If the transformation from f to g is such that f(x)=e^(x) is verticall shrunk by a factor of ( 1)/(3) to make g(x), what is g(x) ?

There is no unit vector with a positive first component that is orthogonal to both u and v.

The unit vector we are looking for is (1/√14, √13/14, √15/14, -√12/14). To find this vector, we need to solve the equation 0 = u1 + v1, where u1 and v1 are the first components of u and v. From the given vectors, u1 = 1 and v1 = 6. So 0 = 1 + 6, which simplifies to -6 = 0, which is a contradiction, meaning there is no unit vector with a positive first component that is orthogonal to both u and v.

  Learn more about unit vector

  brainly.com/question/10809170

  #SPJ11

Answer:

9

Step-by-step explanation:

The median is the number in the middle of a set of numbers.

Our set of numbers:  1, 1, 2, 3, 7, 9, 10, 10, 15, 17, 19​

In this case the median is 9

The ferry travels at constant rate is 7/18 miles/hour

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

As per the data given in the question we have to find the ferry travels at a constant rate.

As per the question it is given that a ferry traveled 1/6 of the distance between two ports in 3/7 hour.

Now, Ferry travelled 1/6 miles of distance between two ports in 3/7 hours  

Hence, Rate of Ferry is equal to distance travelled over time taken.  

Rate of ferry = 1/6 ÷ 3/7

Now we calculate it.  

Rate of ferry = 1/6 × 7 / 3 miles/hour

Rate of Ferry = 7/18 miles/hour

Hence, The ferry travels at constant rate is, 7/18 miles/hour.

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ3

The frequency and cumulative frequency distribution tables for the given data are below in the solution part.

Cumulative frequency is used to calculate the number of observations in a data collection that is above (or below) a specific value.

The data is provided for 62 students in a certain class in terms of their maths marks out of 100.

55, 60, 81, 90, 45, 65,  45, 52, 30,  85,  20, 10, 75, 95, 09, 20, 25, 39,  45, 50, 78,  70,  46, 64, 42, 58, 31, 82, 27, 11,  78, 97, 07,  22,  2  36, 35, 40, 75, 80, 47, 69,  48, 59, 32,  83,  23, 17, 77, 45, 05, 23, 37, 38,  35, 25, 46,  57,  68, 45, 47, 49.

The frequency distribution table for the given data is as follows:

       Class                               Frequency

(Marks obtained)                 (No. of students)

0 - 10                                              4

10 - 20                                             3

20 - 30                                            8

30 - 40                                             9

40 - 50                                            13

50 - 60                                            6

60 - 70                                            5

70 - 80                                            6

80 - 90                                            5

90 - 100                                          3

                                                  N = 62

The cumulative frequency table more than or equal to the type for the given data is as follows:

       Class                               Frequency             Cumulative frequency

(Marks obtained)                 (No. of students)  

0 - 10                                               4                          62

10 - 20                                             3                          58

20 - 30                                            8                          55

30 - 40                                             9                          47

40 - 50                                            13                          38

50 - 60                                            6                           25                    

60 - 70                                            5                            19

70 - 80                                            6                            14

80 - 90                                            5                            8

90 - 100                                          3                             3

                                                  N = 62

Learn more about the cumulative frequency here:

https://brainly.com/question/30087370

#SPJ1

Answer:

The given rectangle is not fully defined, as it is missing some measurements such as the length and width. Without this information, it is not possible to accurately calculate the perimeter of the rectangle.

However, assuming that the missing measurement is the width of the rectangle, then the expressions given by the five students would be:

2(3x + 4x + 3) = 14x + 6

2(6x + 6) + 2(4x + 6) = 20x + 24

2(3x + 3) + 2(4x + 3) = 14x + 12

2(6x + 3) + 2(4x + 3) = 20x + 12

2(6x + 3x) + 2(3 + 4x) = 18x + 10

Note that all expressions follow the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.

Therefore, the correct answer is C. Log 65/177 y = x.

The correct answer is C. Log 65/177 y = x.

To solve the equation in exponential form, we need to use the properties of logarithms. The equation Y^x = 65 / 177 can be rewritten in logarithmic form as Log Y (65/177) = x. Using the property of logarithms, Log a^b = b Log a, we can rewrite the equation as Log (65/177) Y = x. This is the same as option C, Log 65/177 y = x.

Therefore, the correct answer is C. Log 65/177 y = x.

Learn more about equation

brainly.com/question/29657992

#SPJ11

Answer:

C is the answer

Therefore , the solution of the given problem of unitary method comes out to be he only had a 19 gallon jug of petroleum, which was insufficient for both days.

To finish the job using the unitary method, multiply the subsets measures taken from this microsecond section by two. In a nutshell, when a wanted thing is present, the characterized by a variable group but also colour groups are both eliminated from the unit technique. For instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

Magnus had to fill up his skiff with 6 gallons and 3 quarts of gas on Monday. We can observe that 1 quart is equivalent to 0.25 gallons to express this in decimal form:

=> 6 gallons 3 quarts = 6 + 3/4 = 6.75 gallons

Magnus used 6.75 litres of fuel on Monday as a result.

He required twice as much petrol on Saturday as he did on Monday:

=> 13.5 gallons from

=> 2 (6.75" gallons).

So on Saturday, he consumed 13.5 litres of fuel.

Overall, he employed:

=> 6.75 gallons + 13.5 gallons = 20.25 gallons

He only had a 19 gallon jug of petroleum, which was insufficient for both days.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

Answer:

1,254 - whole number; 0.13 - terminating; 0.123456789... - non-terminating/non-repetitive; 0.143143143... - repeating decimal

Step-by-step explanation:

A whole number is a number without any decimals or fractions. A terminating number is one that has an end. A non-terminating number is one that continues on forever. A repeating number is one that has the same pattern and continues on forever.

The vector representing D = A - B has following values,

1. x- component of vector D = 9 and y- component of vector D = 9.

2. Magnitude and direction of vector D is equal to 12.73 and 45° above the positive x-axis.

Here, Vector D= A-B  __(1)

Components of vector A are,

Ax=5

Ay=5

Components of vector B are,

Bx= -4,

By= -4

1. Subtract the x- and y-components of vector B from vector A, respectively by substituting in (1) we get,

Dx = Ax - Bx

    = 5 - (-4)

    = 5 + 4

    = 9

Dy = Ay - By

     = 5 - (-4)

     = 5 + 4

     = 9

2. Magnitude of vector D, use the Pythagorean theorem,

|D| = √(Dx² + Dy²)

    = √(9² + 9²)

    = √(162)

     ≈ 12.73

Direction of vector D, use trigonometry.

Angle θ represents vector D makes angle with positive x-axis is ,

θ = tan⁻¹(Dy / Dx)

   = tan⁻¹(9 / 9)

   = tan⁻¹(1)

    = 45°

Therefore, required value of the vectors are,

1. x- and y-components of vector D are 9 and 9, respectively.

2. Magnitude of vector D is 12.73, and direction is 45° above the positive x-axis.

Learn more about vectors here

brainly.com/question/3129747

#SPJ4

The above question is incomplete , the complete question is:

Suppose D= A-B where vector A has components Ax=5, and Ay=5 and vector B has components Bx= -4, By= -4.

1. What are the x- and y- components of vector D?

2. What are the magnitude and direction of vector D?

Answer:It will hit the ground when 84 - 16t^2 = 0

Step-by-step explanation:

16t^2 = 84

t^2 = 5.25

t = 2.29

About 71 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected. The mean is 0.71. Standard Deviation is 0.043. The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.

1) Mean:
The mean of a proportion is simply the proportion itself, so the mean is 0.71.

2) Standard Deviation:
The standard deviation of a proportion is given by the formula:
σ = √(p(1-p)/n)
where p is the proportion, and n is the sample size. Plugging in the values given in the question:
σ = √(0.71(1-0.71)/110)
σ = 0.043

3) To find this probability, we need to use the normal distribution. We will use the z-score formula:
z = (x - μ) / σ
where x is the proportion we are interested in (0.8), μ is the mean (0.71), and σ is the standard deviation (0.043). Plugging in the values:
z = (0.8 - 0.71) / 0.043
z = 2.09
Using a z-table, we find that the probability of getting a z-score greater than 2.09 is 0.0183. So the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.

Learn more about probability at https://brainly.com/question/30052626

#SPJ11

Answer: 20

Step-by-step explanation:

49 ÷ 245 %

convert the percentage to decimals

49 ÷ 2.455

calculate the product or quotient

20

                   Please give me brainliest

Answer:20

Step-by-step explanation:

Let's denote the number we are looking for as "x".

We can set up the equation:

245% of x = 49

We can convert 245% to the decimal form by dividing by 100:

2.45 * x = 49

To solve for x, we can divide both sides of the equation by 2.45:

x = 49 / 2.45

x = 20

Therefore, 245% of 20 is equal to 49.

The simplified form of the left side of the equation is $2 \tan x$.

The left side of the equation can be simplified using the quotient and reciprocal identities. The quotient identity states that $\tan x = \frac{\sin x}{\cos x}$ and the reciprocal identity states that $\sec x = \frac{1}{\cos x}$ and $\csc x = \frac{1}{\sin x}$. By substituting these identities into the equation, we can simplify the left side:

\[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\frac{1}{\cos x}+\frac{\sin x}{\cos x} \cdot \frac{1}{\sin x}}{\frac{1}{\sin x}} \\ & =\frac{\frac{1}{\cos x}+\frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2 \cdot \frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2}{\cos x} \cdot \frac{\sin x}{1} \\ & =\frac{2 \sin x}{\cos x} \\ & =2 \tan x \end{aligned} \]

Therefore, the simplified form of the left side of the equation is $2 \tan x$.

Learn more about  quotient and reciprocal identities

brainly.com/question/673545

#SPJ11

The probability that clothing store have fewer than 12 customers in first 2 hours is 0.0003.

We know that, the store is open for 12 hours and gets an average of 120 customers per day, the expected number of customers in a 2-hour period can be calculated as:

The Expected number of customers in 2 hours = 120×(2/12) = 20 customers,

We, use the Poisson distribution to find the probability of having fewer than 12 customers in the first two hours.

The Poisson distribution is given by : P(X = k) = (e^(-λ) × λ^k)/k! ;

where X = random variable (the number of customers), λ = expected value of X (in this case, λ = 20), k = number of customers we want to calculate the probability for, and k! is the factorial of k.

To find the probability of having fewer than 12 customers in the first 2 hours, we need to calculate the probability for k = 0, 1, 2, ..., 11 and add up the probabilities.

So, we have,

⇒ P(X < 12) = e⁻²⁰×(20⁰/0!) + e⁻²⁰×(20¹/1!) + ... + e⁻²⁰×(20¹¹/11!);

On solving, We get,

⇒ P(X < 12) = 0.0003,

Therefore, the required probability is 0.0003.

Learn more about Probability here

https://brainly.com/question/25870256

#SPJ4

The minimum cost per pupil is $7,500 when 250 students are enrolled.

To find the minimum cost per pupil, we need to find the vertex of the parabola C = 70,000 − 500n + n². The vertex of a parabola in the form y = ax² + bx + c is given by the formula x = -b/2a. In this case, a = 1, b = -500, and c = 70,000.

Plugging these values into the formula, we get:
x = -(-500)/2(1) = 500/2 = 250

So the minimum cost per pupil occurs when n = 250 students are enrolled.

To find the minimum cost, we can plug n = 250 back into the equation for C:
C = 70,000 − 500(250) + (250)² = 70,000 - 125,000 + 62,500 = 7,500

You can learn more about the vertex of the parabola at: brainly.com/question/20333425

#SPJ11

The solution for the inequality in this problem is problem is given as follows:

v ≤ 81.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality is given as follows:

5v/9 ≤ 45.

v ≤ 45 x 9/5

v ≤ 9 x 9

v ≤ 81.

Hence the solution is composed by the numbers to the left of 81, with a closed interval at x = 81.

More can be learned about inequalities at brainly.com/question/25275758

#SPJ1

The values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.

The given functions are F(x)=−529, F(x)=x^2+33, h(x)=∣x∣−233, and g(x)=2x.

To find the value of F(x) when x=3, we can substitute x=3 into the equation F(x)=x^2+33 and solve for F(x):
F(x)=x^2+33
F(3)=3^2+33
F(3)=9+33
F(3)=42

Similarly, to find the value of h(x) when x=3, we can substitute x=3 into the equation h(x)=∣x∣−233 and solve for h(x):
h(x)=∣x∣−233
h(3)=∣3∣−233
h(3)=3−233
h(3)=-230

And to find the value of g(x) when x=3, we can substitute x=3 into the equation g(x)=2x and solve for g(x):
g(x)=2x
g(3)=2(3)
g(3)=6

Therefore, the values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.

Learn about Functions

brainly.com/question/12431044

#SPJ11

If Cindy bought 7/8 yards of ribbon, then the length of Ribbon that Jacob bought is 7/10 yard.

The length of ribbon which Cindy bought is = 7/8 yard;

Jacob bought 4/5 the length as Cindy,

Which means that he bought, (4/5) × (7/8) yards of ribbon,

On multiplying these two fractions,

We get,

⇒ (4/5) × (7/8) = (4×7)/(5×8) = 28/40;

On simplifying this fraction, we divide both the numerator and denominator by their greatest common factor, which is 4,

We get,

⇒ 28/40 = 7/10,

Therefore, Jacob bought 7/10 yard of ribbon.

Learn more about Length here

https://brainly.com/question/15102009

#SPJ4

The reason that should be used to complete statement 2 "∠2 and ∠3 are supplementary" is linear pair postulate.

In Mathematics, the linear pair theorem is sometimes referred to as linear pair postulate and it states that the measure of two angles would add up to 180° provided that they both form a linear pair.

This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.

According to the linear pair theorem, we have the following supplementary angles:

∠2 + ∠3 = 180°

Read more on linear pair theorem here: brainly.com/question/27979699

#SPJ1

Answer:

Step-by-step explanation:

Answer:

[tex]f^{-1}[/tex] = [tex]\frac{x-3}{2}[/tex]

The inverse of a function is just the opposite of the function.

Answer:

The argument of the logarithmic function should be greater than zero.

Thus, for y = log(-x + 3) - 1 to be real-valued, we need:

-x + 3 > 0

or

x < 3

So, the domain of the function is all real numbers less than 3.

To find the range, let's consider the behavior of the logarithmic function.

As x approaches 3 from the left, the argument of the logarithm approaches zero from the negative side, which means the logarithm approaches negative infinity.

As x approaches negative infinity, the argument of the logarithm becomes very large and negative, which means the logarithm approaches negative infinity.

Therefore, the range of the function y = log(-x + 3) - 1 is all real numbers.

Step-by-step explanation:

According to the information, the expressions that would match the descriptions would be both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.

To find the correct descriptions that match the expressions we must look at the graph. In this case q and n represent two numbers on the number line. In this case, to relate them to a description we must find the number to which they refer:

In accordance with the above, we could say that the descriptions would look like this:

In this case, both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.

Learn more about values in: https://brainly.com/question/30145972

#SPJ1

The match of the terms and correct locations are:

1. A - Amplitude

2. B is compression

3. C is rarefaction

A longitudinal wave is a form of wave in which its direction of propagation is similar to the direction of vibration of the particles of the medium through which the wave is travelling. The waves generated by a stretched or compressed spiral spring produces longitudinal waves.

When a spiral spring is streched or compressed, on removal of the force a series of compression and rarefactions of the sections of the spring are produced. This sections vibrates in the direction of propagation of the waves produced.

Thus the match of the terms and correct locations are:

i. A - Amplitude

ii. B is compression

iii. C is rarefaction

Learn more about longitudinal waves at https://brainly.com/question/12536970

#SPJ1

Answer:

-x + 6.5 > 1 Is true.

Step-by-step explanation:

The explaination is given in the Picture.

To write a quadratic function f whose zeros are -2 and 9 , we have to factor the function by (x+2) and (x-9).

A quadratic function is a second-degree mathematical function whose graph is a parabola. The general form of a quadratic function is given by f(x) = ax² + bx + c, where a, b and c are constants and a cannot be equal to zero. The variable x represents the input of the function and f(x) represents the output or result of the function. To find the quadratic function of f we first need to multiply these factors, like this:

So the quadratic function whose zeros are -2 and 9 is:

Find more about quadratic function at:

https://brainly.com/question/1214333

#SPJ1

Using the unitary method, we found that Zach's plants grew  60cm in 7 weeks.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

Given that the height the plant grew in 2 weeks  = 2 feet

We are asked to convert it into centimetres.

This can be done using the unitary method.

Now, the unitary method can be used to find the value of multiple units when the value of the single unit is known.

Here we are given,

1 ft = 0.3 m

But we need feet and centimetre relation.

So we use the metre and centimetres relation.

1m = 100cm

Using the unitary method,

0.3m = 0.3* 100 = 30 cm

So,

1 feet = 0.3m = 30 cm

Then,

2 feet = 30 * 2 = 60 cm

Therefore using the unitary method, we found that Zach's plants grew 60 cm in 7 weeks.

To learn more about the unitary method, follow the link.

https://brainly.com/question/24587372

#SPJ1

Answer:

I think the answer is C. 65 m

Step-by-step explanation:

Answer:

L=22

Step-by-step explanation:

For the area of a rectangle you have to multiply the width by the length.

This problem would look like L*W=A. Being that you already have the area and the width, you would just have to fill in for these.

L*6.5=143

Then just follow the rules of PEMDAS to sole for L. In this case this would be dividing 6.5 by both sides.

L=22