Make x the subject of h = 4(x + 3y) + 2

PLUG IN 2 IN THE PLACE OF X IN THE FUNCTION THEN SIMPLIFY

f(2)= |5×2|

f(2)=|10|

[tex]f(2) = 10[/tex]

ATTACHED IS THE SOLUTION

Answer:

[tex]\rm f(2)=|5\;^*\;2|=|10|=10[/tex]

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol.  "Absolute value" means how far a value is from zero.   Therefore, the absolute value of a number is its positive numerical value.

Given absolute value function:

[tex]f(x)=|5x|[/tex]

To find f(2), substitute x = 2 into the given function:

[tex]\begin{aligned}\implies f(2)&=|5 \cdot 2|\\&=|10|\\&=10\end{aligned}[/tex]

Answer:

75.40 cubic meters

Explanation:

Given:

• The diameter of a cylinder is 4 m.

• The height is triple the radius

We want to find the volume of the cylinder.

First, determine the radius of the cylinder.

Next, we find the height.

Substitute these values into the formula for the volume of a cylinder:

The value closest to the volume of the cylinder is 75.40 cubic meters.

The graph of the linear function and it's inverse is given at the end of the answer.

The inverse function is: [tex]h^{-1}(x) = -6x + 55[/tex]

To find the inverse function, we exchange x and y in the original function, then isolate y.

In the context of this problem, first we have to find the function h(x), which is a linear function going through points (1,9) and (3,2), hence the slope is given by:

m = (2 - 1)/(3 - 9) = -1/6.

Then:

y = -x/6 + b.

When x = 1, y = 9, hence we can find the intercept b as follows:

9 = -1/6 + b

b = 54/6 + 1/6

b = 55/6.

Then the equation is:

h(x) = -x/6 + 55/6

Then:

y =  -x/6 + 55/6

6y = -x + 55

6x = -y + 55

y = -6x + 55.

Hence the inverse function is:

[tex]h^{-1}(x) = -6x + 55[/tex]

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The point-slope form of a line is given by:

y - k = m ( x - h)

Where m is the slope of the line and (h, k) is a point through which the line passes.

We are given the values of m = 1/4 and the point (0, -1).

Substituting:

Final Exam accounts for 65% of total.

The rest is 100 - 65 = 35%

On the 35%, he has 74% or 74 out of 100.

Let's say the final exam is out of 100 and we want to find how much he can afford to get to take him to "B".

Let's say his score needs to be "x" in order to get B.

The overall weighted average of the course would be counted as:

Breaking it down:

74 out of 100 means WHAT out of 35? (let's call the unknown "y")

y would be:

So, he currently has 25.9 out of 35.

He would need 83 to get overall average to 83%.

He would need:

83 - 25.9 = 57.1 out of 65

That is:

Basically he would need a percentage of 87.85% (MINIMUM) on the final exam to make his overall average to 83% (which is the bare minimum for a B grade).

Using the Fundamental Counting Theorem, the number of possible plates is given as follows:

1,000,000.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is given according to the following rule:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this question, the plate is composed by six independent digits, hence the parameters are given as follows:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = 10[/tex]

(as there are 10 possible digits, from 0 to 9).

Hence the number of possible plates is calculated as follows:

N = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10^6 = 1,000,000.

This problem is incomplete, hence we suppose that it asks for how many plates can be built.

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Answer:

11

Step-by-step explanation:

A = lw

l = A/w

l = 77/7

l = 11

Hope that helps

Given

the age of the winner for best actor was 38 and the age of the winner for best actress was 51.

For all best​ actors, the mean age is 46.8 years and the standard deviation is 5.7 years.

For all best​ actresses, the mean age is 31.9 years and the standard deviation is 10.8 years.​

Find

who had the more extreme age when winning the​ award, the actor or the​ actress

Explanation

the Z- score is given by

Best Actor

X = 38

mean = 46.8 years

standard deviation = 5.7 years.

so ,

Best Actress

X = 51

mean = 31.9 years

standard deviation = 10.8 years.

so ,

the best actress's age is farther from the mean so he has the more extreme age when the winning the award.

Final Answer

Hence , the z- score for best actor is -1.54 and for best actress = 1.77

Actress has more extreme age

Answer: The number is 4,000.

Step-by-step explanation:

        First, we will turn 0.2% into a decimal.

0.2% / 100 = 0.002

        Next, we will set up an equation. Let x be equal to "what number:"

0.2% of what number is 8 ➜ 0.002x = 8

        Lastly, we will solve by dividing both sides by 0.02.

0.002x = 8

x = 4,000

        If we wish to, we can check our answer.

4,000 * 0.002 = 8

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This is a combination of the form:

So:

Answer:

21

The total number associated to barre class is 207 + 196 = 403

Therefore, the probability that a attendee does not attend a barre class is given by 403/2153 = 0.1872

Answer:

x-intercept: (-0.5,0)

y-intercept: (0,1)

Slope: 2

Domain: All real values

Range: All real values

Step-by-step explanation:

x-intercept:

The x-intercept is the value of x when y = 0. In this graphic, we have that when y = 0, x = -0.5. So the x-intercept is given by: (-0.5,0)

y-intercept:

The y-intercept is the value of y when x = 0. In this graphic, we have that when x = 0, y = 1. So the y-intercept is given by: (0,1).

Slope:

To find the slope, we select two points. The slope is given by the division of the change in y by the change in x.

Two points: (-0.5, 0) and (0,1)

Change in y: 1 - 0 = 1

Change in x: 0 - (-0.5) = 0 + 0.5 = 0.5

Slope: 1/0.5 = 2

Domain and range:

In a line, the domain is all real values, the same for the range.

ANSWER :

EXPLANATION :

ANSWER

EXPLANATION

The area of a triangle using two given sides and the included angle is given as:

where a and b are the sides and C is the included angle.

Therefore, we have to find C given that:

Therefore, we have that:

That is the measure of the included angle.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. The value of P(A) = 1/9.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Total number of 2-digit terms =(99 - 10) + 1 = 90

n(s) = 90

Number of 2 digits that have 4 in tens place = 40, 41, 42 ......49

n(a) = 10

P(A) = n(a)/n(s)

Substituting the values in the above equation, we get

P(A) = 10/90

P(A) = 1/9

The value of P(A) = 1/9.

Therefore, the correct answer is option (d) 1/9.

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Let's simplify the following equation

Top left: Yes, each input corresponds to only one output.

Top right: Yes, each input corresponds to only one output.

Bottom left: Yes, each input corresponds to only one output.

Bottom right: No, the input of -1 corresponds to three different outputs.

Answer:

2 2/4 + 1 3/4 + 2/4 = 4 3/4

4 3/4

Answer:

4 and 3/4

Step-by-step explanation:

2 1/2

+1 3/4

+   1/2

_____

4 and 3/4

Using the Fundamental Counting Theorem, the number of length-n sequences that have at least one pair of adjacent LEDs that light up with the same color is:

[tex]N = 4 - 4 \times 3^{n - 1}[/tex]

It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In the context of this problem, there are n LEDs, each with 4 possible colors, hence he total number of sequences is:

[tex]T = 4^n[/tex]

For sequences with no repeating LEDs, we have that:

Hence the number is:

[tex]T_n = 4 \times 3^{n-1}[/tex]

(n - 1) as the first LED is not included on those with 3 possibilities.

Having at least one repeating and no repeating are complementary events, hence the number of sequences is:

[tex]N = 4 - 4 \times 3^{n - 1}[/tex]

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The first step to this problem is finding the amount of butterfat there are in the 385 gallons milk with 5% of butterfat in it. To do that we need to multiply the percentage by the total amount of milk. This is done below:

There are 19.25 gallons of butterfat on the final mixture, the amount of butterfat from each of the milks we are going to mix need to be equal to that. The first milk contains 8% of butterfat, while the second milk contains 1%. So we have:

Where "x" is the number of gallons from the first milk and "y" is the number of gallons from the second milk. The number of gallons of each milk, when added, should be equal to the number of gallons on the final milk, so we have:

The same is valid for the amount of butterfat.

We have now created a system of equations as shown below:

To solve this system we will multiply the first equation by "-0.01":

Now we need to add both equations.

To find the value of "y" we will use the first equation:

We need 220 gallons from the 8% butterfat milk and 165 gallons from the 1% butterfat milk.

In order to simplify an equation we want to add all the terms with the same unkowns.

In the equation

4 - 2y + (-8y) + 7.3

we can see that there are terms with y and numbers alone.

We combine like terms:

Terms with y: -2y,

Answer:

3x + y = -3

Step-by-step explanation:

(-4, 9), (2, -9)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁      -9 - 9          -18          -18

m = ----------- = ----------- = ---------- = ------- = -3

       x₂ - x₁        2 - (-4)      2 + 4        6

y - y₁ = m(x - x₁)

y - 9 = -3(x - (-4)

y - 9 = -3(x + 4)

y - 9 = -3x - 12

   +9           +9

---------------------

y = -3x - 3

Standard Form:

-3x + y = -3

I hope this helps!

The expresion for the correlation coefficient is :

summation of x = 5 + 7 + 10 + 15 + 19

Summation of x = 56

Summation of y = 19 + 17 + 16 + 12 + 7

Summation of y = 71

Summation of prodcut xy

Summation of x^2 = 25 + 49 + 100 + 225 + 361

Summation of x^2 = 760

Summation of y^2 = 361 + 289 + 256 + 144 + 49

Summation of y^2 = 1099

Substitute tha value in the expression of correlation coefficient

Answer: A) Correlation coefficient is 0.985

Given data:

First squaring both sides we get,

Therefore, the value for the solution which satisfies the above equation are

Thus, the ans is (a) , (b) , (d) , (e)

A)

If the dress costs x and the pair of pants cost $25 dollars less, the cost of the pants will be:

B)

We know that the dress costs x and the pants cost x-25. Molly bought 2 dresses and 3 pairs of pants, with the total amount of $675. Thus:

If x is the dress cost, so the dress will cost $150. And the pants:

The pants will cost $125.

In an ordered pair (x,y), x denotes the domain of the relation, and y denotes the range of the relation.

Knowing this, the three ordered pairs that will form a relation with a range of {-3, 4, 7} are

(-1, -3), (0, 4), and (2,7).

SOLUTION

A coin was flipped.

A = probability of it landing on a head

B = probability of it landing on a tail.

We are asked P(A and B), that means probability of landing on a head and on a tail.

A coin can only land on a head or it can land on a tail. It can't land on a head and a tail at the same time.

Therefore the probability of landing on a head and a tail is 0.

Hence, the answer is 0.

Consider the given unbalanced equation which says " 16 divided by 8 " in the Left Hand Side, while it says " 16 divided by 8 then minus one ". This can be represented as,

Consider two things. First, acording to BODMAS rule, division is dprferred over subtraction. Second,

Notice that [tex](x,y,-z)[/tex] is a gradient field:

[tex]\nabla f(x,y,z) = (x,y,-z) \implies \begin{cases} f_x = x \\ f_y = y \\ f_z = -z \end{cases}[/tex]

That is, there exists a scalar function [tex]f(x,y,z)[/tex] whose gradient is the given vector field. Solve for [tex]f[/tex].

[tex]\displaystyle \int f_x \, dx = \int x \, dx \implies f(x,y,z) = \frac12 x^2 + g(y,z)[/tex]

[tex]f_y = g_y = y \implies \displaystyle \int g_y \, dy = \int y \, dy \implies g(y,z) = \frac12 y^2 + h(z)[/tex]

[tex]f_z = h_z = -z \implies \displaystyle \int h_z \, dz = - \int z \, dz \implies h(z) = -\frac12 z^2 + C[/tex]

[tex]\implies f(x,y,z) = \dfrac{x^2+y^2-z^2}2 + C[/tex]

By the gradient theorem, it follows that

[tex]\displaystyle \int_{(1,0,-3)}^{(6,4,8)} x \, dx + y \, dy - z \, dz = f(6,4,8) - f(1,0,-3) = \boxed{-2}[/tex]

The various algebraic properties used for each of the given expressions are;

1) Symmetric property of equality.

2) Distributive property of equality.

3) Addition property of equality.

4) Division property of equality.

5) Addition property of equality.

6) Transitive property of equality.

7) Associative property of equality.

8) Multiplication property of equality

9) Commutative property of equality.

There are different properties of equality or algebra such as;

1)  If AB=CD, then CD=AB; Property used here is Symmetric property of equality because it suits the definition.

2) 5(x-4) = 5x-20; Property used here is Distributive property of equality because it suits the definition.

3) 3x - 17 = 8, then 3x = 25; Property used here is Addition property of equality because it suits the definition.

4) 22m=440, then m=20; Property used here is Division property of equality because it suits the definition.

5) :(2a+3a)-4a=7a+55, then (5a)-4a=7a+55; Property used here is Addition property of equality because it suits the definition.

6) If GH=2x+17, and 2x+17=JK, then GH=JK; Property used here is Transitive property of equality because it suits the definition.

7) 2b+(b-7)=17, then (2b+b)-7=17; Property used here is Associative property of equality because it suits the definition.

8) (x+7)/3=13, then x+7=39.; Property used here is Multiplication property of equality because it suits the definition.

9) m 10:4+x=13, then x+4=13; Property used here is Commutative property of equality because it suits the definition.

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