Write the equation for the function g(x), which can be described as a
vertical shift 13 units up from the function f(x) = In x –1

Answer:

About 0.5

Step-by-step explanation:

By the law of sines:

\(\dfrac{2}{\sin 105}=\dfrac{c}{\sin 15} \\\\\\c=\dfrac{2}{\sin 105}\cdot \sin 15\approx 0.5cm\)

Hope this helps!

Answer:

15/20=d/16

20d. =15×16

20d=240

d=12 cm

Answer: 6 feet long

Step-by-step explanation:

1ft. = 12 in

62 inches = 5 feet and 2 inches

Break down 62 into 60 and 2

60 divided by 12 = 5 (12x5=60)

60in. = 5ft.

2in. = 2in.

5ft. and 2in.

10in.= 10in.

Add the inches

10in. + 2 in. = 12 in.

12in.= 1ft.

5ft. + 1ft. = 6ft.

Answer: Nancy’s rope is 6ft. long

The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

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9514 1404 393

Answer:

  14.  C) 136°

  15.  C) 40°

Step-by-step explanation:

Inscribed angles are half the measure of the arc they intercept. For an inscribed quadrilateral, this means opposite angles are supplementary.

__

14) ∠H +∠W = 180°

  34x +55x +2 = 180

  89x = 178 . . . . . . . . . subtract 2

  x = 2 . . . . . . . . . . . . . divide by 89

  arc VX = 2(34x) = 68(2) = 136 . . . degrees

__

15) The sum of angles in the triangle is 180°.

  ? + 80° + (120°/2) = 180°

  ? = 40° . . . . . . . . . . subtract 140°

Answer:

Solution given:

14.

34x+55x+2=180°[sum of opposite angle of a cyclic quadrilateral is supplementary]

89x=180°-2

x=178/89

x=2°

now

m arc VX=2× <H[ central angle is twice the inscribed angle standing on a same base]

m arc VX=2(34×2)=136°

Option C.

15.

Solution given:

<B=80°

<C=½ arc AB[central angle is twice the inscribed angle standing on a same base]

<C=½×120°=60°

we have

<A+<B+<C=180°[ sum of interior angle of a triangle is 180 ]

<A=180-80°-60°

<A=40°

option C.

The explicit formula for the sequence 12, 112, 212, 312, 412 is a_n = 100n + 12.

The explicit formula for the given sequence is:

a_n = 100n + 12

In the given sequence, each term is obtained by adding 100 to the previous term. The first term is 12, and each subsequent term is obtained by adding 100 to the previous term.

Using the formula, we can calculate any term in the sequence by substituting the corresponding value of n. For example:

a_1 = 100(1) + 12 = 112

a_2 = 100(2) + 12 = 212

a_3 = 100(3) + 12 = 312

a_4 = 100(4) + 12 = 412

Therefore, the explicit formula for the sequence 12, 112, 212, 312, 412 is a_n = 100n + 12.

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Answer:

64 (1/2) n

ssssssssssssssssssssssssssssssssssssssssssssss

Answer:

Means:

1.55

1.73

Standard Deviation:

0.1434

0.1338

Coefficient of variation:

9.2

7.7

the limited data listed here shows evidence of stealing by the security service​ company's employees.

Step-by-step explanation:

Given data:

security Service Company          Other Companies    

               x₁                                                 x₂

               1.5                                              1.8

               1.7                                               1.9

               1.6                                               1.6

               1.4                                                1.7

               1.7                                                 1.8

               1.5                                                 1.9

               1.8                                                 1.6

               1.4                                                  1.5

               1.4                                                  1.7

               1.5                                                  1.8

      n₁ = 10                                                 n₂ = 10

To find:

coefficient of variation for each of the two​ samples

Solution:

The formula for calculating coefficient of variation of sample is:

Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100%

Calculate Mean for Security Service Company data:

Mean =  (Σ x₁) / n₁

         = (1.5 + 1.7 + 1.6 + 1.4 + 1.7 + 1.5 + 1.8 + 1.4 + 1.4 + 1.5) / 10

         = 15.5 / 10

Mean = 1.55

Calculate Standard Deviation for Security Service Company data:

Standard Deviation = √∑(x₁ - Mean)²/n₁-1

                                = √∑(1.5-1.55)² + (1.7-1.55)² + (1.6-1.55)² + (1.4-1.55)² + (1.7-1.55)² + (1.5-1.55)² + (1.8-1.55)² + (1.4-1.55)² + (1.4-1.55)² + (1.5-1.55)² / 10-1

=√∑ (−0.05)² + (0.15)² + (0.05)² + (−0.15)² + (0.15)² + (−0.05)² + (0.25)² +  (−0.15)² +  (−0.15)² +  (−0.05)² / 10 - 1

= √∑0.0025 + 0.0225 + 0.0025 + 0.0225 + 0.0225 + 0.0025 + 0.0625 +        0.0225 + 0.0225 + 0.0025 / 9

= √0.185 / 9

= √0.020555555555556

= 0.14337208778404

= 0.143374

Standard Deviation = 0.143374

Coefficient of Variation for Security Service Company:

CV = (Standard Deviation / Mean) * 100%

     = (0.143374 /  1.55) * 100

     = 0.09249935 * 100

     = 9.249935

CV  = 9.2

CV  = 9.2%

Calculate Mean for Other Companies data:

Mean =  (Σ x₂) / n₂

          =  (1.8 + 1.9 + 1.6 + 1.7 + 1.8 + 1.9 + 1.6 + 1.5 + 1.7 + 1.8) / 10

          =   17.3 / 10

Mean  = 1.73

Calculate Standard Deviation for Other Companies data:

Standard Deviation = √∑(x₂-Mean)²/n₂-1

                                = √∑[(1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.7-1.73)² + (1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.5-1.73)² + (1.7-1.73)² + (1.8-1.73)²] / 10 - 1

                                = √∑ [(0.07)² + (0.17)² + (-0.13)² + (-0.03)² + (0.07)² + (0.17)² + (-0.13)² + (-0.23)² + (-0.03)² + (0.07)²] / 9

                                = √∑ (0.0049 + 0.0289 + 0.0169 + 0.0009 + 0.0049 + 0.0289 + 0.0169 + 0.0529 + 0.0009 + 0.0049) / 9

                                = √(0.161 / 9)

                                = √0.017888888888889                                

                                = 0.13374935098493

                                =  0.13375

Standard Deviation = 0.13375

Coefficient of Variation for Other Companies:

CV = (Standard Deviation / Mean) * 100%

     = (0.13375 / 1.73) * 100

     = 0.077312 * 100

     = 7.7312

CV = 7.7

CV = 7.7%

Yes, the limited data listed here shows evidence of stealing by the security service​ company's employees because there is a significant difference in the variation.

Answer:

210 ways

Step-by-step explanation:

7 P 3 = 210  ways

or    7 C 3 = 35     choices of 3 posters which can bearrranged in 6 different ways     6 * 35 = 210 ways

The value of c in the domain of f(x) depends on the specific function f(x) and its domain.

In order to determine which value of c is in the domain of f(x), we need to know the function f(x) and its domain. A domain is the set of all possible input values of a function.

If a value of c is in the domain of f(x), then we can plug it into the function and get a valid output.

In general, a function f(x) can have a restricted domain due to certain conditions or limitations. For example, a square root function cannot have negative values under the radical because that would result in an imaginary number.

Thus, the domain of a square root function is restricted to non-negative values.

In order to find the domain of a function, we need to consider any restrictions on the input values. For example, if we have the function f(x) = 1/x, we cannot plug in x = 0 because that would result in division by zero, which is undefined.

Therefore, the domain of f(x) is all real numbers except 0. We can write this as D(f) = {x : x ≠ 0}.Once we know the domain of f(x), we can check which value of c is in the domain by seeing if it satisfies the condition.

For example, if the domain of f(x) is D(f) = {x : x > 2}, then c = 3 is in the domain because 3 is greater than 2. On the other hand, c = 1 is not in the domain because 1 is less than 2.

Therefore, the value of c in the domain of f(x) depends on the specific function f(x) and its domain.

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The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.

The z-score formula is:

z = (x - μ) / σ

where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For the lower bound of 93, the z-score is:

z = (93 - 105) / 20 = -0.6

For the upper bound of 117, the z-score is:

z = (117 - 105) / 20 = 0.6

Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:

normalcdf(-0.6, 0.6, 0, 1)

This gives us a probability of 0.6827.

Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

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Answer:

a + 5b

Step-by-step explanation:

3*(a + b). In this multiply each term with 3 and in -2(a- b), multiply each term with (-2).

3*(a +b) - 2*(a - b) = 3*a + 3*b + (-2)*a + (-2)*(-b)

                             = 3a + 3b - 2a  + 2b

                             = 3a - 2a + 3b + 2b  {Combine like terms}

                             = a + 5b

Like terms have same variable with same power. Here, 3a and (-2a) are like terms. So, combine the coefficients of the like terms

3a + (-2a) = a.

Answer:

The posters will be 1 foot away from each other

Step-by-step explanation:

The equation is right

Answer:

D

Step-by-step explanation:

It's decreasing then once it hits the origin, it starts to increase again. I hope this helps you:)

Answer:

D

Step-by-step explanation:

Answer:

2n-5

Step by step Explanation:

You must put 2 in front of "n" to represent the multiplication of the 2 numbers. Then put a subtraction sign and five the show the number is decreased by 5.

Hope this helps!

Using the function  f(x) = 28.7 + 1.2log (x + 1) that models the salinity of the ocean to depths of 1000 meters the salinity to the nearest hundredth is 32.18 g/kg

The salinity s calculated using the logarithmic function model

f(x) = 28.7 + 1.2log (x + 1)

given that f(x) is in grams of salt per kilogram of seawater and x is the depth in meters

for x = 797 meters

f(x) = 28.7 + 1.2log (x + 1)

f(x) = 28.7 + 1.2log (797 + 1)

f(x) = 28.7 + 1.2log (798)

f(x) = 28.7 + 1.2 * 2.902

f(x) = 28.7 + 3.4824

f(x) = 32.1824

f(x) = 32.18  (to the nearest hundredth)

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The equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is 16 = 2 1/2 + 2 1/4b (option b)

To start with, we know that the farmer picks 16 quarts of berries. Out of those, 2 1/2 quarts cannot be used, which means the farmer has 16 - 2 1/2 quarts of berries that can be used to make jam.

Now, the recipe requires 2 1/4 quarts of berries to make one batch of jam. Let's represent the number of batches of jam the farmer can make with the remaining berries as "b".

Therefore, the equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is written as,

=> 16 = 2 1/2 + 2 1/4b

Hence the correct option is (b).

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The function is constant in the interval (-6 to 0).

The correct option is (C).

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

If the value of one of the variables does not alter the value of the other, the function is said to be constant.

As we can see, the function is constant in the range from x=-6 to 0, because the value of y in the function does not change as the value of x changes (-6 to 0).

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Answer:

6

Step-by-step explanation:

hope it helps

Answer:

A= 47 1/2

Step-by-step explanation:

The magnitude of the vector having the initial point P and the terminal point Q is 17.

What is magnitude ?

Simply said, "distance or amount" is the definition of size. In terms of motion, it shows the absolute or relative size, direction, or movement of an item. It is used to describe something's size or scope. Magnitude in physics often refers to a size or amount.

Given: p (- 3,2) , q (5,17)

vector  = (17-2)i + (5+3)j

= 15i + 8j

Magnitude = \(\sqrt{(15^{2}+8^{2} ) }\)

magnitude =17

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Answer:

-2x + 3y = 6

Rearrange

-2x + 3y - 6 = 0

ax + by + ca = 0

a = -2

b = 3

If ca was a typo, and you meant c, then c = -6.

However, if ca wasn't a typo, then:

ca = -6

-2c = -6

c = -6 / -2

c = 3

Answer:

True

Step-by-step explanation:

Simplify the left side. Combine like terms (terms with the same amount of variables).

11 + 2 = 13

-5x + 4x = 4x - 5x = -x

-x + 13 = 13 - x (True)

True is your answer.

~

The area of the shaded region under the standard normal curve with z = 0.49 is 1.

The area of the shaded region under the standard normal curve with z = 0.49 is 1.

What is curve?

In mathematics, a curve is a continuous and smooth (i.e., differentiable) mathematical object that represents a path or a trajectory. Curves can be defined in different ways, depending on the context in which they are used.

What is area of curve?

The area of a curve refers to the amount of space enclosed by a curve on a two-dimensional plane. Finding the area of a curve can be a challenging problem, especially when the curve is not a standard geometric shape such as a circle or rectangle.

To find the area of the shaded region under the standard normal curve with z = 0.49, we need to use a standard normal distribution table or a calculator with a normal distribution function.

Using a standard normal distribution table, we find that the area to the left of z = 0.49 is 0.6864. This means that the area to the right of z = 0.49 is 1 - 0.6864 = 0.3136.

Since the normal curve is symmetric about the mean (z = 0), the area to the left of z = -0.49 is also 0.6864. Therefore, the area between z = -0.49 and z = 0.49 is:

0.6864 (area to the left of z = 0.49) + 0.3136 (area to the right of z = 0.49) = 1

So the area of the shaded region under the standard normal curve with z = 0.49 is 1.

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greater, above I hope this helps out!

Answer:

The number -7/5 is less than - 1 1/5 because -7/5 lies below -1 1/5 on a vertical number line.

Step-by-step explanation:

Don't let it confuse you, if you convert -7/5 to a whole number like -1 1/5, it turns out to be less than -1 1/5. When you convert -7/5 you get -1 2/5. That is less than -1 1/5 because it is further away from 0. Therefore it is less than and below -1 1/5 on a vertical number line. I hope this helps you! :)

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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Answer:

A. 2,4,1,3

B. 2,1,3,4

C. 2,1,3,4

D. 1,2,4,3

Step-by-step explanation:

its always cell the simplest among the choices then tissue which is comprised of cells then organs which comprised of tissues and lastly the systems in our body that is comprised of organs