What is the circumference of the circle below?
10 centimeters

The function that correctly defines S(x) is S(x) = 5x - 2(20 - x) + 20

We have the following definitions in the question

If the total questions is 20, then

Incorrect answers = 20 - x

So, the points gained/lost are

Gained = 5 * x = 5x

Lost = -2 * (20 - x) = -2(20 - x)

Bonus = 20

Add the above points to get the function S(x)

S(x) = 5x - 2(20 - x) + 20

Hence, the definition is S(x) = 5x - 2(20 - x) + 20

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Answer:

2.5 %

Step-by-step explanation:

P(A | B) = P(A∩B) / P(B)

2.5%

The probability of this occurring when he has less than 11.5 oz of cola will be 0.02275.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

A 12-ounce container of Bubbly cola has a mean volume of 12 oz, with a standard deviation of 0.25 oz. He has under 11.5 oz of cola.

Then the z-score is given as,

z = (11.5 - 12) / 0.25

z = -2

Then the probability is given as,

P(x < 11.5) = P(z < -1)

P(x < 11.5) = 0.02275

The probability of this occurring when he has less than 11.5 oz of cola will be 0.02275.

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Answer:

it droped 40 degres

Step-by-step explanation:

Answer:

The temperature dropped 4 degrees per 1000 feet.

Step-by-step explanation:

90 - 50)/(10,000:1,000) = 40/10 = 4 degrees per 1000 ft

Answer:

The answer to this question can be defined as follows:

a)

cosine: 0.707

correlation: 0

Euclidean: 3.16

b)

cosine: 1

correlation: 1

Euclidean: 0

Jaccard: 1

c)

cosine: -0.4082

correlation: 0.5774

Euclidean: 2.64

d)

cosine: -0.333

correlation:  -0.3333

Jaccard: 0.5

e)

cosine: -0.7075

correlation: 0.2132

Step-by-step explanation:

a) cosine:

\(x \times y( 0 \times 2+ 0 \times 2 +1 \times 2+1 \times 2) = 4\\\\ x= \sqrt{2} = 1.414\\\\y= \sqrt(16)=4\\\\\cos (x\times y) = \frac{x\times y}{x\times y}\\\\\cos (x\times y) = \frac{4}{1.414\times 4}\\\\= 0.707\)

correlation:

\(\ corr(x,y) =[\frac{covariance (x,y)}{standec(x) \times standdev(y)}]\\X \ mean = 0.5\\Y \ mean = 2\\covariance (x,y) = 0\\standdev(x) = 0.5774\\standdev(y) = 0\\corr(x,y) = 0\)

Euclidean:

\(d(x,y) = \sqrt((0-2)^2+(0-2)^2+(1-2)^2+(1-2)^2)\\d(x,y) = 4+4+1+1\\d(x,y)= \sqrt(10)\\d(x,y)= 3.16\\\)

by applying above formula we get all the values.

b)

cosine: 1

correlation: 1

Euclidean: 0

Jaccard: 1

c)

cosine: -0.4082

correlation: 0.5774

Euclidean: 2.64

d)

cosine: -0.333

correlation: -0.3333

Jaccard: 0.5

e)

cosine: -0.7075

correlation: 0.2132

Answer:

x = 5cm

Step-by-step explanation:

We Know

The x-scale is 1:5

Find x.

We Take

25 ÷ 5 = 5 cm

So, x = 5cm

Answer:

= - 2.43%

Step-by-step explanation:

From the information given:

Since the variable (daily returns) is normally distributed, Then, using empirical rule at 95% confidence interval level, we have:

\(( \mu - 1.96 \sigma \ , \ \mu + 1.96 \sigma)\)

where;

The expected mean daily return \(\mu = 0.05 \%\)

The standard deviation \(\sigma = 1.5\%\)

Given that the 95% confidence interval is expected to be a maximum loss, then the probability is left-tailed which is 1.65\(\sigma\) away from the average.

Thus the distribution of the lower boundary can be computed as:

= \((0.05 - 1.65 \times 1.5)\%\)

= \((0.05 - 2.475)\%\)

= \(( - 2.425)\%\)

= - 2.43%

Answer:

Step-by-step explanation:

Even though no answer choices are given, the main benefit of this is that by choosing a randomly from a population it allows every single individual to have the same chance of getting chosen and observed. This randomness allows for that sample group to much more accurately represent the entire population that is being observed without having to conduct additional research. Therefore, becoming extremely useful in such studies.

A sample is a  group that is taken out of the population to be tested.

A random sampling occurs when subjects are being selected for a study  

The benefit of using random sampling is that each subject in the population is equally likely to be selected and the resulting sample is likely representative of the population.

Random sampling allows for unbiased estimates to be created, but at the cost of efficiency within the research process

Some advantages of random sampling shown below,

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Answer:

x = 15

y = 13

Step-by-step explanation:

6x - 4 = 5x + 11

x = 15

4y + 3 + 3y + 86 = 180

7y = 91

y = 13

Answer:

x = 23°

Step-by-step explanation:

Looking at the diagram above, we can see that it is Pentagon.

The sum of interior angles in a Pentagon (5 sides polygon) = 540°

This is because in a Pentagon, from the vertex we can draw 2 diagonals that would result in 3 triangles.

Sum of angles in a triangle = 180°

Hence, the sum of angles in a Pentagon = 3 × 180°

= 540°

Hence,

540° = 85° + 5x° + 5x° + 5x + 5° + 5x - 10°

540° = 85° + 5° - 10°+ 5x° + 5x° + 5x° + 5x°

540° = 80° + 20x°

540° - 80° = 20x°

460° = 20x°

x° = 460/20

x = 23°

Therefore, the value of x = 23°

Answer:

6

Step-by-step explanation:

We can establish 6 as an upper bound, since 1*2*3 = 6, and 6 is clearly the greatest number that is a divisor of itself.

We can show that the product of any three consecutive numbers is divisible by 6, because out of any three consecutive integers, at least one must be divisible by 3, and at least one must be divisible by 2. Since the product must have factors of 2 and 3, it must also have 6 as a factor.

Answer:

20/4

Step-by-step explanation:

5 = x/4

mulitply both sides by 4

x = 20

so the fraction is 20/4

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer:

65.04<x<68.96

Step-by-step explanation:

The confidence interval formula is expressed as;

CI = x ± z*s/√n

x is the mean = 67

z is the 95% z score = 1.96

s is the standard deviation = 8

n is the sample size = 64

Substitute;

CI = 67 ± 1.96*8/√64

CI = 67 ± 1.96*8/8

CI = 67 ± 1.96

CI = (67-1.96, 67+1.96)

CI = (65.04, 68.96)

Hence the confidence interval for the mean of the population is between 65.04<x<68.96

F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

19/31

Step-by-step explanation:

since there are 15 squares and 4 circles, both is 19

and since the total pieces 31

so the probability that he will grab a square or circle is 19/31

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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The adjusting journal entry will include a debit to the allowance for credit losses of R4,400.

the correct answer is C. debit to allowance for credit losses of R4,400.

To determine the adjusting journal entry for J&amp;L Electrical Services, we need to calculate the ending balance of accounts receivable and the necessary adjustment for the allowance for credit losses.

Beginning balance of accounts receivable: R200,000

Services delivered on credit: R660,000

Collections from debtors: R640,000

To find the ending balance of accounts receivable, we subtract the collections from the sum of the beginning balance and services delivered on credit:

Ending accounts receivable = (Beginning balance + Services delivered) - Collections

Ending accounts receivable = (R200,000 + R660,000) - R640,000

Ending accounts receivable = R220,000

Now, we need to calculate the adjustment for the allowance for credit losses. J&amp;L Electrical Services estimates that 2% of the ending accounts receivable will not be collected:

Allowance for credit losses adjustment = Ending accounts receivable * Estimated uncollectible percentage

Allowance for credit losses adjustment = R220,000 * 2% = R4,400

Since the allowance for credit losses has a beginning balance of R4,000, we need to increase it by R4,400 to match the estimated uncollectible amount:

the correct answer is C. debit to allowance for credit losses of R4,400.

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A linear function is a function that has a constant rate of change of the

output per unit change in the values of the input.

Reasons:

The initial rate of change of temperature with time = Quick (rapidly) Later change of temperature with time = Slowly (less rapidly)

Given that the tea is initially hot and is expected to cool, we have;

Where;

From the above, we get;

Which gives that the graph will be nonlinear because the rate of change

over a given time period is not constant.

Therefore;

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Answer:

is c

Step-by-step explanation:

Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?

It is linear because the graph decreases over time.

It is linear because there is both an independent and a dependent variable.

It is nonlinear because linear functions are increasing functions.

It is nonlinear because linear functions increase or decrease at the same rate.

Answer:

$32.2

Step-by-step explanation:

28/100×15%= 32.2

For the coin: 2 possibilities, either head or tail. So probability of head is 1/2.

For the cube (assuming numbers are 1 to 6): 6 possibilities (1 2 3 4 5 6). We have 3 odd numbers, so probability of odd number is 3/6=1/2.

You want both head and an odd number, so you multiply the 2 probabilities: 1/2×1/2=1/4.

So the answer is 1/4.

You can use a tree to better understand probabilities.

The area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

To find the area of the bounded region by the curves(refer to attached picture):

\(\rm A= \int\limits^2_1 {(\frac{1}{x}-\frac{1}{x^2}) } \, dx\)

After solving:

A = 0.193 square units

Thus, the area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.

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The principal amount was £1260, and the annual interest rate is 5.5%.

Given that, Olivia gets £1606.50 and £1675.80 after 5 years and 6 years of investment in simple interest respectively.

SI = principal × rate × time / 100

So,

P + 5pr = £1606.50

P = £1606.50 - 5pr............(i)

P + 6pr = £1675.80

P = £1675.80 - 6pr.........(ii)

Therefore,

£1606.50 - 5pr = £1675.80 - 6pr

Pr = 69.3

Put the value of pr in eq(i)

P + 5(69.3) = 1606.50

P = 1606.5 - 346.5

P = 1260

Now,

(1260)r = 69.3

r = 0.055

The annual interest is 5.5%

Hence, the principal amount was £1260, and the annual interest rate is 5.5%.

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If we assume that I = E(R + r), then I/I = R/E + r/E​.

The inverse of a value of a number is known as the reciprocal of the number. The reciprocal can be found out by replacing the numerator with the denominator and vice versa. For example, reciprocal of a number x will be 1/x and vice versa.

Here, we are given that I = E/(R + r)

Taking reciprocals of both sides we get-

Reciprocal of I will be- 1/I

Reciprocal of E/(R + r) will be- (R + r)/ E

Thus,

1/I = (R + r)/ E

Simplifying the equation further, we get-

1/I = R/E + r/E

Hence, proved

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Answer:

74 units squared

Step-by-step explanation:

we know that the area of a square or rectangle is A = L × w

so we should just separate the object into it's individual rectangles/squares, solve for their areas, then add them together.

so I'll start with the middle square its length is 8 and width is 8 too.

A = 8 × 8

A = 64

now we'll move on to the other small ones to the side.

the one on the right side it's length is 2 and width is 2.

A = 2 × 2

A = 4

and then the last one on the left, Length is 3, width is 2.

A = 2 × 3

A = 6

now we'll add up all of the areas to get the total area.

Total = 64 + 4 + 6

Total = 74 units squared

Answer:

Graph: (2.12,-4.06) and (3,0)

Step-by-step explanation:

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

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A relation that has more than one output of each input. That is not a function. A function only has one output of each input. Function a and function b are linear functions. Function a is represented by the table values. function b is represented by the equation y=3x+4.

Domain, is a term that is used to measure the independent variable’s values. Also known as the “x” values. It tells you what values of “x” are applicable in the function. What values will satisfy the function.

Range, is a term used to measure the dependent variable’s values. Also known as the “y” values. It tells you what values of why does the graph of the function extends till.

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Subtracting decimals, just like adding decimals, is similar to subtracting whole numbers. Just like adding decimals, the only difference is that we line up according to the decimal point instead of the last digit

One type of number that has a whole number and a fractional component separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

Comparable to subtracting whole numbers is the operation of adding and subtracting decimals. The only difference between adding decimals and doing so is that we line up according to the decimal point rather than the last digit.

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Answer:

first off the park you've listed is no match for the fact its more then 0.86.

Step-by-step explanation:

\(tan^{-1} (\frac{7}{420} )\\\\= arctan (\frac{7}{420} )\\\\= arctan (\frac{1}{60} )\\= 0.95\)

so basically it equals 0.95°

which basically means 0.86 < 0.95.