Jane has a carton of orange juice.
The carton is in the shape of a cuboid.
20cm-
6cm
10 cm
The depth of the orange juice in the carton is 8 cm.
Jane closes the carton.
Then she turns the carton over so that it stands on the shaded face.
Work out the depth, in cm, of the orange juice now.

1.   4x − 2y = 10 and 2x − y = 5

Lines are coincident.

2.  y = 2x − 3 and −2x + y = −5

Lines are parallel.

3.  2x − 5y = 14  and 3x + 4y = 10

Lines are intersecting.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

1.   4x − 2y = 10 and 2x − y = 5

2.  y = 2x − 3 and −2x + y = −5

3.  2x − 5y = 14  and 3x + 4y = 10

\(\rm \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2} \ \ \ \ \ \ \ \ \ \ \ Lines\ are\ intersecting\\\\\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}\ \ \ \ Lines \ are\ parallel\\\\\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2} \ \ \ \ Lines\ are\ coincident\)

1.   4x − 2y = 10 and 2x − y = 5

Lines are coincident.

2.  y = 2x − 3 and −2x + y = −5

Lines are parallel.

3.  2x − 5y = 14  and 3x + 4y = 10

Lines are intersecting.

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Answer:

-7

Step-by-step explanation:

3=-3x-18

3x=-18-3

3x=-21

x=-7

\(\Large \begin{aligned}\\&(a^b)^c=a^{bc}\\\\&\left(x^{\frac{1}{6}\right)^3=x^{\frac{3}{6}}=x^{\frac{1}{2}}\end{aligned}\)

Random variables can be either discrete or continuous.

Sample spaces need not consist of numbers.  In statistics, we are most often interested in numerical outcomes such as the "count" of an occurrence.  We call X a random variable because its values vary when the phenomenon is repeated.  We use capital letters near the end of the alphabet like X or Y.

A random variable is a variable whose value is a numerical outcome of a random phenomenon.  When a random variable describes a random phenomenon the sample space S just lists the possible values of the random variable.  There are two ways of assigning probabilities to the values of a random variable that will dominate our application of probability as we study statistical inference.

Random variables can be either discrete or continuous.  A discrete random variable X has a "countable number of possible values.  The probability distribution of X lists the values and their probabilities in table form.  The probabilities must satisfy two requirements:

1)  every probability pi is a number between 0 and 1

2) p1 + p2 +,,,+pk = 1.

The probability of any event is found by adding the probabilities pi of the particular values xi that makes up the event.

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The total number of miles that Parker would have to run is given as follows:

88.41 miles.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

As the number of miles increases by 5% each week, the common ratio is obtained as follows:

100% + 5% = 105% = 1.05.

Hence the number of miles each week is given as follows:

Then the total number of miles is given as follows:

16 + 16.8 + 17.64 + 18.52 + 19.45 = 88.41 miles.

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Answer:

Step-by-step explanation:

800 J/kgC

What is the specific heat of a material that gains 600 joules of energy when a 0.25 kg object increases in temperature by 3C?

it is 800 J/kgC

Answer:

x = 36, y = 84

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for x

x = 180 - (96 + 48) = 180 - 144 = 36

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an exterior angle of the triangle, thus

y = 48 + 36 = 84

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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Answer:

\(\frac{y^{2}}{2x}\)

Step-by-step explanation:

a) simplify

\(\frac{y^{2} }{2x}\)

Answer:

ez y² /2x

Step-by-step explanation:

Answer: There are 7 marbles in the bag and in the first attempt, all 7 marbles are there. After one marble is taken away, then we have 6 marbles to choose from. Therefore we will multiply 7*6 = 42.

Hence, there are 42 possible outcomes.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{8 {y}^{2} + 4y - 8}}}}}\)

Step-by-step explanation:

Given,

Length of a rectangular garden ( l ) = 2y - 4

Width of a rectangular garden ( w ) = 4y²

Perimeter of the garden = ?

Finding the perimeter of a rectangular garden having length of 2y-4 and width of 4y²

\( \bold{ \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(l + w)}}}\)

\( \longrightarrow{ \sf2(2y - 4 + 4 {y}^{2}})\)

Distribute 2 through the parentheses

\( \longrightarrow{ \sf{4y - 8 + 8 {y}^{2} }}\)

Arrange it in standard form

\( \longrightarrow{ \sf{8 {y}^{2} + 4y - 8}}\)

Hope I helped!

Best regards! :D

The quadratic function \(y = -9x^{2} + 18x + 6\) can be rewritten in vertex form as \(y = -9(x - 1)^{2} - 6\), with vertex at (1, -6).

A quadratic function is a type of function that can be written in the form \(f(x) = ax^{2} + bx + c\), where a, b, and c are constants, and x is the independent variable. In other words, a quadratic function is a polynomial of degree 2, which means the highest exponent of the variable x is 2.

To rewrite the quadratic function\(y = -9x^{2} + 18x + 6\) in vertex form, we need to complete the square by adding and subtracting a constant term that will allow us to express the function as a squared expression plus a constant.

First, we factor out the common factor of -9 from the quadratic terms:

\(y = -9(x^{2} - 2x - (6/(-9)))\)

Next, we complete the square inside the parentheses by adding and subtracting the square of half of the coefficient of the x term, which is (-2/2) = -1:

\(y = -9(x^{2} - 2x + 1 - 1 - (6/(-9)))\)

Notice that we added -1 inside the parentheses, but since we multiplied by -9 outside the parentheses, we need to subtract -9(-1) = 9 outside the parentheses to keep the expression equivalent:

\(y = -9(x^{2} - 2x + 1 - 1 - (6/(-9))) - 9(9)\)

Now, we can simplify the expression inside the parentheses by factoring the perfect square trinomial:

\(y = -9((x - 1)^{2} - (6/(-9)) - 9)\)

Simplifying further:

\(y = -9((x - 1)^{2} - (2/3))\)

Finally, we can write the function in vertex form by rearranging the terms:

\(y = -9(x - 1)^{2} - 6\)

Therefore, the quadratic function \(y = -9x^{2} + 18x + 6\) can be rewritten in vertex form as \(y = -9(x - 1)^{2} - 6\), with vertex at (1, -6).

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Answer:

number of students in a van=12

number of students in a bus=52

Step-by-step explanation:

let number of students in a van=x

number of students in a bus=y

1x+6y=324     ...(1)

9x+3y=264   ...(2)

multiply (2) by 2

18x+6y=528   ...(3)

(3)-(1) gives

17x=204

x=204/17=12

put in (1)

12+6y=324

6y=324-12=312

y=312/6=52

Answer:

number of students in a van=12

number of students in a bus=52

Step-by-step explanation:

let a number of students in a van=x

number of students in a bus=y

1x+6y=324 ...(1)

9x+3y=264 ...(2)

multiply (2) by 2

18x+6y=528 ...(3)

(3)-(1) gives

17x=204

x=204/17=12

put in (1)

12+6y=324

6y=324-12=312

y=312/6=52

Answer:

x plus 4 divided by 5 minus 9

x + 4 / 5 - 9

Answer:

it's ok no problem take care

Answer:

\(15+m^{6}\)

Step-by-step explanation:

\(8m^{2} +3m+m^{3}+4\\8+4+3+m^{3} +m^{2} +m\\8+4+3+m^{6} \\15+m^{6}\)

The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

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Answer:

your mom

1234567891011

Answer:

yes

Step-by-step explanation:

They both have a 25 degree angle, and the second one is just the first one but put on the page at a different angle

The correct choice is: B. There are infinitely many solutions. The solution is X1 = 85t and X2 = t, for any real number t.

To determine the solution of the system, we need to convert the given augmented matrix to row echelon form and then to reduced row echelon form.

Starting with the given matrix:

[ 1 -4 170 0 0 ]

Divide the first row by 1:

[ 1 -4 170 0 0 ]

Add the first row to the second row four times over:

[ 1 -4 170 0 0 ]

[ 0 -16 680 0 0 ]

Subtract 170 times the first row from the third row:

[ 1 -4 170 0 0 ]

[ 0 -16 680 0 0 ]

[ 0 676 -28900 0 0 ]

Divide the second row by -16:

[ 1 -4 170 0 0 ]

[ 0 1 -85 0 0 ]

[ 0 676 -28900 0 0 ]

Subtract -676 times the second row from the third row:

[ 1 -4 170 0 0 ]

[ 0 1 -85 0 0 ]

[ 0 0 -39180 0 0 ]

Divide the third row by -39180:

[ 1 -4 170 0 0 ]

[ 0 1 -85 0 0 ]

[ 0 0 1 0 0 ]

Now the matrix is in reduced row echelon form, and we can see that the third equation is X2 = 0, which means that X2 can take any value. The second equation is X1 - 85X2 = 0, which means that X1 = 85X2. Therefore, the solution to the system is X1 = 85X2 and X2 can take any value.

Thus, the correct choice is:

B. There are infinitely many solutions. The solution is X1 = 85t and X2 = t, for any real number t.

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Answer:

8343420.417

Explanation:

Using the BIDMAS Rule. It stands for Brackets, Indices , Division, Multiplication, Addition and Subtraction.

First we solve all the division parts:

40005698÷32÷5÷33

= 7576.837

Now multiplying:

7576.837 x 50 x 22

= 8334520.417

Lastly addition:

8334520.417 + 8900

= 8343420.417

The length of line segment AB in the triangle using the midsegment theorem is 64.

The Midsegment Theorem states that "the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side."

From the diagram:

Midsegment = 3x + 5

Third side = 7x + 1

First, we solve for x, using the midsegment theorem:

( 3x + 5 ) = 1/2 × ( 7x + 1 )

Multiply both sides by 2:

2( 3x + 5 ) = ( 7x + 1 )

6x + 10 = 7x + 1

Collect and add like terms:

7x - 6x = 10 - 1

x = 10 - 1

x = 9

Now, we solve for line AB:

Line AB = 7x + 1

Plug in x = 9

Line AB = 7(9) + 1

Line AB = 63 + 1

Line AB = 64

Therefore, the line segment AB is 64.

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10.59 is the value of the given side b.

In our case, we know that side A has a length of 15 units and is opposite angle A, which measures 27 degrees.

Using the sine rule, we can write:

b/sin(27°) = 15/sin(40°)

To find the value of b, we can rearrange the equation:

b = (15 * sin(27°)) / sin(40°)

evaluate the trigonometric functions and calculate b:

b ≈ 10.59

Therefore, using the sine rule of the triangle, we find that the value of side b is approximately 10.59 units.

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Step-by-step explanation:

please mark me as brainlest

Answer:

(x + 1)(x - 6)

Step-by-step explanation:

We can factor x^2 - 5x - 6 using grouping:

Hope this helps!!

Given the gluten ratio of 13 mg/L in the food, the gluten ratio is micrograms per milliliter can be shown as 13 μg/mL.

In the question, we are given that a certain food has a gluten ratio of 13 mg/L.

We are asked to find the gluten ratio in micrograms per milliliter.

We know the conversion rates:

1 milligram (mg) = 1000 micrograms (μg).

1 Liter (L) = 1000 milliliters (mL).

Applying these conversion rates to the given gluten ratio for the food, we get:

13 mg/L

= 13 (1 mg)/(1 L)

= 13 (1000 μg)/(1000 mL)

=  13 μg/mL.

Thus, given the gluten ratio of 13 mg/L in the food, the gluten ratio is micrograms per milliliter can be shown as 13 μg/mL.

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Answer:

17 * 4

Step-by-step explanation:

A quotient is the answer to a multiplication problem.

Step-by-step explanation:

you cannot further simplify 17/7. so, the answer remains 17/7

Answer: \(2\frac{3}{7}\)

Step-by-step explanation:

It is in the simplified form already. Perhaps you mean simplifying this fraction into mixed form.

First, start by dividing the numerator by the denominator to find the GCF.

\(17/7's\ GCF\ is\ 2.\)

Also, it can be considered that the highest number you can multiply 7 by to get close to 17 is 2. That is 14. If we try 7*3, that is 21 and too high. So the 2 will be the number that sits outside the fraction

Next, we need to use the 17 in the numerator and subtract by that 14, which we got from the number of times we can divide 17 by 7. We get 3, the numerator.

Now, we keep the denominator the same, the 7, and put all the pieces together:  \(2\frac{3}{7}\).

Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of different sizes.

Frequency distributions can show the actual number of observations falling in each range or the percentage of observations. In the latter sample, the distribution is called a relative frequency distribution.

Frequency distribution tables can be utilised for both categorical and numeric variables. Continuous variables should only be used with class intervals, which will be described shortly.

A relative frequency distribution displays the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.

--This question is incomplete; the complete question is

"Relative frequency distributions are generally more useful than frequency distributions when _____."--

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The data described in the first statement, "The movie ratings of a critic with possible ratings being 0 stars, one-half star, 1 star, and so on," is discrete data.

Discrete data consists of distinct, separate values or categories that have gaps between them. In this case, the possible movie ratings are specifically defined as 0 stars, one-half star, 1 star, and so on. Each rating is a distinct category with no intermediate values or measurements. The ratings are not continuous and cannot take on any value within a range.

In contrast, continuous data represents measurements or values that can take on any value within a range or interval. For example, if the movie ratings were described as a continuous scale from 0 to 5 stars, where any fractional value within that range is possible, it would be considered continuous data.

Since the movie ratings in the given statement are defined as specific categories without any intermediate values, they are classified as discrete data.

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Answer:

The selling price of the bag is $22.5

Step-by-step explanation:

Buying Price = $25,

Selling Price = ?

Since they sold it at a loss of 10%,

So, they sold it for a price 10% less than the buying price,

or at 90% or 0.9 of the buying price,

so,

Selling Price = (0.9)(25) = $22.5

The equation r-6=0 is given in the cylindrical coordinates. The shape of this equation is not a sphere; it is a cylindrical shell. This equation is a cylindrical shell rather than a sphere.

Therefore, the given statement, "The shape of this equation is a sphere" is FALSE.

Cylindrical coordinates (r, θ, z) are a coordinate system that defines a point in three-dimensional space. It is similar to the polar coordinate system, except that the z-axis is added, resulting in the use of a cylindrical surface to specify the point location.

Let's find the solution.The cylindrical coordinate system is a three-dimensional coordinate system that is defined by the distance from a point in the xy-plane to a fixed point known as the origin, the angle that the point makes with the x-axis, and the vertical height of the point from the xy-plane, which is referred to as the z-coordinate of the point.

When defining a point in three-dimensional space, cylindrical coordinates are commonly used.

A sphere is a three-dimensional object with a curved surface that is equidistant from a single point in space. A spherical coordinate system is often used to specify the position of a point on a sphere. A cylindrical coordinate system, on the other hand, is commonly used to specify the position of a point on a cylindrical shell.

The equation

r - 6 = 0

is given in cylindrical coordinates. This equation is a cylindrical shell rather than a sphere.

Therefore, the given statement, "The shape of this equation is a sphere" is FALSE.

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