find a polynomial p3 such that fp0; p1; p2; p3g (see ex-ercise 11) is an orthogonal basis for the subspace p3 of p4. scale the polynomial p3 so that its vector of values is . 1; 2 ; 0; 2 ; 1/.

Answer:

gj got the answer lol

Step-by-step explanation:

The rule for counter-clockwise (ccw) rotation is (x,y) change to (-y,x). Lmk if you're still stumped :D

Answer:

R384,480

Step-by-step explanation:

Please note that annual means one year.

With this in mind, we multiply the amount by 12 because twelve months make up a year.

That is 32,040 x 12 = R384,480

Therefore, Mrs.Chauke’s annual income if she earns R32 040 per month is:

By direct multiplication, we will see that Mrs. Chauke's annual income is R384,480

We know that she earns R32,040 per month.

To get the annual income, we need to multiply what she earns each month by the number of months in one year.

We know that in one year there are 12 months, so the annual income is just:

A = R32,040*12 = R384,480

The annual income is  R384,480

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Using binomial probability, the probability of having exactly 4 dice on 4, 5 or 6 is 5/32.

Using binomial probability, we can calculate the probability that out of the 5 dice thrown, the probability of having exactly 4 dice on 4, 5 or 6 can be calculated as;

\(P(X=k) = C(n, k) * p^k * (1-p)^(^n^-^k^)\)

In the given data;

n = 5

k = 4

p = 3/6 = 1/2

Using the binomial probability formula, we can calculate:

P(X=4) = C(5, 4) * (1/2)⁴ * (1 - 1/2)⁵⁻⁴

P(X=4) = 5 * (1/2)⁴ * (1/2)¹

P(X=4) = 5 * (1/16) * (1/2)

P(X=4) = 5/32

Therefore, the probability that exactly 4 dice land on a 4, 5, or 6 when rolling five fair dice is 5/32.

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Answer:

(1) The formula to calculate simple interest (SI), with principal = 600$, annual rate = 4% = 0.04, and time = 9 months is:

SI = principal x rate x time

   = 600 x (0.04/12) x 9

   = 18$

(2) The formula to calculate the time that man walked 3.75 km, with rate of 1.25:

Time = Distance/Rate

         = 3.75/1.25

         = 3

Hope this helps!

The equation to solve the height of the trapezoid is 45h = 1,575

Given data ,

Let the area of the trapezoid be A

Now , the value of A = 1,575 cm²

And , the Top(base2) = 63cm and  Bottom(base1) = 27 cm

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

On simplifying , we get

1,575 = (63 + 27) / 2 x h

1575 = 45h

Hence , the equation is 1575 = 45h

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The complete question is attached below :

The trapezoid has an area of 1,575 cm2, Which equation could you solve to find the height of the trapezoid?

A 850.5h = 1,575

B 1,701h = 1,575

C 90h = 1,575

D 45h = 1,575

Top(base2) = 63 cm

Bottom(base1) = 27 cm

Answer:

-9

Step-by-step explanation:

Let x be the "other" number

(4-5+2+x)/4 = -2

(1 + x) = -8

x = -9

The average of 4, -5, 2, and -9 is -2

Answer:

\(12\ gallons\)

Step-by-step explanation:

Step 1:  Determine the unit rate

\(Miles / Gallons\)

\(162\ miles / 9\ gallons\)

\(18\ miles/gallon\)

Step 2:  Determine the amount of gasoline used for 216 miles

\(216\ miles * (gallon / 18\ miles)\)

\(12\ gallons\)

Answer:  \(12\ gallons\)

Answer:

12

Step-by-step explanation:

1. Figure out how many miles the car can go with one gallon of gasolline

162 ÷ 9 = 18

1 gallon = 18 miles

2. Figure out how many times 18 can go into 216

216 ÷ 18 = 12

12 gallons = 216 miles

*We do this because we know that every time the car drives 18 miles its uses another gallon of gas.

The car will use 12 gallons of gasoline to travel 216 miles.

The height of the tower is equal to (p x P x (T + t)) / (t x (P - T)).

To determine the height of the tower, we need to use the principles of similar triangles and proportionality. Let's assume that the pole and the tower are standing upright, and their shadows are also straight and perpendicular to the ground.

We can start by measuring the length of the shadow cast by the pole and the length of the shadow cast by the tower at the same time of day when the sun is at the same angle.

Let's call these lengths "P" for the pole's shadow and "T" for the tower's shadow.

Next, we need to measure the height of the pole. To do this, we can measure its shadow's length and use proportionality to find its height. Let's call the height of the pole "h" and its shadow's length "p."

Using similar triangles, we know that:

h/p = (h+x)/P

where x is the distance between the pole and the tower. We can rearrange this equation to solve for h:

h = (p x P) / (P - T)

Now that we have found h, we can use a similar equation to find the height of the tower. Let's call its height "H" and its shadow's length "t."

H = (h x (T + t)) / t

Substituting our previous equation for h, we get:

H = (p x P x (T + t)) / (t x (P - T))

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Answer:

the last option

you get cos^2(135)-sin^2(135) =cos(270)

The exact value of cos 270° is 0 as this correlates to the x-coordinate on the unit circle for a 270° angle.

The question is asking for the exact value of cos 270°. In Trigonometry, we have the unit circle which defines cosine and sine of angles based on the coordinates of points on the circle. On the unit circle, cos 270° is equivalent to the x-coordinate of the point where the angle intercepts the unit circle.

The angle of 270° corresponds to the point on the unit circle where the x-coordinate is 0 and the y-coordinate is -1. Therefore, the exact value of cos 270° is 0.

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Answer:

31/40

Step-by-step explanation:

3/8+2/5

Find the common denominator.

15/40+16/40

Add.

=31/40

Answer: 31/40

Step-by-step explanation:

3/8+2/5

make denominators equal, multiply by 8and 5

15/40+16/40=31/40

The spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

To determine how much further the spring will stretch when a 0.60 kg block is added to the 1.2 kg block, we need to consider Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Let's assume that the spring is initially stretched by a certain amount x when only the 1.2 kg block is attached. The force exerted by the spring is given by F = kx, where k is the spring constant.

When the 0.60 kg block is added, the total mass becomes 1.2 kg + 0.60 kg = 1.8 kg. The force exerted by the spring remains the same, but the total mass affects the acceleration of the system according to Newton's second law, F = ma.

Using F = ma, we can find the acceleration of the system: F = (1.8 kg)(9.8 m/s^2) = 17.64 N.

Since F = kx, we can rearrange the equation to find x: x = F/k.

Now, if we assume the spring constant k remains constant, the displacement x will increase by a factor of 1.8 kg/1.2 kg = 1.5.

Therefore, the spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

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Answer: k= -10x+12

Step-by-step explanation:

The solution to the system of equation is as follows:

System of equation can be solved with different methods such as elimination method, substitution method and graphical method.

The system of equation can be solved with elimination as follows:

Hence,

-3y + 5x = 26

-2y - 5x  = -16

add the equation to eliminate x

Hence,

-5y = 10

divide both sides of the equation by -5

y = 10 / -5

y = -2

Hence,

- 3(-2) + 5x = 26

6 + 5x  = 26

5x = 26 - 6

5x = 20

x  = 20 / 5

x = 4

Therefore,

x = 4

y = -2

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4.92*10^5 times the annual flow of the Mississippi River fit in the Atlantic Ocean

Given that,

Volume of the Atlantic Ocean = 3.1*10^17cubicmetres

Annual flow of the Mississippi River = 6.3*10^11cubicmeters

Now, we have to find how many times the annual flow of the Mississippi River fit in the Atlantic Ocean

So,

= Volume of the Atlantic Ocean / Annual flow of the Mississippi River

= 3.1*10^17 / 6.3*10^11

= 0.4921*10^6 (Approximately)

=4.92*10^5

Therefore,

It takes 4.92*10^5 times for the Mississippi River to fit into the Atlantic Ocean.

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By using a sampling technique  we ensure that we choose a sample of students that is representative of all 8:00 am classes.

There are  varieties of sampling strategies: chance sampling includes random selection, permitting you to make sturdy statistical inferences approximately the complete organization. Non-opportunity sampling entails non-random selection primarily based on convenience or different standards, permitting you to without problems gather records.

Random sampling is part of the sampling technique wherein every sample has an same possibility of being chosen. A sample chosen randomly is meant to be an unbiased representation of the overall population.

explanation;

we conclude the

Since the students' lecture hallsare on different building the samples are

Dividing the students into groups, the students will be grouped by the buildings of their lecture halls.

The number of students in each building is:

There are 100 students in each building

Then select at random an equal proportion of student from each building let 20 students in each building.

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Answer:

a=6

Step-by-step explanation:

-6(2+a)=-48

-12-6a=-48

-6a=-36

a=6

6 × 3,725 is equivalent to the value of 22,350.

We have,

To find the value of 6 × 3,725, we multiply the number 6 by the number 3,725.

This can be done by adding 3,725 to itself 6 times or by adding 6 to itself 3,725 times.

However, it is more efficient to use the multiplication operation, which is a shorthand way of adding a number to itself multiple times.

Using the multiplication operation, we can write 6 × 3,725 as:

6 × 3,725 = 6 × (3,000 + 700 + 20 + 5)

= (6 × 3,000) + (6 × 700) + (6 × 20) + (6 × 5)

= 18,000 + 4,200 + 120 + 30

= 22,350

Therefore,

6 × 3,725 is equivalent to the value of 22,350.

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Answer:

43-7=x

Step-by-step explanation:

Answer:

the equation is : 2x+7+x=43

ant the 2 numbers are : 12 and 31

The volume of the box is given by:

V = lwh

where l = 10 cm, w = 16 cm, and h = 5 cm.

The differential of V with respect to l is:

dV = (wh)dl + (lh)dw + (lw)dh

The differential of V with respect to w is:

dV = (lh)dw + (lw)dh + (wh)dl

The differential of V with respect to h is:

dV = (lw)dh + (wh)dl + (lh)dw

Using the maximum error of 1 mm for each measurement, we have:

dl = 0.1 cm

dw = 0.1 cm

dh = 0.1 cm

Substituting these values into the differentials above, we get:

dV ≈ (wh)(0.1) + (lh)(0.1) + (lw)(0.1)

dV ≈ (16 cm x 5 cm)(0.1) + (10 cm x 5 cm)(0.1) + (10 cm x 16 cm)(0.1)

dV ≈ 8 cm^2 + 5 cm^2 + 16 cm^2

dV ≈ 29 cm^2

Therefore, the maximum error in the calculated volume of the box is approximately 29 cm^3.

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Answer:

y=-x+5

Step-by-step explanation:

Hope this helps!

And can I have brainliest!

Answer:

the answer is -4, yeah it's -4

Answer:

-4 I think I'm new at this but I did try me best the reason this answer is so long is because it wont let me help u without like 20 characters

Answer:

The answer is Y=3x

Step-by-step explanation:

Answer:

A and B are  the correct answers for the check all that apply

Step-by-step explanation:

Sorry if i'm to late

The value of the given expression will be 3√5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression c² = 45 will be solved as below:-

c² = 45

Take the square root of the number 45.

c = √45

c = √ 9 x √5

c = 3√5

Therefore, the value of the given expression will be 3√5.

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By answering the presented question, we may conclude that As a result, function the kite is around 54.96 feet above Boo.

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

To get h, we may utilise the tangent function:

tan(30) = h / 90

Because tan(30) equals 3 / 3, we may reduce the equation to:

√3 / 3 = h / 90

We may cross-multiply and simplify to find h:

h = 90 * √3 / 3

h ≈ 51.96 ft

Therefore the kite is approximately 51.96 feet above Boo. Nevertheless, because Boo is holding the kite rope at a height of 3 feet, we must add it to our answer in order to get the height of the kite above Boo:

h + 3 h above Boo

h above Boo is 54.96 feet tall.

As a result, the kite is around 54.96 feet above Boo.

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Answer:

240$

Step-by-step explanation:

we multiply 40 with 6

(40×6)

Answer:

The surface area of each mini muffin that needs to be covered by paper is the lateral surface area of the cylinder plus the area of each circular base. The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height. The formula for the area of a circle is πr^2. Using the given dimensions, the radius of each mini muffin is 1 inch, and the height is 1 and 1/4 inches. So the surface area of each mini muffin is: 2π(1)(1 and 1/4) + π(1)^2 = 5π/2 + π = 7.07 square inches (approx.) To wrap 6 mini muffins, we need 6 times this amount of paper: 6 x 7.07 = 42.42 square

Step-by-step explanation:

give me the brianlst

Answer:

It is not.

Step-by-step explanation:

Using the Pythagorean Theorem, a squared + b squared = c squared, we get 25 + 64 = 100, and this is not true.