a multiple of 4 because 8 is divisible by 4. For example, 8 is a multiple of 4 (8 = 2 x 4) and 16 is a multiple of 8 (16 = 2 x 8) and also a multiple of 4 (16 = 4 x 4). So, any number that is a multiple of 8 will also be a multiple of 4.  So any number that is a multiple of 8 will also be a multiple of 4. Note that 80 is a multiple of 8, but not 4.

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The family's monthly payment for their new minivan is $6,664.52

To calculate the monthly payment, we first need to find the total amount that the family is financing by subtracting the down payment from the total cost of the minivan: $45,000 - $12,000 = $33,000.

Then, we can use the monthly payment factor to calculate the monthly payment. The formula to do this is:

Monthly Payment = Financed Amount * Monthly Payment Factor

So in this case:

Monthly Payment = $33,000 * 0.202764 = $6,664.52

Therefore, the family's monthly payment for their new minivan is $6,664.52

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