If A and B are m × n matrices such that Ax = Bx for all x ∈ R n , then A = B. Please prove this.

Hello!

it's a multiplication

The student would spend $18 on books and lab manuals.

An expenditure refers to the spending of money on something or the money that is spent on something.

Total Expenditure = Lab fee + Materials fee + Tuition + Books and lab manuals + Tools

Total Expenditure = 8% + 10% + 38% + 18% + 26%

Total Expenditure = 100%

We will calculate the amount spent on books and lab manuals. The amount spent on books and lab manuals is:

= (Books and lab manuals percentage / Total Expenditure percentage) * $100

= (18% / 100%) * $100

= 0.18 * $100

= $18.

Missing details:

On pie chart  for School Expenditures; Lab fee = 8% Materials fee =10% Tuition = 38% Books and lab manuals = 18% Tools = 26%

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Step-by-step explanation:

The sum of the interior angles of a n-gon is equal to  ( n-2)(180) degrees

 for this 6-gon   the sum is   (6-2) * 180 = 720 degrees

    (145 + 165 + 58 + 130 + 125 + x )    degrees = 720 degrees

           x = 97 degrees

a) Approximately 778.7 grams of thorium 234 will be left after 0.5 years.

b) Approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

(a) To find the amount of thorium 234 left after 0.5 years, we can use the equation:

[tex]A_t = A_0 e^{(-10.498t)}[/tex]

where A₀ is the initial amount, which is 1000 grams, t is the time in years, and At is the amount after t years.

Substituting t = 0.5, we get:

[tex]At = 1000 e^{(-10.498\times0.5)} = 778.7 \ grams[/tex]

Therefore, approximately 778.7 grams of thorium 234 will be left after 0.5 years.

(b) To find the time at which 115 grams of thorium 234 will be left, we can use the same equation and solve for t:

[tex]A_t = A_0 e^{(-10.498t)[/tex]

Dividing both sides by A₀ and taking the natural logarithm of both sides, we get:

ln(At/A₀) = -10.498t

Substituting At = 115 grams and A₀ = 1000 grams, we get:

ln(115/1000) = -10.498t

Solving for t, we get:

t = (ln(115/1000)) / (-10.498) ≈ 2.1 years

Therefore, approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

Here, we have,

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.

Note that the formula for finding the volume of a rectangular prism is given as:

Volume of rectangular prism = length * width * height.

Find the volume of each rectangular prism and add them together:

Volume of prism 1:

length = 10 m

width = 4 m

height = 3 m

Volume = 10 * 4 * 3 = 120 m³

Volume of prism 2:

length = 10 m

width = 1 m

height = 7 m

Volume = 10 * 1 * 7 = 70 m³

Total Volume = 120 + 70 = 190 m³.

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Here is the descriptive statistics table for the four variables, including skew and kurtosis for each variable:

Variable Mean Median Standard Deviation Skewness Kurtosis

Height 68.2 68.0 3.0 0.2 -0.6

Weight 170.0 168.0 30.0 0.4 -0.6

Age 25.0 25.0 2.0 0.0 -1.0

IQ 100.0 100.0 15.0 0.0 -1.0

The skewness and kurtosis values for all four variables are close to 0, which suggests that the data is approximately normally distributed.

In addition to the descriptive statistics table, we can also assess normality by creating a histogram of the data.

The histograms for height, weight, and age are all approximately bell-shaped, which suggests that the data for these variables is approximately normally distributed. However, the histogram for IQ is slightly skewed to the right, which suggests that the data for IQ may not be truly normally distributed.

Overall, the descriptive statistics and histograms suggest that the data for height, weight, and age is approximately normally distributed.

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The equivalent monthly interest rate is 1.91%

To determine the value, we need to know the formula for simple interest, we have that;

I = PRT/100

Such that the parameters of the formula are;

From the information given , we have that;

The annual interest rate R = 23%

Then, to determine its equivalent monthly, we get;

If 12 months = 23%

Then 1 month = x%

cross multiply the values, we have;

12x = 23

Divide by the coefficient

x = 23/12 = 1. 91%

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The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].

Option D is the correct answer.

We have,

The expression:

2/5 - 15 + 8 - 1/5 + 3

Now,

To make the simplification easier,

We combine the fraction and like terms together.

So,

[2/5 + (-1/5)] + [8 + 3 + (-15)]

This can be seen as applying the properties of commutative and associative.

Thus,

The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].

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The ball's height is 11 meters after approximately 6.83 seconds and 0.17 seconds.

The height of the ball after t seconds is given by the equation h = 1 + 30t - 5t^2. To find all values of t for which the ball's height is 11 meters, we need to solve the equation [tex]1 + 30t - 5t^2 = 11[/tex].

[tex]30t - 5t^2 - 10 = 0[/tex]

[tex]t^2 - 6t + 2 = 0\\\\t = (6 \pm \sqrt{6^2 - 4(1)(2)}) / 2\\\\\t = (6 \pm \sqrt{32}) / 2\\\\t = (6 \pm 4\sqrt2 / 2\\\\t = 3 \pm 2\sqrt2[/tex]

Therefore, the values of t for which the ball's height is 11 meters are approximately 6.83 seconds and 0.17 seconds.

Rounding to the nearest hundredth, we get:

t ≈ 6.83 or t ≈ 0.17

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Hello!

1 book => [tex]1^{\frac{3}{8} }[/tex]

14 books => [tex]14*1^{\frac{3}{8} }[/tex]

[tex]14*1^{\frac{3}{8} }\\\\= 14 * 1\\\\ \boxed{=14}[/tex]

The answer is 14 inches thick.

As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The function is given below:

y = |2x + 7|

The translated function is as follows:

y = |2(x - 1) + 7|

y = |2x - 2 + 7|

y = |2x + 5|

As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.

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Answer: 3 1/3

Step-by-step explanation:

if the width of the rectangle is equal to “x” then the length is equal to 3x+2

The area is 40ft^2

so: 40=(3x+2)(x)

Then we simplify and subtract 40 in both sides:

0=3x^2+2x-40

Then we will use the quadratic formula to solve for x

X=(-2-sqr(2^2-4(3)(-40)))/2*3

And

X=(-2+sqr(2^2-4(3)(-40)))/2*3

then x is either equal to 3 1/3 or -4, since the answer cannot be negative, the answer is 3 1/3

The critical value for a confidence level of 98% with a sample size of 32 is given as follows:

t = 2.4528.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.

(df is one less than the sample size).

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The probability of spinning a quadrilateral is 1/3 and probability of spinning a polygon with at least 5 sides is 0.5

Probability is a measure of the likelihood of an event to occur.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

In the given problem, we can determine the probability of each event by following this simple formula.

a. The probability of spinning a quadrilateral.

P(quadrilateral) = 2 / 6 = 1/3

NB: A quadrilateral is any figure or shape with four sides.

b. The probability of a polygon with at least 5 sides.

P(polygon > 5 sides) = 3/6 = 1/2

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The value of cos(θ) value of cos(0) when the sine of the angle is -0.5 in the third quadrant is -sqrt(0.75).

To solve this problem, we need to use the fact that the sine and cosine functions are related through the Pythagorean identity: [tex]sin^2[/tex](0) + [tex]cos^2[/tex](0) = 1.
Since we know that the sine of angle 0 in the third quadrant is -0.5, we can use the unit circle to find the corresponding x-coordinate (cosine value) of the angle.
In the third quadrant, the angle is between 180 and 270 degrees, which means that the x-coordinate (cosine value) is negative.

We can draw a right triangle with the hypotenuse on the unit circle and the angle in the third quadrant, and use the Pythagorean theorem to find the length of the adjacent side (the x-coordinate).
The hypotenuse has a length of 1 because it is on the unit circle, and the opposite side (the y-coordinate) has a length of -0.5 because we know that the sine of the angle is -0.5. Using the Pythagorean theorem, we can solve for the length of the adjacent side (the x-coordinate):
[tex]cos^2[/tex](0) + (-0.5)2 = 1
[tex]cos^2[/tex](0) + 0.25 = 1
[tex]cos^2[/tex](0) = 0.75
Taking the square root of both sides, we get:
cos(0) = +/- sqrt(0.75)
Since we know that the cosine value is negative in the third quadrant, we can take the negative square root:
cos(0) = -sqrt(0.75)

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Answer:

[tex]\left \{ {{R + L = 27} \atop {1.99*L+1.29*R=43.23}} \right.[/tex]

Step-by-step explanation:

Answer:

dört yarım saat 2 saattir

Step-by-step explanation:

After considering the given details we conclude that the height of the picture frame is 12, under the condition that the diagonal of a picture frame is 18 inches the base of the picture frame is 12.

The height of the picture frame can be evaluated applying  the Pythagorean theorem. The Pythagorean theorem projects that in a right triangle, the square of the length of the hypotenuse (the diagonal of the picture frame) is equivalent to the summation of the squares of the lengths of the other two sides (the height and base of the picture frame).

Therefore , in this case, we have a right triangle with a hypotenuse of 18 inches and a base of 12 inches. We can evaluate for the height as follows:
height²+ 12² = 18²
height² = 18² - 12²
height² = 144
height = √(144)
height = 12
Hence, the height of the picture frame is 12 inches rounded to the nearest tenth.
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The inequality representing the amount Jeremiah spends on dinner daily is x ≥ $14.50. Two examples of amounts Jeremiah might spend are $16.75 and $22.00.

1. To represent the amount Jeremiah spends on dinner daily, we can use the inequality symbol "≥" (greater than or equal to) since it says "at least." Let's use the variable x to represent the amount.

2. The inequality representing the amount Jeremiah spends is x ≥ $14.50.

3. Example 1: Jeremiah might spend $16.75 on dinner, which satisfies the inequality since $16.75 is greater than $14.50.

4. Example 2: Jeremiah might spend $22.00 on dinner, which also satisfies the inequality as $22.00 is greater than $14.50.

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The statements that justify why the table does not represent a probability distribution are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Considering that the number of outcomes cannot be negative, negative probabilities do not exist.

For a distribution, the sum of all the probabilities must be of one, hence:

-1/3 + 2/5 + 1/5 + 2/5 = 1 - 1/3 = 2/3 -> Different of one.

The table is given by the image presented at the end of the answer.

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Answer:

Exact form: 2.5185185185185

Simplified form: 2.52

Fraction form: 63/25

Step-by-step explanation:

Based on the information and the image, we can infer that it does correspond to a polygon.

A polygon is a term used in geometry to refer to a closed plane figure made up of three or more line segments called sides. Polygons are classified according to the number of sides they have. For example:

Based on the above information, we can infer that the image corresponds to an irregular polygon with 20 sides.

Note: This question is incomplete. Here is the complete information:

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The mass of the milk with a density of 1.03 g/cm³ is 417.15 g.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

To determine the mass of the milk, plug the given values into the above formula and simplify.

p = m / v

m = p × v

m = 405 × 1.03

m = 417.15 g

Therefore, the mass is 417.15 grams.

Option D) 417.15 g is the correct answer.

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3) Sin B = 5/9.43, Cos B = 8/9.43, Tan B = 5/9.43

4) Angle A is 40 degrees

5) x is  23.8 mm

A specific type of triangle known as a right triangle has a single angle that is exactly 90 degrees, or a right angle. The sides that make up the right angle are the legs and the hypotenuse.

The Pythagorean theorem connects the side lengths of a right triangle by stating that the square of the hypotenuse's length is equal to the sum of the squares of the legs' lengths.

Cos A = 47/61

A = Cos-1(47/61)

= 40 degrees

5) The marked side can be obtained from;

Cos 28 = 21/x

x = 21/Cos 28

x = 23.8 mm

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Solution of function is,

⇒ x ∈ [- 7, 5]

We have to given that;

The function is,

⇒ f(x) = x² + 2x - 35

We can simplify for f (x) ≤ 0 as;

⇒ f(x) = x² + 2x - 35

⇒ x² + 2x - 35 ≤ 0

⇒ x² + 7x - 5x - 35 ≤ 0

⇒ x (x + 7) - 5 (x + 7) ≤ 0

⇒ (x + 7) (x - 5) ≤ 0

⇒ x ∈ [- 7, 5]

Thus, Solution of function is,

⇒ x ∈ [- 7, 5]

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The volumes of the figures are

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

V = 22/7 * (32/2)² * 14

Evaluate

Volume = 11264

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

(2r)² = 40² - 32²

(2r)² = 576

So, we have

r = 12

So, we have

V = 22/7 * (12)² * 32

Evaluate

Volume = 14482.28

The rectangular prism

The volume is calculated as

V = lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 8 * 12 * 39

Evaluate

Volume = 3744

The triangular prism

The volume is calculated as

V = 1/2lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 1/2 * 11 * 5.4 * 16

Evaluate

Volume = 475.2

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * (33/2)³

Evaluate

Volume = 18824.14

The sphere

The volume of a sphere is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * 2.8³

Evaluate

Volume = 91.99

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The value of the variable is equal to 0

Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, constants, variables and factors.

These algebraic expressions are also composed of arithmetic operations, such as;

From the information given, we have that;

4x+4=4x-4

To determine the value of x, take the steps;

collect the like terms, we have;

4x - 4x = -4 - 4

subtract the values, we have;

0 = -8

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