1. Let

U = {(x, y, z) = R³ | x+y=2z = 0 = x - y},

and let

V = span {(1, 0, -1), (3, 1, 2)}.

Determine the dimensions of both U and V, proving your results.
Note that to prove the dimension, you should use the definition, which
means you need to find a basis. It is not enough to just state a basis,
you must explain why it is a basis.

Answer:

27/8

Step-by-step explanation:

First, note that 3 3/8 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

3 = whole number

3 = numerator

8 = denominator

To convert mixed number 3 3/8 to improper fraction, you follow these steps:

1. Multiply the whole number by the denominator

  3 × 8 = 24

2. Add the product from Step 1 to the numerator

   24 + 3 = 27

3. Write answer from Step 2 over the denominator

   27/8

The mixed number 3 3/8 converted to improper fraction is therefore :

27/8

Answer:

k = 56 degrees

Step-by-step explanation:

The big triangle is isosceles so the base angles are congruent.  The total angle measure is 180, so the base angles are half of 180 - 56 = 124.  The base angle at the lower right measures 62 degrees.

The inner triangle is also isosceles.  Both its base angles must measure 62 degrees (total = 124, again!).  The remaining angle,  k , measures 180 - 124 = 56.

Let, number of children and adults swam at the public pool that day is x and y.

So, x + y = 379   .....1)

It is given that daily prices are $1.75 for children and $2.00 for adults.

Also, the  receipts for admission totaled $693.50.

So, 1.75x + 2y = 693.50  .....2)

Putting value of y from equation 1 to equation 2 , we get :

1.75x + 2( 379 - x ) = 693.50

758 - 2x + 1.75x = 693.50

0.25x = 64.5

x = 258

So, y = 379 - 258 = 121

Therefore, number of children are 258 and adults are 121.

Answer:

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Based on the given conditions, formulate: 25 - 14

Calculate the sum or difference: 11

get the result: 11

Answer:

9/30 and 20/30

Step-by-step explanation:

You must find the least common denominator. To do this, list the multiples of each denominator, and find the lowest number that is the same between them.

10 = 10, 20, 30, 40, 50....

3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33....

the lowest multiple that is the same between them is 30.

Area = 1/2*b*h

[tex]1 \times 2 \times b \times h[/tex]

The equation of the line is y = 4x + 1 , where the slope of the line is m = 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the number of blocks be y

Let the stage number be x

Let the first point be represented as P = P ( 1 , 5 )

Let the second point be represented as Q = Q ( 2 , 9 )

Now , the slope of the line between the points be

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 9 - 5 ) / ( 2 - 1 )

Slope m = 4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = 4 ( x - 1 )

On simplifying the equation , we get

y - 5 = 4x - 4

Adding 5 on both sides of the equation , we get

y = 4x + 1

Therefore , the value of A is y = 4x + 1

Hence , the equation of line is y = 4x + 1

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Her class of 30 pupils can be divided into 10 groups using 5 groups of 2 students and 5 groups of 4 students each.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle.

given

10 groups of 3 students = 30 students :

5 groups of 2 students + 5 groups of 4 students = 30 students : 7 groups of 3 students + 3 groups of 3 students = 30 students

so Her class of 30 pupils can be divided into 10 groups using 5 groups of 2 students and 5 groups of 4 students each.

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Answer:

the graph would show a line with a y-intercept of 7 and a slope of -2/3

Step-by-step explanation:

y - 3 = -2/3x + 4

y = -2/3x + 7

the graph would show a line with a y-intercept of 7 and a slope of -2/3

Answer:21/2

Step-by-step explanation:

Answer:

Their are 166 students

are brought food

Answer:

incorrect

Step-by-step explanation:

y= 1/3x+2 because the slope(m) going up by 1 takes up 3 spaces going out and u it in rise/run form rise being up and run being out and the y intercept(b) is where the y axis and the slope meet (basically it starts at the 2)

Using Continuous compounding in 15.07 months, the bike's value will be less than £1200.

Continuous compounding refers to the process of compounding interest at an infinitely frequent rate. It is a way to figure out how much an asset will depreciate over time or how much an investment will increase.

[tex]A=Pe^{rt}[/tex]

where:

A is the asset's final value

P is its initial value

r is the interest rate (or rate of depreciation in the case of a depreciating asset)

t is the time periods (months, years, etc.)

A= 1200

P= 2550

r= -0.05

We want to find t, so we can rearrange the formula to solve for t:

[tex]t=\frac{log\frac{A}{P}}{r}\\\\t=\frac{log\frac{1200}{2550} }{-0.05} \\ \\t=15.07months[/tex]

In 15.07 month motorbike value will depreciate to less than £1200

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answer: -3 lmk if you want an explanation!

Answer:

Step-by-step explanation:

10400

Answer:

3200 cm^3

Step-by-step explanation:

1. Calculate the sides of the right triangle to get the height

We know that side c = 26 and the shortest leg is 10 cm (20cm/2) because this right triangle splits the 20cm in two)

[tex]10^{2} + b^{2} = 26^{2} \\100 + b^{2} = 676\\b^{2} = 576 \\b = \sqrt{576} \\b = 24[/tex]

a = 10, b = 24, c = 26

2. Use the formula for the volume of a square pyramid now that you have the height (which is b)

[tex]V = a^{2} \frac{h}{3} \\\\V = 20^{2} * \frac{24}{3} \\V = (400)(8)\\V = 3200 cm^{3}[/tex]

V = 3200

I hope this helped! :)

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the sum of angle 1 and angle 4 is 180

the answer is A because 53 + 127 = 180

Answer:

You to it right, 18

Step-by-step explanation:

Answer:

27 ft I think

Step-by-step explanation:

The answer is 27

Therefore , the solution of the given problem of domain is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.

A function's domain is the set of values that can be sent into it. This collection represents all x values in a function like f. (x). A function's range is the set of possible values that it can accept. This collection includes the values that the return statement when we enter an x value. Assume that x and y are indeed the independent and dependent variables of a function with the formula y = f(x). If a function f provides a way to generate a single value y successfully while using a value of x .

Here,

In this case, f(x)=-3x-2 x < 4

3/4x-1 x≥ 4

Domain

This range, which is the range of -3x-2 (-14,), is a subset of the range of f(x).

Therefore , the solution of the given problem is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.

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Answer:

1/ 4

Step-by-step explanation:

The least amount of sap is represented on the horizontal Axis. The least amount means the treetgatvproduced the smallest amount of sap. Which will be the value to the left of the line dot plot as the values are ordered. Hence, we can say that three trees produced the smallest amount of sap which is 1/4

Answer:

80+30h

Step-by-step explanation:

The equation of the exponential function represented by the table will be y = 4(3)ˣ.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

Take two points from the table, then the points are (0, 4) and (1, 12).

The equation passes through (0, 4), then we have

4 = a(b)⁰

a = 4

The equation passes through (1, 12), then we have

12 = 4(b)¹

b = 3

Then the equation of the exponential function represented by the table will be y = 4(3)ˣ.

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Answer:

$38.90

Step-by-step explanation:

$2.00 per mile x 18 miles is 36.00 then add the 2.90

Answer:

2209

Step-by-step explanation:

The interquartile range is the 3rd quartile minus the 1st quartile. To find the quartiles, you need to find the median.

First, put the values in order.

17012, 18140, 17362, 16697, 14387 becomes

14387, 16697, 17012, 17362, 18140

The median is the value in the middle, so 17012. The first quartile is the median of the numbers to the left of the median. The numbers to the left are 14387 and 16697. Because there are an even amount of numbers, there's no middle. So the median of those values is the average (aka the sum divided by the number of values).

14387 + 16697 = 31084. Then divide that by 2 (the number of values) and you get 15542. So 15542 is the first quartile.

The 3rd quartile is the median of the values to the right. It is 17751 because 17362 and 18140 are the numbers to the right of the median. 17362 + 18140 = 35502 and 35502/2 = 17751.

The interquartile range is the 3rd quartile minus the 1st quartile

17751 - 15542 = 2209

The volume of each drinking cup is 7.9 cubic inches.

An office uses paper drinking cups in the shape of a cone, with dimensions as shown.

The formula provides the volume of a cone.

V =  (1/3) * π * r² * h.

We can find the solution by entering the already-known data into the formula.

d = 2.75 m.

Since radius is half of d, we can say

0.5 * 2.75 = 1.375 in.

4 inches is listed as the height.

The result of plugging all of them into the original formula is:

V = (1/3) * π(1.375)² (4) = 7.9

Our final response, rounded to the closest tenth, is:

V = 7.9 cubic inches.

The volume of each drinking cup is 7.9 cubic inches.

The complete question is An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the nearest tenth of a cubic inch, what is the volume of each drinking cup?

d = 2.75 m.

h = 4

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Answer:

True

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

As the normal distribution is symmetric, we have that [tex]P(z < -A) = P(z > A)[/tex]

For example:

[tex]z = -2[/tex] has a pvalue of 0.0228, which means that [tex]P(z < -2) = 0.0228[/tex]

[tex]z = 2[/tex] has a pvalue of 0.9772, which means that [tex]P(z > 2) = 1 - 0.9772 = 0.0228[/tex]

True or False?

As shown above, this statement is True, due to the symmetry of the normal distribution.