The function f(x)=3x+4 is a linear function. Let g(x) represent f(x) after a horizontal trabslation 2 unuts to the left. What is the equation for the function g(x)?
Enter your answer in the box.
G(x)=?​

Answer:

5 =x

Step-by-step explanation:

10(x-1)-7x=x

Distribute

10x-10-7x = x

Combine like terms

3x-10 =x

Subtract 3x from each side

3x-10-3x = x-3x

-10 = -2x

Divide each side by -2

-10/-2 = -2x/-2

5 =x

By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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Answer:

Step-by-step explanation:

a) Probability-Above 30 min = 5.72% = .0572

b) Probability-Above 15 min =  99.11% = .9911

c) *Probability-Between  1 - 59.49% = .4051

d) 19.136 minutes  z = -1.28

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

What do you mean by normal distribution ?

A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.

Let assume the time taken for a one way trip be x .

x ⇒ N( μ , σ ²)

x  ⇒ N( 24 , 3.8 ²)

a)

The probability that trip will take at least 1/2 hour or 30 minutes will be :

P ( x ≥ 30)

= P [ (x - μ) / σ ≥ (30 - μ) / σ ]

We know that , (x - μ) / σ = z.

= P [ z ≥ (30 - 24) / 3.8)]

= P [ z ≥ 1.578 ]

= 1 - P [  z ≤ 1.578 ]

Now , using the standard normal table :

P ( x ≥ 30)

= 1 - 0.9394

= 0.0606

b)

The percentage of the time the lawyer is late for work will be :

P ( x  ≥ 15)

= P [ z ≥ -2.368 ]

= P [  z ≤ 2.368]

= 0.9918

or

99.18%

c)

The probability that lawyer misses coffee :

P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)

= P [  z < 0.263] - P ( z < -2.368)

or

= 0.3659

d)

The length of time above which we find the slowest 10​% of trips :

P( x ≥ X ) ≤ 0.10

=  0.5438

e)

Let's assume that y represents the number of trips that takes at least half hour.

y ⇒ B ( n , p)

y ⇒ B ( 3 , 0.0606)

So , the probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is :

P ( Y = 2 )

= 3C2 × (0.0606)² × ( 1 - 0.0606)

= 0.0103

Therefore , the answers are :

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

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Answer:

Yes, they make sense outside the context of temperature.

Step-by-step explanation:

If you are standing in a line, and mark your current position as 0 then if you take two steps ahead it can be counted as positive and if you take two steps back from your current position it can be counted as negative. The positive and negative can denote your forward and backward movement respectively.

If we denote the growth in companies revenue as positive and dip as negative then it would also make sense. A positive number would mean profit for the company while a negative sign would show loss.

Answer:

(2, 8), (0, 8), (-1, 5), (-1, 3), (-2, 3)} is {-1, 0, 2, 3}

Step-by-step explanation:

Answer:

y = 1/2x +3

Step-by-step explanation:

Since they are parallel lines the slope will remain the same

now we need to find the y intercept and we will have the equation

Lucky we know that our y intercept is three

y = (slope)*x + (y intercept)

y = 1/2 x +3

Answer:

42°

Step-by-step explanation:

This is right triangle and sum of 2 angles is 90°:

y+48°=90°

so y= 90°- 48°= 42°

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer: A

because slope are

Answer:

\(x\) is greater than 1.8

Step-by-step explanation:

Adding 1.4 to both sides of the equation yields \(x=3.2>1.8\).

The required reasoning for the given expression is that x is greater than 1.8. Option B is correct.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.

here,
Given expression,
x  - 1.4 = 1.8

The above expression refers that, when we subtract 1.4 from x it gives 1.8, which implies that x is a number greater than 1.8.
So the reasoning can be complied as x is greater than 1.8.

Thus, the required reasoning for the given expression is that x is greater than 1.8. Option B is correct.

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Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

30

Step-by-step explanation:

Start by substituting

2(5+3²) +2 = ___

Parenthesis

3²= 3 · 3 = 9

add that to 5 = 14

2(14) +2 = ___

2 times 14 = 28.

28 + 2 = 30

Answer:

30.

Step-by-step explanation:

2(5+ x^2)+ y

x=3, y=2

Using the given information for x and y and distributing that into the equation, the equation becomes:

2(5+ 3^2)+ 2

Now, use order of operations or PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction) to solve the problem.

The answer you should get is 30. :,)

Answer:

D

Step-by-step explanation:

Area of 1 surface=1×16=16 square units

hence, 16×6=96 square units

for all of them its base times height

v=bh

1) (8*6/2)*9.5=228

2) (4.5/2)^2 *8= 40.5

3) (3.3* 8.3/2) *5.4= 74.0

4) ((3.2+4.8)/2)* 2.7 *4.4= 47.5

Answer:

\(\frac{8}{x}\)

Step-by-step explanation:

what is the sum 3/x+9+5/x-9

\(\frac{3}{x} + 9 + \frac{5}{x} - 9 =\)     (add \(\frac{3}{x}\) and \(\frac{5}{x}\))

\(\frac{8}{x} + 9 - 9 =\)            (solve 9 - 9 = 0)

\(\frac{8}{x}\)                           ( your answer)

Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

Answer:

A. This statement A is false.

B. This statement A is false.

C. This statement is true .

Step-by-step explanation:

Determine which of the following statements is true.

From the statements we are being given , we are to determine if the statements are valid to be true or invalid to be false.

SO;

A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V

This statement A is false.

This is because any set of exactly 6 elements in V is linearly independent vectors of V . Hence, it can't be automatically a basis for V

B. If there exists a set that spans V, then dim V = 3

The statement B is false.

If there exists a set , let say \(v_1 ...v_3\), then any set of n vector (i.e number of elements forms the basis of V)  spans V. ∴ dim V < 3

C. If H is a subspace of a finite-dimensional vector space V  then dim H ≤ dim V is a correct option.

This statement is true .

We all know that in a given vector space there is always a basis, it is equally important to understand that there is a cardinality for every basis that exist ,hence the dimension of a vector space is uniquely defined.

SO,

If  H is a subspace of a finite-dimensional vector space V  then dim H ≤ dim V is a correct option.

Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

Let x be the cost of Jumbo popcorn and let y be the cost of chocolate chip

x + 2y = 5

x + 4y = 6

Subtract equation first equation from the second equation

2y = 1

Divide both-side of the equation by 2

y = 1/2

y = 0.5

substitute 0.5 into the first equation and solve for x

x + 2(0.5) = 5

x + 1 = 5

subtract 1 from both-side of the equation

x = 5 - 1

x = 4

Therefore each Jumbo popcorn costs $4 and each chocolate chip costs $0.5

The inequality that describes the given word problem is;

x + 1.5 < 48

Let x represent how tall Keenan was last summer. Thus;

x = Keenan's height last summer in inches

If he was x inches last summer, and has since grown an additional 1.5 inches up to date, then it means that his total height now is;

x + 1.5 inches.

The conditons state "riders must be at least 48 inches tall to ride the Night Eagle roller coaster". So it means that his height must be equal to 48 inches, or larger than 48 inches, to make him eligible to ride the roller coaster.

But since he is still too short to ride, this means the expression x+1.5 is smaller than 48 and as such the inequality of this problem is;

x + 1.5 < 48

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The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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\(\huge\text{Hey there!}\)

\(\mathsf{(\dfrac{7}{8})^4}\)

\(\mathsf{= \dfrac{7}{8}\times\dfrac{7}{8}\times\dfrac{7}{8}\times\dfrac{7}{8}}\)

\(\mathsf{= \dfrac{7\times7\times7\times7}{8\times8\times8\times8}}\)

\(\mathsf{= \dfrac{49\times49}{64\times64}}\)

\(\mathsf{= \dfrac{2,401}{4,096}}\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

\(\huge\boxed{\mathsf{\dfrac{2,401}{4,096}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer: The range is [3, infinity).

Step-by-step explanation: The "[" means that it is apart of the graph. The ")" means it is not apart of the graph.

The graph's range (which is it's highest lowest to highest y-value), the lowest is 3 on the y axis, and then stems on to infinity. The reason why infinity is not apart of the graph is because it has no end and infinity is not a number.

Rays: BD, AC, CA, AB. Lines:  AC

A line is a straight path of points that has no beginning or end

A ray is a portion of a line which has one endpoint and extends forever in one direction

Let's put the definitions:

Note: the arrow is an indication no endpoint

So we have ray BD (it starts from the dot at B and the arrow shows it extends forever  in the direction of D)

We have ray AC (it starts from the dot at A and the arrow shows it extends forever  in the direction of C)

We also have ray CA (it starts from the dot at C and the arrow shows it extends forever  in the direction of A)

Then ray AB (it starts from the dot at A and the arrow shows it extends forever  in the direction of B)

Then  line AC (it's bounded by 2 arrows, so it has no endpoint)

Therefore, the rays are BD, AC, CA and AB, and the line is AC. So the 1st option is the answer

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Answer:

  $28.40

Step-by-step explanation:

You want the cost of gas for a 389.2 mile trip in a vehicle averaging 29.6 miles per gallon using gas costing $2.16 per gallon.

The cost can be figured by converting miles to dollars using the given conversion factors.

 \((389.2\text{ mi})\times\dfrac{1\text{ gal}}{29.6\text{ mi}}\times\dfrac{\$2.16}{1\text{ gal}}=\dfrac{\$2.16\cdot389.2}{29.6}=\boxed{\$28.40}\)

The gasoline for the trip will cost about $28.40.