In Exercises 3-4, use the Subspace Test to determine which of the sets are subspaces of Mnn 3. a. The set of all diagonal n × n matrices. b. The set of all n x n matrices A such that det(A) = 0. c. The set of all n x n matrices A such that tr(A) = 0. d. The set of all symmetric n x n matrices

A line chart is a type of graph used to show the relationship between two variables.

It is used for plotting data points that are connected by a straight line. The two variables can be either continuous or categorical. The line chart is useful for visualizing the relationship between the two variables and how they change over time. Line charts can be used to display data over a period of time, such as stock prices, or to compare different categories of data.

A pyramid chart is a type of graph used to compare different groups of data. It is usually used to show the relative sizes of different categories within a data set. The pyramid chart is generally preferred over the column chart because it is easier to compare the relative sizes of the different categories.

Pie charts are a type of graph used to show the relative size of different categories in a data set. They are useful for visualizing the proportions of the different categories. Pie charts can generally be used instead of bar charts, but they are not as useful for comparing the relative sizes of different categories or for displaying data over a period of time.

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Answer:

Answer:

b2 = 2A/h - b1

Step-by-step explanation:

The vector field f(x, y, z) = i + 2j + 3k represents a constant vector field that points in the direction of the positive x-axis with magnitude 1, positive y-axis with magnitude 2, and positive z-axis with magnitude 3.

The plot of this vector field would consist of parallel arrows pointing in the same direction, where each arrow represents the magnitude and direction of the vector at a specific point in space. The arrows would be evenly spaced and extend indefinitely in the positive x, y, and z directions. The length of the arrows would represent the magnitude of the vector, with longer arrows indicating larger magnitudes.

In summary, the plot of the vector field f(x, y, z) = i + 2j + 3k would consist of evenly spaced, parallel arrows pointing in the positive x, y, and z directions, representing a constant vector field with magnitudes 1, 2, and 3 along the respective axes.

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Answer:

6 cups of sugar

Step-by-step explanation:

a) how do you even mess up a cookie recipe that bad, she’s going to have 7 batches more than she wanted (ignore this)

and b) Alice put in 8 times as much butter more than she should’ve (1/8x8=1 cup), so multiply the amount of sugar by 8.

3/4x8=24/4, or 6 cups of sugar

If Alice puts in 1 cup of butter by mistake. Then the amount of the sugar that is needed will be 6 cups.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

The cookie recipe needs 3/4 cup of sugar and 1/8 cup of butter.

Then the ratio will be

r = (3/4) / (1/8)

r = 3/4 x 8/1

r = 6

If Alice puts in 1 cup of butter by mistake.

Then the amount of the sugar that is needed will be

We know that the ratio remains constant. Then we have

Let x be the amount of sugar that is needed.

x / 1 = r

   x = 6

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As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

c) 80⁰

isosceles triangle, two sides and angels are equal.

Step-by-step explanation:

180⁰= full triangle

80⁰+20⁰=100⁰

180-100=80⁰

Answer:

Step-by-step explanation:

The Probability of Landing a heads is (1/2)

Now, to find the probability of landing it five times in a row, it is

1/2 x 1/2 x 1/2 x 1/2 x 1/2

( 1/2 is multiplied to the number of times to get a head )

The final answer will be,

Probability of landing heads 5 times in a row = 1/32

Answer:

Yes

Step-by-step explanation:

Since Jenny makes a profit of $2 for each bar of chocolate that she sells, if she sells a total of 500 chocolate bars, her profit would be:

Profit for 500 chocolate bars = profit for each chocolate bar * 500 bars

Profit for 500 chocolate bars = $2 per bar * 500 bars

Profit for 500 chocolate bars = $1000

Also she want to buy a laptop worth $998. This would be possible after selling 500 bars because $1000 > $998. After buying the laptop she would have $2 remaining ($1000 - $998)

Answer:

84

Step-by-step explanation:

6.3+16.1=22.4

22.4/2=11.2

11.2x7.5=84

Answer:

78.12 cm^2

Step-by-step explanation:

i will call the 6.3 cm line A, 7.5 line B and 16.1 cm C

first we divide this into two shapes, a rectangle and a triangle

THE RECTANGLE:

the formula to find the area of a rectangle: L x W

A x B

6.3 x 7.5 = 47.25 cm^2

THE TRIANGLE:

this is a right angle triangle

formula to find the area of a right angle triangle: (1/2) x BASE x H

B is parallel to H and share the same length

to find BASE we need to subtract 6.3cm from 16.1cm (check attachment)

16.1 - 6.3 = 9.8

(1/2) x 9.8 x 6.3 = 30.87 cm^2

FINAL VALUE:

now we simply add our two values of area together

30.87 + 47.25 = 78.12 cm^2

Jack can sell 12 bird feeders with 4 lb of birdseed. We can use Proportion method to calculate this :

Assuming that Jack mixes 1/3 pound of birdseed for each bird feeder, we can find out how many bird feeders he can sell with 4 pounds of birdseed by using a proportion.

Let x be the number of bird feeders Jack can make with 4 pounds of birdseed. We can set up the proportion:

1/3 pounds of birdseed per bird feeder = 4 pounds of birdseed / x bird feeders.

Simplifying this equation, we get:

1/3 = 4/x

To solve for x, we can cross-multiply:

1x = 12

x = 12

Therefore, Jack can make and sell 12 bird feeders with 4 pounds of birdseed.

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Answer:

(8, -3)

Step-by-step explanation:

The coordinates of the midpoint are the average of the endpoints.

5 = (x + 2) / 2

10 = x + 2

x = 8

1 = (y + 5) / 2

2 = y + 5

y = -3

According to the graph the rational function represented in the graph is \(F(x) = \frac{x-2}{(x+1 )(x-3)}\), and option A is correct answer.

At the margins of the coordinate plane, the curve approaches lines known as asymptotes. When the denominator of such a rational function gets close to zero, vertical asymptotes happen. Since it would divide by zero, a rational function never traverse a vertical asymptote. A graph's vertical asymptote is a vertical line with the equation x=a, where the graph tends to positive or negative infinity as the inputs go closer to a.

For the given graph we can see that the vertical asymptotes are -1 and 3, and there is no horizontal asymptote.

In option A:

\(F(x) = \frac{x-2}{(x+1 )(x-3)}\)

The horizontal asymptote is none.

The vertical asymptote is -1 and 3.

Hence, this is the correct option.

Option B:

\(F(x) = \frac{1}{(x-2)(x+1 )(x-3)}\)

The horizontal asymptote is 0.

The vertical asymptote is 2, -1 , and 3.

Hence, option B is incorrect.

Option C:

\(F(x) = \frac{x-2}{(x-1 )(x+3)}\)

The horizontal asymptote is none.

The vertical asymptote is 1 and -3.

Hence, option C is incorrect.

Hence, according to the graph the rational function represented in the graph is \(F(x) = \frac{x-2}{(x+1 )(x-3)}\), and option A is correct answer.

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Answer:

A. The number of actual outcomes is 6 (since there are 6 sides to the block).

B. The number of all possible outcomes would be the number of ways the block could land on the table, which is also 6 (since each of the 6 sides is equally likely to face up).

C. The probability that the block will land with either the T, C or R facing up is the probability of landing on any one of those 3 sides. Since there are 3 such sides, and each side is equally likely to face up, the probability is 3/6 or 1/2.

Answer:

Step-by-step explanation:

The velocity is halved, the kinetic energy is halved.

Joint variation is variation in which a quantity varies as two or more variables.

Since the kinetic energy, K, of an object varies jointly with its mass, m, and the square of its velocity, v., we have that

K ∝ mv²

⇒ K = kmv²

Since the mass of an object stays the same, but the velocity of the object is halved. How is the kinetic energy of the object affected, we see that the

So, K' = km(v/2)²

K' = kmv²/4

K' = (kmv²/2)/2

K' = K/2

Since the velocity is halved, the kinetic energy is halved.

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Answer:

The kinetic energy is quartered.

Step-by-step explanation:

(15×4)÷6[{32÷4(7×2-15+5)}+3]

=60÷6[{32÷4(14-15+5)}+3]

=60÷6[{32÷4(19-15)}+3]

=60÷6[{32÷4(4)}+3]

=60÷6[{32÷16}+3]

=60÷6[{2}+3]

=60÷6[5]

=60÷30

=2

Step-by-step explanation:

2p - 12 = 8p - 12

Bringing like terms on one side

-12 + 12 = 8p - 2p

0 = 6p

0 - 6 = p

-6 = p

The height of building is 0.2 miles.

The given points form a right angled triangle. Top of the building to base of building is the perpendicular, base of building to the angle of elevation is base and angle of elevation to top of the building is hypotenuse. So, considering this, tan of angle of elevation related the two sides of triangle as follows -

tan theta = perpendicular ÷ base

tan 6° = perpendicular ÷ 2

Perpendicular = 2 × tan 6°

Keep the value of tan 6°

Perpendicular = 2 × 0.1

Performing multiplication

Perpendicular = 0.2 miles

Hence, the height of the building is 0.2 miles.

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The ratio of the number of tulips to the number of roses in Julia's garden is 5:4.Let's represent the number of roses as 'r' and the number of tulips as 't'.

According to the given information, one half of the number of roses is equal to two fifths of the number of tulips. Mathematically, this can be expressed as:

(1/2) * r = (2/5) * t

To find the ratio of the number of tulips to the number of roses, we divide both sides of the equation by 'r':

(1/2) = (2/5) * t / r

Now, we can simplify the equation:

(1/2) = (2/5) * (t/r)

To eliminate the fraction, we can multiply both sides of the equation by 2:

2 * (1/2) = 2 * (2/5) * (t/r)

1 = (4/5) * (t/r)

Finally, to isolate the ratio of tulips to roses, we divide both sides of the equation by (4/5):

1 / (4/5) = (4/5) * (t/r) / (4/5)

5/4 = (t/r)

Therefore, the ratio of the number of tulips to the number of roses in Julia's garden is 5:4.

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The value of x can be found by using the formula for the area of a trapezoid. The value of \($x$\) is \($4$\) inches.

Area is a two-dimensional measurement that is used to measure the size of a shape or surface. It is measured in square units, such as square centimeters, square meters, square kilometers, and so on. The formula for the area of a trapezoid is: \((a+b)/2 *h\), where a and b are the lengths of the parallel sides, and h is the height. Mrs. Katz needs to calculate the value of x by plugging in the lengths of the parallel sides and the height into the formula.

We know that the opposite sides of a trapezoid are parallel, so we have \(AB \parallel DC.\)

Using the given information, we can set up an equation in terms of \($x$\) and solve for it. We know that the height of the trapezoid is \($8$\) inches, and we know that the bases are \($x$\) inches and \($16$\) inches.

Using the formula for the area of a trapezoid, we have:

\(\text{Area} = \frac{1}{2}(AB+DC)(\text{height})\)

Plugging in the values we know, we get:

\(\text{Area} = \frac{1}{2}(x+16)(8)\)

We are also given that the area of the trapezoid is \($100$\) square inches, so we can set up an equation:

\(100 = \frac{1}{2}(x+16)(8)\)

Simplifying and solving for \($x$\), we get:

\(100 &= \frac{1}{2}(x+16)(8)\20 &= (x+16)\x &= 4\)

Therefore, the value of \($x$\) is \($4$\) inches.

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Answer:

-13/10

Step-by-step explanation:

It wont be -7/10 because to change a mixed number to an improper fraction, we multiply the whole number by the denominator and then add this product with the numerator.

Answer:

6.61387 stones

Step-by-step explanation:

Answer:

6.6 stones

Step-by-step explanation:

1 kg= 2.2 pounds

1 stone =14 pounds ⇒ 1 pound= 1/14 stone

42 kg= 42*2.2 pounds= 92.4 pounds  

92.4 pounds = 92.4 * 1/14 stone= 6.6 stones

The probability of winning at least once when playing the instant lottery twice is 0.19, or 19%.

To find the probability of winning at least once in the instant lottery when playing twice, we can use the complement rule.

The complement rule states that the probability of an event occurring (in this case, winning at least once) is equal to 1 minus the probability of the event not occurring (in this case, not winning both times).
Determine the probability of not winning in a single game, which is 1 - 0.1 = 0.9.
Calculate the probability of not winning both times, since outcomes are independent, by multiplying the probabilities of not winning each time: 0.9 * 0.9 = 0.81.
Finally, find the probability of winning at least once by subtracting the probability of not winning both times from 1: 1 - 0.81 = 0.19.

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Answer:269.6 square centimeters

Step-by-step explanation:

Solution

We want to use coordinate geometry to determine if the triangle is a right triangle

We can find the distance between all the three vertices.

The formula for distance between two points ( x1 , y1 ) and ( x2, y2) is given as :

Let us start by finding the distance AB

Let us find the distance BC

Now let us find the distance AC

The triangle will be a right triangle if it obeys pythagoras theorem

Pythagoras' theorem says if we square the longest side in a right triangle , then it must be equal to the sum of the squares of the other two sides

Let us see if that works. If it works, the triangle is right triangle. If it doesn't work, we conclude otherwise.

So we can say that only right triangle obeys pythagoras' theorem.

Now lets verify

Longest side is AC

Let us find the sum of the squares of AB and BC

Now we observe that ;

The triangle given is a right triangle

Our choice is Yes

Answer:

27 x 52  = ( 20 + 7 ) x ( 50 + 2 )  = 1404

Step-by-step explanation:

27 x 52

( 20 + 7 ) x ( 50 + 2 )

(20 x 50) + (20 x 2) + (7 x 50) + (7 x 2)

= 1000 + 40 + 350 + 14

= 1404  

Answer:

0.0300300030000...

Step-by-step explanation:

An irrational number has endless non-repeating digits to the right of the decimal point. They can be written as decimals, but not as fractions.

1632 can be written as 3264/2

0.25 can be written as 1/4

0 could be written as 0/0

but 0.0300300030000 cannot be written as a fraction, and it satisfies the condition of an irrational number having endless non-repeating digits to the right of the decimal point.

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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The volume of the solid is approximately 807.08 cubic units.

To determine the volume of the solid, we can use the method of cylindrical shells.

Imagine taking a slice of the solid parallel to the base, with the cross-sectional area being a square of side length x (where x is a function of the height). The volume of this slice is the product of the square area and the height. The height of the slice is equal to the difference in the radii of two consecutive circular cross sections.

The radius of the larger circular cross-section can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the radius) is equal to the sum of the squares of the other two sides (the height and half the side length of the square). Thus, we have:

r² = x² + (15-x)²

Solving for x, we get:

x = 15 * √(1 - (r/15)²)

The volume of the slice is then given by:

V = x² * (15 - x)

To find the total volume of the solid, we integrate this expression with respect to r from 0 to 15. The result is approximately 807.08 cubic units.

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