the line plot shows the cost of 5 books.A teacher buys all 5 books.She pays with a $100 bill. How much change should she get?

The solution of the matrix in vector form is [-13 3 -3 4]

The given matrix equation is Ax = b, where A is a matrix with 1 row and 4 columns, and b is a matrix with 1 row and 3 columns

In this case, the augmented matrix is a 5x4 matrix, with the first 4 columns being A and the last column being b. The augmented matrix for this system is then:

=> [tex]\left[\begin{array}{ccc}1&2& 3\\3& 5 &2 \\-4 &2 &5 \\-13 &11 &8\end{array}\right][/tex]

To solve the system, we can use Gaussian elimination, which is a method of solving a system of linear equations by transforming the augmented matrix into a row-echelon form.

After applying Gaussian elimination to the augmented matrix, we get the following row-echelon form:

=> [tex]\left[\begin{array}{ccc}1& 0& 0 \\-1& 0 &-3 \\-3& 0& 4 \end{array}\right][/tex]

We can then find the solution of the system by back-substitution:

=> x₁ = -13, x₂ = 3, x₃ = -3, and x₄ = 4.

Therefore, the solution of the linear system is x = [-13 3 -3 4]

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The following is a graph that illustrates the inequality system: (B) The graph displays a solid line with shading below it that goes through the points 0 commas 2, and 1 comma negative 3.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.

Hence, inequality emerges from a lack of balance.

A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.

For writing and comprehending an inequality plotted on a graph, there are two (2) main rules in mathematics, and these are as follows:

1. When the inequality symbol is (or), the line on a graph should be solid.

2. When the inequality symbol is (> or ), the line on a graph should be dashed (dotted).

The boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be indicated with the larger than (>) inequality sign.

Moreover, the y-value for this inequality graph meets the x-axis at -1.5.

Therefore, the following is a graph that illustrates the inequality system: (B) The graph displays a solid line with shading below it that goes through the points 0 commas 2, and 1 comma negative 3..

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Complete question:

The following inequalities represent a system.

y ≥ −5x + 2

y > 3x − 1.5

Which of the following graphs represents the system?

A. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.

B. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.

C. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

D> The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

Answer:

12x + 50 =210

Step-by-step explanation:

Given the data on the world problem, we know that one of our terms will be 12x because it says "each month" in the problem. If his mom is going to give him 50 dollars, and the Jordans cost 210, then we can write  a simple equation.

x = number of months it will take him

[tex]12x+50=210[/tex]

Answer: 5.8=x

Step-by-step explanation:

$210=Price

$12=Each Month

$50=From Mom

120-50=70

70/12=5.8 Months

The conversion of 180 centimetres in feet is equals to the 5.90 feet. Thus, conversion factor for conversion of units, centimetres to feet is 5.90/180 = 0.032.

A conversion is defined as to convert one set of units into another set of units by multiplication or division. A number or value which used in conversion is called conversion factor. If conversion is necessary, a conversion factor suitable for equivalent value must be used. For example, to convert meters to centimetres, the appropriate conversion value is 100 centimetres equal 1 meter. It includes converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units. How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. Thus conversion factor is 3.28 feet. So, 180 meters

= 180 × 3.28 feet

= 590.4 feet --(1)

But we need to convert 180 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 180 meters = 18000 centimeters --(2). Now from equations (1) and (2),

18500 centimeters = 590.4 feet,

Divide both parts by 100,

=> 180 centimetres = (590.4/100 ) feet

= 5.90 feet

Hence required value is 5.90.

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Answer:

Step-by-step explanation

To make the problem easier, we are gonna have to change the denominator into 16

8*2=16 after we times 8 with 2 we now have to do the same 7

So this would show 7*2=14

Now it would be 6 14/16 - 6 15/16

All we have to do now is minus 14 with 15 which equals -1.

Now for the whole numbers, you can just minus the 6’s with eachother 6-6=0. Taking the denominator, we now have -1/16.

Hope this is the answer you are looking for.

A pound is about equivalent to 0.453592 kilos. By multiplying the amount of pounds by 0.453592, you may convert pounds to kilogrammes.

So, the value of 77 kg is equal to 169.755 lbs.

The kilogramme is the primary mass unit in the metric system (kg). The masses of one kilogramme and one thousand cubic centimetres of water are comparable.

The weight of one pound is about equivalent to 454 grammes. A kilogramme is equivalent to 2.20462 pounds.

The value of One pound is 0.45359237 kilograms.

To convert kilograms to pounds,

We have to multiply given figure by 2.20462

To convert 77 kg to lbs, you can multiply 77 by 2.20462:

77 kg X 2.20462 lbs/kg

= 169.755 lbs

Therefore, 77 kg is nearly equal to 169.755 lbs.

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Answer:

Below

Step-by-step explanation:

Similar triangles due to A - A - A

Set up ratios

QR is to RS   as  QP is to TS

(x+2) / (2x-5) = 3/5       Cross multiply to get

5x+10 = 6x-15               subtract 5x from both sides of the equation

10 = x - 15                     add 15 to both sides

25 = x

The amount of tip that Ethan receives on every order, we can use the formula Tip amount = (Tip percentage) x (Cost of order) and plug in the values accordingly.

To calculate the amount of tip that Ethan receives on every order, we can use the formula:

Tip amount = (Tip percentage) x (Cost of order)

In this case, the tip percentage is `15\%` and the cost of order is the variable we need to find.

Let's assume that the cost of an order is $100. Using the formula above, we can calculate the amount of tip that Ethan receives:

Tip amount = (`15\%`) x ($100)
Tip amount = $15

Therefore, Ethan receives a $15 tip on an order that costs $100.

If the cost of an order is different, we can simply plug in the new value into the formula and calculate the tip amount accordingly. For example, if the cost of an order is $50, the tip amount would be:

Tip amount = (`15\%`) x ($50)
Tip amount = $7.50

In conclusion, to calculate the amount of tip that Ethan receives on every order, we can use the formula Tip amount = (Tip percentage) x (Cost of order) and plug in the values accordingly.

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Exponential functions are mathematical functions that involve an exponent or power. There are two types of exponential functions: growth and decay.

1. Exponential Growth Functions: These functions have the form y = a*b^x, where a > 0 and b > 1. They model exponential growth, where the value of y increases rapidly as x increases. For example, the function y = 2^x is an exponential growth function, as the value of y doubles for each increase in x.

2. Exponential Decay Functions: These functions have the form y = a*b^x, where a > 0 and 0 < b < 1. They model exponential decay, where the value of y decreases rapidly as x increases. For example, the function y = (1/2)^x is an exponential decay function, as the value of y is halved for each increase in x.

Both types of exponential functions are important in many fields, including finance, biology, and physics. They are used to model phenomena such as compound interest, population growth, and radioactive decay.

D. No, because the probability of being left-handed is greater, x must count the number of left-handed adults.

The binomial probability formula can be used to calculate the probability of a certain number of successes (or left-handed individuals) in a given number of trials (100 adults). In order for the binomial probability formula to be used, the trials must be independent, meaning that the selection of one person does not affect the selection of the next one. Since the probability of being left-handed is greater, the binomial probability formula cannot be used in this case and x must count the number of left-handed adults.

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There were 24 pepperoni pizza, 16 veggie pizza and 72 combo pizza

Pizza is a dish of Italian origin consisting of a usually round, flat base of leavened wheat-based dough topped with tomatoes, cheese, and often various other ingredients, which is then baked at a high temperature, traditionally in a wood-fired oven. A small pizza is sometimes called a pizzetta.

Calculation of the each kind of pizzas:

Let us assume the number of pepperoni pizzas be x

So,

pepperoni = x

veggie = x - 8

combo = 3x  

Since

The total Pizza is 112

So,

x + x - 8 + 3x = 112

5x - 8 = 112

5x = 112 + 8

5x = 120

x = 24

Now

x - 8 = 16

3x = 72

There were 24 pepperoni pizza, 16 veggie pizza and 72 combo pizza

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Answer: C. $725

Step-by-step explanation: To find the answer, let's first calculate the increase. A 16% increase causes the cost to go up by 16% of its own value, so let's calculate that by doing 0.16 x 12.5, giving us 2. Next, we add 2 to 12.50, giving us 14.5. Finally, we multiply 14.5 by 50 to find the cost for 50 students, giving us $725. So, $725 is our answer.

Hope this helped :D

When rotated about its center, a regular hexagon has 6 rotational symmetries. In addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry.

Geometry is a branch of mathematics that deals with the study of spatial relationships and properties of shapes, sizes, positions, and dimensions of objects. It is concerned with points, lines, angles, curves, surfaces, and solids in both two and three-dimensional space. Geometry has practical applications in fields such as engineering, architecture, computer graphics, and physics. It is also a fundamental part of mathematical education, helping students develop skills such as logical reasoning, problem-solving, and spatial visualization. Finally, geometry has a rich history, dating back to ancient civilizations such as the Greeks, Egyptians, and Babylonians.

When rotated about its center, a regular hexagon has 6 rotational symmetries. In addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry, where each line passes through a vertex and the midpoint of the opposite side.

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Using the volume formula the number of cubic inches of hot chocolate needed to completely fill the thermos is 192π.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The formula to find the volume of a cylinder is -

Volume = πr²h

where π is pi (approximately 3.14159), r is the radius of the base of the cylinder, and h is the height of the cylinder.

In this case, the radius of the cylinder is given as 4 inches and the height is given as 12 inches.

So we can use the formula above to find the volume of the thermos -

Volume of thermos = π x (4 inches)² x 12 inches

= π x 16 square inches x 12 inches

= 192π cubic inches

Therefore, volume for thermos is 192π.

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Recursive form of sequence is given by f(n)  = f(n-1) - 3

What is function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The explicit form of sequence is  given as

      f(n) = −3n + 2

So nth term is given by

           f(n) = −3n + 2

(n-1)th term is given by    

           f(n-1) = −3(n-1) + 2

We have

         f(n) -  f(n-1) = −3n + 2 - (−3(n-1) + 2)

          f(n) -  f(n-1) = −3n + 2 +3(n-1) - 2

          f(n) -  f(n-1) = −3n + 2 +3n -3 - 2

          f(n) -  f(n-1) = -3

          f(n)  = f(n-1) - 3

Recursive form of sequence is given by f(n)  = f(n-1) - 3

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Based on the assertion and the reason regarding the weight of an object and upthrust experienced by the body in a fluid; Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). The correct option is A.

The principle of floatation states that an object will float in a fluid if the upthrust that is experienced by the object is equal to or greater than the weight of the object.

The upthrust experienced by a body is the upward force that a liquid or gas exerts on a body floating in it.

Upthrust on a body depends on the acceleration due to gravity, the density of the liquid, and the volume of the body immersed in the liquid.

The weight of a body is the force of gravity acting on the body. The weight of a body acts downward.

Thus in a fluid, the weight of an object acts downward while the upthrust on the object acts in an upward direction.

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The average read speed is defined as the rate at which a person can read and comprehend written text

The average read speed refers to the rate at which a person can read and comprehend written text. This is typically measured in words per minute (wpm). According to studies, the average reading speed for adults is around 200 to 300 wpm, although this can vary depending on factors such as reading proficiency, familiarity with the material, and reading conditions.

Factors that can affect reading speed include:

Word length and complexity: Longer and more complex words can slow down reading speed.

Font size and style: Smaller fonts and difficult-to-read styles can also slow down reading.

Reading experience: Frequent readers tend to have higher reading speeds than occasional readers.

Comprehension level: Reading speed can decrease if the reader is trying to understand difficult or technical material.

It's important to note that while reading speed is a useful metric, it's not always the most important factor in reading. Comprehension and retention of the material are also crucial, so it's important to find a balance between reading speed and comprehension.

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Using the probability formula the value for the largest piece is obtained as 3/4.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Let X be the length of the largest piece when a unit stick is broken into three random pieces.

We want to find E(X), the expected value of X.

To solve for E(X), we can use the law of total probability and consider all possible lengths for the first cut.

Let Y be the length of the first piece, which can take any value between 0 and 1.

Then, we can write -

E(X) = ∫[0,1] E(X|Y=y) fY(y) dy,

where fY(y) is the probability density function of Y and E(X|Y=y) is the expected value of X given that the first piece has length y.

Now, let's consider the possible cases for the lengths of the other two pieces -

If the second cut is made in the interval [0,Y], then the largest piece has length Y.

If the second cut is made in the interval [Y,1-Y], then the largest piece has length 1-Y.

If the second cut is made in the interval [1-Y,1], then the largest piece has length Y.

Therefore, we can write -

E(X|Y = y)

= y × 1 + (1 - y) × 1/2 + (1 - y)×1  

= 1/2 + y/2.

Substituting this into the previous formula and using the fact that the density function for a uniform distribution on [0,1] is fY(y) = 1 for 0 ≤ y ≤ 1, we get -

E(X) = ∫[0,1] (1/2 + y/2) dy

= [y^2/4 + y/2] from 0 to 1

= 3/4.

Therefore, the expected length of the largest piece is 3/4.

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As a result, the rectangular pyramid has two conceivable dimensions: a base of 3 inches by 3 inches with a height of 3 inches, and a base of 1 inch by 9 inches with a height of 9 inches.

Volume is a fundamental physical quantity that measures the amount of three-dimensional space occupied by an object or a substance. In simpler terms, it refers to the amount of space that an object takes up or occupies. The standard unit of measurement for volume is the cubic meter (m3), which is defined as the amount of space occupied by a cube that has edges that measure one meter in length. However, in everyday life, other units of measurement are commonly used, such as liters, gallons, or cubic feet.

Here,

The volume of the rectangular prism is:

V = lwh = 6 * 1 * 1/2 = 3 cubic inches.

Let's call the base of the rectangular pyramid "b" and its height "h". The volume of a pyramid is given by:

V = (1/3)bh.

We want the volume of the pyramid to be the same as that of the rectangular prism, so we can set the two expressions for V equal to each other and solve for h:

3 = (1/3)bh

h = 9/b

Now we can choose any value for b and calculate the corresponding value for h that would result in the same volume as the original rectangular prism.

For example, we could choose b = 3, which would give us:

h = 9/b = 9/3 = 3

So one set of possible dimensions for the rectangular pyramid is a base of 3 inches by 3 inches, with a height of 3 inches.

Another set of possible dimensions could be b = 1, which would give us:

h = 9/b = 9/1 = 9

So another set of possible dimensions for the rectangular pyramid is a base of 1 inch by 9 inches, with a height of 9 inches.

Therefore, two sets of possible dimensions for the rectangular pyramid are: A base of 3 inches by 3 inches, with a height of 3 inches, A base of 1 inch by 9 inches, with a height of 9 inches.

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To convert 8 cups to quarts, you can divide the number of cups by 4 to get 2 quarts.

To convert cups to quarts, you can use the following conversion factor:

1 quart = 4 cups

Therefore, to convert 8 cups to quarts, you can divide the number of cups by 4:

8 cups ÷ 4 = 2 quarts

So, 8 cups is equal to 2 quarts.

It's important to keep in mind that cups and quarts are units of volume measurement commonly used in cooking and baking. Cups are often used to measure smaller amounts of liquid or dry ingredients, while quarts are used for larger amounts.

In many recipes, the measurements are given in cups, but in some cases, you may need to convert from cups to quarts or other units.

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A critical t-value calculator is an online tool that helps you determine the critical value for the t-distribution for a given level of significance (alpha) and degrees of freedom (df). The critical t-value is the value that separates the area under the t-distribution curve into the rejection region and the non-rejection region for a two-tailed hypothesis test.

In statistical hypothesis testing, the t-distribution is used when the sample size is small, and the population standard deviation is unknown. The t-distribution is a family of distributions that depend on the degrees of freedom (df) and is bell-shaped, with a mean of 0 and a standard deviation of 1.

To use a critical t-value calculator, you need to input the significance level (alpha) and the degrees of freedom (df) and select whether the test is one-tailed or two-tailed. The calculator will then provide you with the critical t-value that separates the rejection and non-rejection regions for the given alpha and df.

It's important to note that the critical t-value depends on the level of significance (alpha) and the degrees of freedom (df). As the level of significant increases or the degrees of freedom decrease, the critical t-value also changes. Therefore, it's essential to use a critical t-value calculator to obtain the correct value for your hypothesis test.

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A critical t-value calculator is a tool used to calculate the critical value of t in a Student's t-test for a given significance level (alpha) and degrees of freedom (df).

When the sample size is small or the population standard deviation is unknown, the t-distribution is used to estimate the population mean.

The critical t-value in a Student's t-test is the value of t that separates the rejection region from the non-rejection region in a t-distribution. The null hypothesis is rejected if the calculated t-value is greater than the critical t-value, indicating that there is a significant difference between the sample mean and the population mean.

To use a critical t-value calculator, enter the t-significance test's level (alpha) and degrees of freedom (df). The degrees of freedom are defined as the number of observations minus one and are proportional to the sample size. The calculator will output the critical t-value for the given significance level and degrees of freedom once you enter these values.

For example, the degrees of freedom for a two-tailed t-test with a sample size of 20 and a significance level of 0.05 would be 20-1=19. The critical t-value at a significance level of 0.05 and 19 degrees of freedom is approximately 2.093, according to a critical t-value calculator.

Knowing the critical t-value is useful in hypothesis testing because it allows you to compare the calculated t-value from the sample data to the critical t-value to determine whether the null hypothesis should be rejected

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One milliliter (mL) is equal to 0.033814 fluid ounces (fl oz). Therefore, to convert milliliters to fluid ounces, you need to divide the number of milliliters by 29.5735.

So, the value of 75 mL is equal to 2.53605 fluid ounces.

The metric system uses millilitres as the unit of volume, denoted by the letters ml or mL. One cubic centimetre, or one thousandth of a litre, is equivalent to one millilitre.

Fluid ounces is a measure of liquid; in Britain, 0.0284 of a litre.

Here, we want to convert the 75 mL into fluid ounces.

To convert milliliters (mL) to fluid ounces (oz), you can use the conversion factor of 0.033814.

So to convert 75 mL to ounces:

75 mL x 0.033814 oz/mL

= 2.53605 oz (rounded to five decimal places)

Therefore, 75 mL is approximately equal to 2.53605 fluid ounces.

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This type of scientific experiment is commonly used in microbiology and is called a bacterial culture or bacterial colony.

The scientist likely used a sterile nutrient-rich medium in a petri dish to create an environment in which the bacteria could grow and reproduce. By observing the growth and behavior of the bacteria in the colony, the scientist can study various aspects of bacterial biology, such as metabolism, genetics, and response to environmental conditions. Bacterial cultures can also be used in medical and industrial settings to produce antibiotics, vaccines, and other products.

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To simplify the expression, we can divide each term of the polynomial by the monomial:

30c^8d^3 / 12c^2d = 2.5c^6d^2

-3bc^6d^2 / 12c^2d = -0.25bc^4

6c^3d / 12c^2d = 0.5c

Therefore, the simplified expression is:

2.5c^6d^2 - 0.25bc^4 + 0.5c

Answer:

The answer is $11.60

Step-by-step explanation:

Answer: 43.2 minutes or 43 minutes and 12 seconds

Hi there, so first step I would do is to state the area of a cylinder which is 2πrh+2πr^2

Next step, I would place the value into the equation, so for the first pool, it is as follows: 2 x π x 20 x 5+2 x π x 20^2 which is = 1000π

which means 1000π = 50 minutes so each minutes must be equals to 20π

Then fit in the values for the second pool

2 x π x 18 x 6 + 2 x π x 18^2 = 864π

Then divide 864π by 20π to get how many minutes

The answer is equal to 43.2 minutes

Hope this helps

Looking at z table you can find the probability = 0.8643.

Describe Probability?

The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A certain occurrence has a chance of 1, while an impossible event has a probability of 0. The odds of two complementing events A and B happening, either A happens or B happens, sum up to 1.

Probability that bulb will last at most 610 hours is same as bulb 1-probability that bulb will last more than 610 hours. Any way we can find the probability.

Pr <= 610 hours

Using Z statistic,

610-580/(900)^1/2 = 33/30 = 1.10

So we have z value = 1.10

Now looking at z table you can find the probability,

= 0.8643

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Answer:  

Step-by-step explanation: To fidn the median I think you add all multiply by how many numbers you have and then divide I think PLS HELP MY QUESTION.

The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns.

Thus, if the null space of a 4 x 5 matrix is three-dimensional, then the rank of the matrix is 5 - 3 = 2.

Answer to Question 2:

The dimension of the solution space of A x = 0 is 6 - 2 = 4, since the number of columns of A is 6 and its rank is 2. The solution space of A x = 0 is the null space of A, which has dimension 4 by the rank-nullity theorem.

Answer to Question 3:

No, the columns of A do not necessarily have to be linearly independent. The column space of A is the span of its columns, which has dimension p. However, the columns of A may be linearly dependent, which means that some columns can be expressed as linear combinations of the others.

Answer to Question 4:

To prove that H + K is a subspace of V, we need to show that it satisfies three conditions:

It contains the zero vector: 0 = 0 + 0 belongs to H + K, since it can be expressed as the sum of the zero vectors in H and K.

It is closed under vector addition: if w1 and w2 belong to H + K, then there exist h1 and k1 in H and K such that w1 = h1 + k1, and there exist h2 and k2 in H and K such that w2 = h2 + k2. Therefore, w1 + w2 = (h1 + h2) + (k1 + k2) belongs to H + K, since it can be expressed as the sum of vectors in H and K.

It is closed under scalar multiplication: if w belongs to H + K and c is a scalar, then there exist h and k in H and K such that w = h + k. Therefore, c w = c h + c k belongs to H + K, since it can be expressed as the sum of vectors in H and K.

Since H + K satisfies these three conditions, it is a subspace of V.

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Answer: A=77  B=103   C=90  D=90  E=103   F=77   G=77

Note: This may not be right.

Step-by-step explanation: