Find an equation of the plane that passes through the point P0(- 3,3,1) with a normal vector n = (1,4, -3). Which of the following equations is an equation of the plane that passes through the point P0( - 3,3,1) with a normal vector n (1,4, -3)?

a. An equation for the plane is -3x+3y + Z = 6.
b. An equation for the plane is x+ 3y +z = 19.
c. An equation for the plane is x + y+ z = 26.
d. An equation for the plane is x +4y - 3z= 6.

9514 1404 393

Answer:

  22. E

  23. C

Step-by-step explanation:

These questions are asking you to make use of a couple of trig identities for converting products to sums.

  sin(x)cos(y) = 1/2(sin(x+y) +sin(x -y))

  cos(x)cos(y) = 1/2(cos(x+y) +cos(x -y))

  sin(-x) = -sin(x)

  cos(-x) = cos(x)

__

22. sin(2β/3)cos(4β/3) = (1/2)(sin((2+4)β/3) +sin((2-4)β/3))

  = 1/2sin(2β) +1/2sin(-2β/3) = 1/2sin(2β) -1/2sin(2β/3)

__

23. cos(3θ)cos(5θ) = (1/2)(cos(3θ+5θ) +cos(3θ -5θ)) = 1/2cos(8θ)+1/2cos(2θ)

Answer:

30%.

Step-by-step explanation:

The probability of getting an Ethiopian with blood type A is \(\frac{20}{100} \cdot 100%%\), which equals to 20%, while the probability of getting an Ethiopian with blood type AB is \(\frac{100-40-30-20}{100} \cdot 100%\), which equals to \(\frac{10}{100} \cdot 100%\) and hence 10%. Therefore, just add the two probabilities together to get 20% +10% = 30%.

Hope this helped!

The number of Walmart Stores are there per 100,000 people is 1.43 stores

What does per 100,000 people mean?

It means the number of stores that could attend to 100,000 customers out of the total store number of 4,740

The first task in this case, is to first of all determine the number of store per person, which is the total number of stores divided by the total population

store per person=4,740/ 332,400,000

number of stores per person= 0.000014260

number of stores per 100,000 people=number of stores per person*100,000

number of stores per 100,000 people=0.000014260*100,000

number of stores per 100,000 people=1.43

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The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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The inequalities which matches the graph are: x ≥ ₋1.5 and ₋1.5 ≤ x

Given, a number line is moving from ₋3 to ₊5 .

Next a mark is made at ₋1.5 and everything to its left is shaded which means not visible.

When we mark the point and shade the left part of it then we can start applying the inequality expressions.

And from that we can match the applicable inequalities while observing the graph.

Therefore the only inequalities the graph represents is  x ≥ ₋1.5 and ₋1.5 ≤ x

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George Kolinsky Washington

Answer:

George Washington

Step-by-step explanation:

On April 30, 1789, George Washington, standing on the balcony of Federal Hall on Wall Street in New York, took his oath of office as the first President of the United States.

As I understand, you want to write a diameter, that currently is in scientific notation, in standard notation.

The standard notation is 0.0000084

First, scientific notation is a way to write really long numbers (particularly those that have a lot of zeros) in a shorter way.

The general form is:

Ax10^n

If n is positive, we add n zeros at the right of our number.

If n is negative, we add n zeros to the left.

Here we have:

8.4x10^-6

So n is negative, meaning that we need to add the zeros at the left (also remember to correctly change the position of the decimal point) we will get:

8.4x10^-6 = 0.0000084

This is the measure in standard notation.

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Approximately 456.3 feet of fence to surround the entire circular yard.

Now, For the amount of fencing needed to surround a circular yard, we have to calculate the circumference of the circle, which is the distance around the circle.

Since, The circumference of a circle is,

⇒ C = πd,

where, C is circumference, d is diameter,

Here, the diameter of the circular yard is 145 feet,

So the radius is half of that,

r = 145/2 = 72.5 feet.

So, Using the formula, we can calculate the circumference as:

C = πd

C = 3.14 x 145

C = 456.3 feet

Therefore, Approximately 456.3 feet of fence to surround the entire circular yard.

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Answer: 32

Step-by-step explanation:

     We will use the Order of Operations. First, we will do parentheses (), then brackets [], then lastly the braces {}, then lastly add 12.

Given:

     {[2+(11+9)]-2)+12

Add 11 to 9:

     {[2+20]-2)+12

Add 2 to 20:

     {22-2)+12

Subtract 2 from 20:

     20 + 12

Add 20 and 12:

     32

Answer:

adjacent, linear pair, supplementary

Step-by-step explanation:

adacent because they are angles side by side

linear because the angles create a straight line

supplementary because the angles equal 180 degrees

The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

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Answer:

(3.5, 2)

Step-by-step explanation:

From the attachment, we have:

\(H = (1,1)\)

\(J= (2,3)\)

\(K=(6,3)\)

\(L = (5,1)\)

Required

Determine the point of intersection

To do this, we simply calculate the midpoints of the diagonals; which are:

HK and JL

Midpoint is calculated as:

\(M = \frac{1}{2}(x_1 + x_2,y_1+y_2)\)

For HK:

\(M = \frac{1}{2}(1+6,1+3)\)

\(M = \frac{1}{2}(7,4)\)

\(M = (3.5,2)\)

For JL:

\(M = \frac{1}{2}(2+5,3+1)\)

\(M = \frac{1}{2}(7,4)\)

\(M = (3.5,2)\)

For both diagonals, the coordinate of the midpoint is (3.5, 2).

Hence, the point of intersection is: (3.5, 2)

Answer:

  4 minutes

Step-by-step explanation:

You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)

The volume of a cylinder can be found using the formula ...

  V = (π/4)d²h . . . . . . . diameter d, height h

Then the volume of the oil tank is ...

  V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³

The time it takes to empty the tank is found by dividing the volume by the rate:

  (7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min

It will take about 4 minutes to empty the tank.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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The transformed equation of \(y = x^{3}\) is \(y = -\frac{1}{7} (x + 8)^{3}\).

Given equation ;  \(y = x^{3}\)

Applying the given transformations, we have:

To have a vertical compression by a factor of  \(\frac{1}{7}\), we need to multiply the function by  \(\frac{1}{7}\). So, we have:

\(y =\)  \(\frac{1}{7}\) \(x^{3}\)

To have a horizontal shift by 8 units to the left, we need to add 8 to x. So, we have:

\(y = \frac{1}{7} (x + 8)^{3}\).

Lastly, to have a reflection over the x-axis, we need to multiply the function by −1. So, we have:

\(y = -\frac{1}{7} (x + 8)^{3}\).

Therefore, the transformed equation is  \(y = -\frac{1}{7} (x + 8)^{3}\).

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Step 1 : Given the function below

Step 2: Write the function for h(3), this is done by substituting 3 for x in the function h(x) above

Step 3: Write the corresponding value for the function g(9) and an inverse function of R⁻¹ (3) on the table.

Step 4: Substitute the g(9) and R⁻¹ (3) values in the h(3) equation and simplify

Hence, the value of h(3) is -11

The second option is the correct answer.

Answer:

D is the correct answer.

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

We have the following:

The volume of the prism is as follows

h = 3, l = 8 and w = 5

replacing:

Therefore the volume is 120 cubic meters

woah thats alot is that a question or you actually doing it

The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

The equation is given as:

2x + 2y = - 10

The point it passes through is given as (6, 2) .

Recall that

2x + 2y = - 10

Divide through by 2

x + y = -5

Make y the subject

y = -x - 5

The slope of the above equation is

m = -1

The slopes of perpendicular lines are opposite reciprocals.

So, we have

m2 = -1/-1

Evaluate

m2 = 1

Recall that the point it passes through is given as (6, 2) .

So, the equation is represented as:

y = m2(x - x1) + y1

This gives

y = 1(x -  6) + 2

Open the bracket

y = x - 6 + 2

Evaluate

y = x - 4

Hence, the equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

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Answer: 20,000

Step-by-step explanation:

We can estimate the product of 5 and 4,257 by multiplying 5 by 4,000

5 * 4,000 = 20,000

The product of 5 and 4,257 is about 20,000

The real answer (not an estimate)

21,285

That is around 20,000 so we are correct

Option B is the correct answer

Answer:

d<-3

Step-by-step explanation:

-7d + 8 > 29

subtract 8 from each side

-7d>21

multiply both side by -1 and reverse the inequality sign

7d<-21

divide both sides by 7

d<-3

hope this helps :)

Answer:

\(f(x)=x^2(x^2+36)\)

Step-by-step explanation:

\(x^2x^2+36x^2\) Factor \(x^2\) out of \(x^4\)

\(x^2x^2+x^2(36)\) Factor \(x^2\) out of \(36x^2\)

Step-by-step explanation:

0 hours -> $500 total cost

1 hour -> $575 total cost (500 + 1×75)

2 hours -> $650 total cost (500 + 2×75)

3 hours -> $725 total cost (500 + 3×75)

P(t) = 75t + 500

Answer:

The answer is B

Step-by-step explanation:

Because the exponent shows how many times you multiply that number

Example: 8^2 would be 8x8 because it is to the second power

Hopefully this helps

Answer:

Step-by-step explanation:

8•8•8•8•8 is the correct answer

Answer:

100 pi cm^2

or approximately 314 cm^2

Step-by-step explanation:

The surface area of a sphere is given by

SA = 4 pi r^2

The radius is 5

SA = 4 *pi * 5^2

SA = 4*pi(25

SA = 100 pi cm^2

If pi is 3.14

SA = 100 *3.14 = 314 cm^2

\(\large\fbox{\underline{Surfαcє αrєα σf sphєrє ís 314 cm ².}}\)

☞ Rαdíus σf sphєrє = 5 cm

☞ Surfαcє αrєα σf sphєrє

☞ Surfαcє αrєα σf sphєrє = 4 π r ²

usíng thє fσrmulα

surfαcє αrєα σf sphєrє = 4 π r ²

suвstítutє thє vαluєs

surfαcє αrєα σf sphєrє = 4 × 3.14 × ( 5×5 ) cm ²

mutíplчíng thє vαluєs

surfαcє αrєα σf sphєrє = 100 cm² × 3.14

Hєncє , Surfαcє αrєα σf sphєrє ís 314cm ².

Answer:

a) The null and alternative hypothesis are:

\(H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0\)

b) Yes.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors.

As the claim is that the proportions differs, the difference to reject the null hypothesis can be positive or negative. Then, this is a two-tailed test.

The null and alternative hypothesis are:

\(H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0\)

The conditions to met for this test are:

- The sampling method for each population is simple random sampling.

- The samples are independent.

- Each sample includes at least 10 successes and 10 failures.

\(\text{Failures (NY):} \, F=200*0.45=90\\\\\text{Failures (T):} \, F=120*0.3=36\\\\\text{Note: we use failures as they have the lower proportions.}\)

- Each population is at least 20 times as big as its sample.

This conditions are met, so all criteria for the hypothesis test is satisfied.