10x f ( 7 ) + 9 x g(-1) =

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I hope this helps.

Answer:-

   ∴x−3y−4z=0

Explanation:

First we rearrange the equation of the surface into the form f(x,y,z)=0

   x2+2z2=y2

   ∴x2−y2+2z2=0

And so we have our function:

   f(x,y,z)=x2−y2+2z2

In order to find the normal at any particular point in vector space we use the Del, or gradient operator:

   ∇f(x,y,z)=∂f∂xˆi+∂f∂yˆj+∂f∂zˆk

remember when partially differentiating that we differentiate wrt the variable in question whilst treating the other variables as constant. And so:

   ∇f=(∂∂x(x2−y2+2z2))ˆi+

                    (∂∂y(x2−y2+2z2))ˆj+

                    (∂∂z(x2−y2+2z2))ˆk

      =2xˆi−2yˆj+4zˆk

So for the particular point (1,3,−2) the normal vector to the surface is given by:

   ∇f(1,3,−2)=2ˆi−6ˆj−8ˆk

So the tangent plane to the surface x2+2z2=y2 has this normal vector and it also passes though the point (1,3,−2). It will therefore have a vector equation of the form:

   →r⋅→n=→a⋅→n

Where →r=⎛⎜⎝xyz⎞⎟⎠; →n=⎛⎜⎝2−6−8⎞⎟⎠, is the normal vector and a is any point in the plane

Hence, the tangent plane equation is:

   ⎛⎜⎝xyz⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠=⎛⎜⎝13−2⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠

   ∴(x)(2)+(y)(−6)+(z)(−2)=(1)(2)+(3)(−6)+(−2)(−8)

   ∴2x−6y−8z=2−18+16

   ∴2x−6y−8z=0

   ∴x−3y−4z=0

Answer:Correct option is

A

10

Given y=(x−11)  

2

⇒y=x  

2

−22x+121

After substitute y=25. we get,

x  

2

−22x+121−25=0

⇒x  

2

−22x+96=0

⇒(x−16)(x−6)=0

⇒x=16,x=6

∴ two points are  A,B are (16,25),(6,25).

Distance between A and B is  

(16−6)  

2

−(25−25)  

2

​

=10

Hence, option A is correct.

Answer:

The theoretical probability of spinning a sum of 9 is 4/36 or 1/9.

Step-by-step explanation:

Answer: 0%

Step-by-step explanation:

Answer:

60 m squared

Step-by-step explanation:

40+7.5+12.5=60

The standard normal distribution that represents the variable in the question indicates that we get;

a. The probability is about 0.42858

b. The probability that the average mpg of 3 randomly selected passenger cars is more than 32 mpg is 0.35197

c. The probability that all the three cars get more than 32 mpg is about0.0788

A standard normal distribution, also known as the Gaussian distribution, and the z-distribution, has a mean of 0, and a standard deviation of one.

a. The standard score (z-score) of 32 mpg can be obtained as follows;

z = (32 - 31.2)/4.5 ≈ 0.178

The probability that a standard normal variable has a z-score, larger than 0.178, obtained from the z-score table is therefore;

P(Z > 0.178) ≈ 1 - 0.57142 = 0.42858

b. The of the sample is μ = 31.2

The standard deviation of the sample is, σ = 4.5/√(3)

z = (x - μ)/(σ/√n)

Therefore;

z = (32 - 31.2)/(4.5/√(3)) ≈ 0.308

The probability that a standard normal variable has a z-score larger than 0.308, from the z-score table, therefore is; p(z > 0.308) = 1 - 0.64803 = 0.35197

c. The mpg ratings are independent, therefore, we get;

P(the three cars get more than 32 mpg) = P(car 1 gets more than 32 mpg) × P(car 2 gets more than 32 mpg) × P(car 3 gets more than 32 mpg)

The probability that a car gets more than 32 mpg is about 0.42858

Therefore;

P(the three cars get more than 32 mpg) = 0.42858 × 0.42858 × 0.4288 ≈ 0.0788

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The Boolean algebra properties used in the equation (a + a') b = (1)b = b are Complement (OR) and Identity (AND).

Boolean algebra is a branch of mathematics that studies mathematical structures that follow the rules of logic operations (conjunction, disjunction, and negation), which are frequently associated with the concepts of binary values and logical operators.

In Boolean algebra, there are three types of operations that can be performed, i.e., AND, OR, and NOT. As the logical values (1 or 0) are used to define binary values, they can be calculated in Boolean algebra.

Here are the two Boolean algebra properties used in the equation (a + a') b = (1)b = b:

1. Complement (OR) The Boolean algebra operation 'complement' is utilized when a situation involves both addition and multiplication, as the Boolean algebra addition of two values is represented by the sum of two variables, and the multiplication operation is represented by the AND gate.

The complement of a variable or function (represented by a bar over it) is defined as the negation of the variable or function. It means if A is the original function, then A' or NOT A is the complement of A.

2. Identity (AND) When an element in a set is added or multiplied with an identity element, the identity property is utilized. In the case of Boolean algebra, the identity element for an AND function is '1,' and the identity element for an OR function is '0.'

Therefore, the properties used in the equation (a + a') b = (1)b = b are Complement (OR) and Identity (AND).

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umm...... No because 1 haven't give any semester

Answer:

7 weeks

Step-by-step explanation:

Answer: The answer is 3.10

Step-by-step explanation: Fisrt of all you add 25+7 which gives you 32. Add 32 and 55, gives you 87. You need to figure out w and b is 270. So 270 divided by 87 is 3.10. So you need 3.10 weeks.

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Answer:

For the first one it is 135 (The second option)

For the second one it is 128 ( The first option)

Step-by-step explanation:

this is correct on edg!

The polynomial which shows algebra tile configuration is \(\rm -x^2 + 3x - 4\).

We have to determine

Which polynomial represents the algebra tile configuration shown?

According to the question

Polynomials are defined as the sums of terms that are represented in the form of k-xⁿ, where k is any number and n is a positive integer.

The polynomial represented by algebra tiles is \(\rm -x^2 + 3x - 4\)

In the given tiles,

2 tiles for = \(\rm -x^2\)

3 tiles for = x

4 tiles for = -4

Now, putting the like terms together, the equation becomes:

\(\rm (x^2+-2x^2) + 3(x+ x+ x ) -(1+1+1+ 1)\)

The like terms can be added such that:

\(\rm -x^2 + 3x - 4\)

Hence, the polynomial which shows algebra tile configuration is \(\rm -x^2 + 3x - 4\).

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The weighted mean takes into account the weight of each investment and can provide a more accurate measure of the overall rate of return on the portfolio than the mean or median.

The weighted mean, mean, and median overall rate of return on this investment portfolio can be calculated using the following formulas:

Weighted Mean: Weighted mean = (R1 x W1) + (R2 x W2) + (R3 x W3) + ...

Mean: Mean = (R1 + R2 + R3 + ...) / N

Median: Median = (N + 1) / 2

where R1, R2, etc. are the returns on individual investments, W1, W2, etc. are the weights assigned to each investment, and N is the total number of investments in the portfolio.

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According to the Bureau of Labor Statistics, there were 645 fatalities in the construction industry in 2009. This is a significant number and highlights the dangers of working in this field.

The construction industry is known for being one of the most dangerous professions, with workers facing a range of risks and hazards on a daily basis.

The statistics reveal that the leading causes of fatalities in the construction industry were falls, followed by being struck by an object, electrocution, and being caught in or between objects. These accidents can occur in a variety of settings, from working on scaffolding or high-rise buildings to operating heavy machinery and equipment.

While these statistics are concerning, there are measures that can be taken to reduce the number of fatalities in the construction industry. These include providing adequate training and safety equipment to workers, implementing strict safety protocols and procedures, and enforcing regulations and standards to ensure compliance.

Overall, the Bureau of Labor Statistics data highlights the importance of prioritizing worker safety in the construction industry. By taking steps to mitigate the risks and hazards associated with this profession, we can work towards reducing the number of fatalities and improving the working conditions for construction workers.

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Answer:

1) 25

2) 32,768

3) 729

4) 16 or 2^4

5) 117,649 or 7^6

6) 5.29 or 2.3^2

Not sure what 7-12 mean

13) 1 mile 64-63=1

14) Mali bought a new car. She drove 63 miles the first month and 100 the second month. How much further did she drive the second month? Explain each step. 37 miles 100-63=37

15) An exponet is a number raised to a power, which means that number times itself that many times. It is used because it's alot easier to go 7^6 than 7x7x7x7x7x7.

16) 8^5= 32,768  6^6= 46,656  5^7= 78,125  5^5= 3,125  4^10= 1,048,576

Step-by-step explanation:

Answer: True

Step-by-step explanation: Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length. The concept of a median extends to tetrahedra.

Answer:

True

Step-by-step explanation:

Answer:

A. The sum of two negative integers is always negative

Step-by-step explanation:

Because if you have -3 and you add -4 it is the same as when you add positive 3 and positive 4 except with a negitive sign at the beginning

The expected value of the square of the distance of the knight after 2016 moves is approximately 462.05.

The expected value of the square of the distance of the knight from the origin after n moves can be calculated using the following formula:

E(d²) = (1/8) * (2 * (E(d²) - 1) + 5)

where d is the distance from the origin, and E(d²) is the expected value of d².

Using this formula, the expected value of the square of the distance after 2016 moves can be calculated iteratively.

Starting with an initial estimate of E(d²), we can use the formula to calculate a better estimate in each iteration. This process can be repeated until the estimate converges to a value within a desired accuracy.

Using this approach, the expected value of the square of the distance after 2016 moves can be approximated to be 462.05.

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Step-by-step explanation:

similar means they have the same angles, and there is one common scaling factor for all pairs of corresponding sides. we need to find it for one pair, and we then have it also for the x pair and can calculate x.

comparing the sides in relation to each other we find that F corresponds to L, H to J and G to K.

so, the scaling factor of LK/FG is then also the scaling factor of JK/HG.

LK × f = FG

45 × f = 27

f = 27/45 = 3/5

JK × 3/5 = 3x + 6

65 × 3/5 = 3x + 6

13 × 3 = 3x + 6

39 = 3x + 6

33 = 3x

x = 11

The general solution to the system of differential equations is:

A = 64t - 2t^2 + C1

To solve the system of differential equations dz/dt = A and dA/dt = 64 - 4t, we can proceed as follows:

First, let's solve the second equation for A. We have dA/dt = 64 - 4t, which is a separable equation. We can rewrite it as dA = (64 - 4t) dt and integrate both sides:

∫dA = ∫(64 - 4t) dt

A = 64t - 2t^2 + C1

where C1 is the constant of integration.

Now, let's substitute this expression for A into the first equation dz/dt = A:

dz/dt = 64t - 2t^2 + C1

This is a separable equation as well. Rearranging the terms, we have dz = (64t - 2t^2 + C1) dt. Integrating both sides:

∫dz = ∫(64t - 2t^2 + C1) dt

z = 32t^2 - (2/3)t^3 + C1t + C2

where C2 is another constant of integration.

Therefore, the general solution to the system of differential equations is:

z = 32t^2 - (2/3)t^3 + C1t + C2

A = 64t - 2t^2 + C1

The constants C1 and C2 can be determined by applying the initial conditions given for t = t0. These initial conditions will provide specific values for z and A, allowing you to solve for the constants and obtain the particular solution for the system.

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The graph the represents the function f(x) = 3.5ˣ is attached below.

Function:

Basically, the function refers the a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given,

Here we have to find the graph for the function f(x) = 3.5ˣ from the given options.

In order to plot the graph for the function,

We need a table.

The table can derived by applying the sample values.

So, here we have to take the value of x is -2, -2, 0, 1, 2,

Then we get the following table.

And then by using the table, we have to plot the graph like the following.

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Answer:

64,81,100

Step-by-step explanation:

Answer: 64,81 and 100

Step-by-step explanation: 8^2=64, 9^2=81 and 10^2=100

The required difference between the amounts of interest Jacob and Christian paid for their loans is $552.

The amount of simple interest on a loan is given by the formula:

\($ I = P \cdot r \cdot t $\)

where I is the amount of interest, P is the principal (the amount borrowed), r is the annual interest rate expressed as a decimal, and t is the time the loan is outstanding in years.

For Jacob's loan, we have:

\($ I_J = 8000 \cdot 0.042 \cdot 3 = 1008 $\)

So Jacob paid $1008 in interest over 3 years.

For Christian's loan, we have:

\($ I_C = 8000 \cdot 0.039 \cdot 5 = 1560 $\)

So Christian paid $1560 in interest over 5 years.

The difference between the amounts of interest Jacob and Christian paid for their loans is:

\($ I_C - I_J = 1560 - 1008 = 552 $\)

Therefore, the difference between the amounts of interest Jacob and Christian paid for their loans is $552.

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Answer:

x = -2.75

Step-by-step explanation:

:D

14 - 3 = 11

11 / -4 = -2.75

Answer:

#1. Fourteen divided by a number.

#2. Four times a number.

#3. A number divided by 14.

#4. A number minus 14.

Step-by-step explanation:

I hope this helps., I just need more points. So sorry.

The Solution:

The correct answer is [option 4]

Given:

Required to select the correct statements.

Thus, the correct answer is [option 4]

Answer:

If you mean 0 + (-1) then it's -1

Answer:

In the step by step

Step-by-step explanation:

Graph 1 : k(x)=(1/4)^x

Graph 2: f(x)=-(1/4)^x

Graph 3: g(x)=4^x

Graph 4: h(x)=-4^x

The answer 6x - 2y = 5

Step-by-step explanation:

The general formula of linear equations is y = mx + c

where m is the slope

so when we put this in the general form, it will be

-2y = -6x + 5

y = 3x - 5/2

and so the slope is 3