2. Use the linear combination method to solve the system of equations. Explain each step of your solution.
2x – 3y = 13
3x + y = -8

Answer:12

Step-by-step explanation:

50% of 20 is 10, 10% of 20 is 2 so just add them together.

The range of values in which at least 88.89% of the fake prices will lie if the standard deviation is $53,500 will be  $84,600 and $391,600.

What does standard deviation mean in plain English?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                         Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The lower boundary of the range is calculated by subtracting two standard deviations from the average sale price

$238,100 - $53,500 = $84,600

The upper boundary of the range is calculated by adding two standard deviations to the average sale price

$238,100 + $53,500 = $391,600

Therefore, the range of values in which at least 88.89% of the fake prices will lie is between $84,600 and $391,600.

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Answer:

We can start by using logarithmic properties. If a, b, and c are positive numbers, then:

loga^b = b * loga

Using this property, we can rewrite the expression as:

x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = x^(logy/logx - logz/logx) * y^(logz/logy - logx/logy) * z^(logx/logz - logy/logz)

Using the change-of-base formula, we can simplify the exponents:

x^(logy/logx - logz/logx) = (logy/logx) / (logz/logx) = logy/logz

Similarly,

y^(logz/logy - logx/logy) = logz/logx

and

z^(logx/logz - logy/logz) = logx/logy

Now, we can substitute these results back into the original expression:

x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = logy/logz * logz/logx * logx/logy

By the transitive property of logarithms, we have:

logy/logz * logz/logx * logx/logy = logy/logx

Finally, using the change-of-base formula again, we can simplify this result:

logy/logx = y^(1/logx) / x^(1/logx)

Since y and x are positive numbers, their exponents must also be positive. Therefore, we have:

y^(1/logx) / x^(1/logx) = 1

So,

x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = 1

And we have proven that the expression is equal to 1.

Step-by-step explanation:

The solution area on the graph is labeled A on the attached figure

From the question, we have the following parameters that can be used in our computation:

The inequalities y-2x≤4,3y+x≥6, y≥27x-9

Express properly

So, we have

y - 2x ≤ 4

3y + x ≥ 6

y ≥ 27x -9

next, we represent the inequalities on a graph

See attachment

The area of the solution set of the graph is labelled A

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Answer:

42.9

Step-by-step explanation:

tan 40 = 36/x

so x = 36/tan 40 =36/0.84 =42.9

The correct statement regarding the solution of the expression is given as follows:

Miguel made no mistakes.

The expression for this problem is defined as follows:

32/[2(2³ - 4)].

The parenthesis has precedence, and inside the parenthesis, the cube has precedence, hence:

32/[2(8 - 4)] = 32/[2(4)]

Multiplying in the denominator and then dividing the numerator by the denominator, the result is given as follows:

32/[2(4)] = 32/8 = 4.

Meaning that no mistake was made.

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The option that is correct is ' This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method. (optionA)

Factoring a polynomial is expressing the polynomial as a product of two or more factors; it is somewhat the reverse process of multiplying. To factor polynomials, we generally make use of the following properties or identities; along with other more techniques. Distributive Property: ab+ac=a(b+c)

To factorize the expression 2x3 + 4x2 + 2x

Let's factor out the Greatest common factor which is 2x

2x( x²+2x+1)

2x( x² +2x + 1)

Therefore the factors of 2x³ + 4x²+ 2x are 2x and x²+2x+1)

Therefore the expression can be factored by finding the GCF and then grouping or using perfect square method.

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The classifications are done as follows

6. < 2 : acute angle

7. < ABC : angle on a straight line

8. < 2 = 41 degrees

9. x = 45

In the figure, BE bisects < DBC hence < 2 = < 3 = y

98 + < 2 + < 3 = 180

y + y = 180 - 98

2y = 82

y = 41

In the figure, < WXY = 88 where the adjacent angles are

< WXZ = 4x - 3 and < ZXY = 2x + 1

4x - 3 + 2x + 1 = 88

4x + 2x = 88 + 3 - 1

2x = 90

x = 45

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Answer:

x≥−1

Step-by-step explanation:

The domain of the inverse of a function is the range of the original function. The range of the cubic root function is y≥−1, so the domain of its inverse would be x≥−1.

Answer:

x≥−1, x is greater than or equal to negative 1

Step-by-step explanation:

The inverse of a function switches the roles of x and y, making the original range the new domain and the original domain the new range. In this case, the original domain is x≥7 and the range is y≥−1, so the inverse has a domain of y≥−1 and a range of x≥7 :)

Hi there, here's your answer.

Given:

A circle with center O.

A, B, C and D lie on the circumference of the circle.

AC is the diameter of the circle.

∠DCA = 33° and ∠BCA = 31°

To find:

∠DAB

Solution:

Since AC is a diameter, ∠CDA and ∠CBA will be equal to 90° (Angles in a semi-circle)

Now, ∠BCD = ∠DCA + ∠BCA

∴ ∠BCD = 33° + 31° = 64°

Now, ∠BCD + ∠CDA + ∠DAB + ∠ ABC = 360° (Angle-sum property of a quadrilateral)

Substituting the values of the angles:

64° + 90° + 90° + ∠DAB = 360°

Or

244° + ∠DAB = 360°

Therefore ∠DAB = 360° - 244° = 116°

Hope it helps!

Answer: Lincoln drove 15 miles in 12 minutes, so he drove a total of 60 minutes because 60/12 = 5.

Thus, Lincoln drove a total of 15 * 5 = 75 miles.

Step-by-step explanation:

Answer:

Step-by-step explanation:

458210 in binary

=10001111001102

The percentage of the ratio 13:20 is approximately 39.39%.

What is the percentage?

In mathematics, a percentage is a way of expressing a number as a fraction of 100. Percentages are often used to represent proportions, rates, or changes in quantities. The word "percent" means "per hundred," so a percentage is equivalent to the corresponding fraction multiplied by 100.

To find the percentage of a ratio, we need to convert the ratio to a fraction and then multiply by 100 to express it as a percentage.

The ratio 13:20 can be written as a fraction by dividing the first term by the sum of the terms

13 / (13 + 20) = 13/33

To express this fraction as a percentage, we multiply by 100:

(13/33) x 100 = 39.39%

The grid can be shaded as below:

Therefore, the percentage of the ratio 13:20 is approximately 39.39%.

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Five general things we get from natural resources are food, energy, raw material, medicine, leisure, recreation.

Resources refer to the materials, substances, and energy sources that exist in the environment and can be used to produce goods and services. They can be natural, such as minerals, water, forests, and wildlife, or human-made, such as technology, infrastructure, and knowledge. The term "resources" also encompasses the availability and accessibility of these materials, as well as the ability to use and manage them sustainably.

Food: Natural resources such as crops, fisheries, and livestock provide us with a source of nutrition.

Energy: Resources such as coal, oil, natural gas, and hydroelectric power are used to produce energy for heating, transportation, and other forms of electricity.

Raw Materials: Natural resources such as minerals, metals, and forests provide the raw materials needed to manufacture a wide range of products, including construction materials, electronics, and consumer goods.

Medicines: Many natural resources, such as plants and minerals, have medicinal properties that can be used to treat and prevent diseases.

Leisure and recreation: Natural resources like parks, forests, lakes, and beaches provide opportunities for outdoor recreation and leisure activities, contributing to our mental and physical well-being.

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The value of sin(x) in terms of cos(x) is √1 - cos²(x). The value of sin(x) is 3/5.

Since x is an angle in the second quadrant, sin(x) is positive and cos(x) is negative.

To write sin(x) in terms of cos(x), we can use the identity sin²(x) + cos²(x) = 1 and solve for sin(x):

                                sin²(x) + cos²(x) = 1

                                sin²(x) = 1 - cos²(x)

                                sin(x) = ± √(1 - cos²(x))

Since sin(x) is positive in the second quadrant, we have:

                               sin(x) = √(1 - cos²(x))

To show that cos(x) = -4/5, we can use the given equation:

                               3sin(x) - 4cos(x) = 5

We can rearrange this equation to get cos(x) on one side:

                              4cos(x) = 3sin(x) - 5

                              cos(x) = (3sin(x) - 5) / 4

Now we can substitute the expression for sin(x) that we found earlier:

                              cos(x) = (3√(1 - cos²(x)) - 5) / 4

Multiplying both sides by 4 and simplifying, we get:

                              4cos²(x) + 3cos(x) - 4 = 0

This is a quadratic equation in cos(x). We can solve it using the quadratic formula:

                             cos(x) = [-3 ± √(3² - 4(4)(-4))] / (2(4))

                             cos(x) = (-3 ± 7) / 8

                             cos(x) = 1/2 or cos(x) = -4/5

Since x is in the second quadrant, we have cos(x) < 0, so cos(x) = -4/5.

Finally, we can use the expression for sin(x) that we found earlier to get:

                            sin(x) = √(1 - cos²(x))

                            sin(x) = √(1 - (-4/5)²)

                            sin(x) = √(1 - 16/25)

                            sin(x) = √9/25

                            sin(x) = 3/5

Therefore, the exact value of sin(x) is 3/5.

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Answer:

x = 6

Step-by-step explanation:

the opposite sides in a rectangle are congruent.

since the rectangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{5x}{18}[/tex] = [tex]\frac{10}{x}[/tex] ( cross- multiply )

5x² = 18 × 10 = 180 ( divide both sides by 5 )

x² = 36 ( take square root of both sides )

x = [tex]\sqrt{36}[/tex] = 6

The fourth vertex of the parallelogram is (3,-5) .

A vertex is a point on a polygon where the sides or edges of an object meet, or where two rays or line segments meet. The plural form of vertex is vertex.

vertex - side or edge

For example, in the figure above, points A, B, C, D, and E are vertices.

Let  A(-1, 0), B(1, 3), C(5,-2) and D(x, y) be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other.

∴   Coordinates of the mid-point of AC=Coordinates of the mid-point of BD(

([tex]\frac{-1+5}{2}[/tex],[tex]\frac{0-2}{2}[/tex])=([tex]\frac{1+x}{2}[/tex],[tex]\frac{3+y}{2}[/tex])

([tex]\frac{4}{2}[/tex],[tex]\frac{-2}{2}[/tex])=([tex]\frac{1+x}{2}[/tex],[tex]\frac{3+y}{2}[/tex])

Equating both side coordinate respectively

[tex]\frac{1+x}{2}[/tex]=2

1+x=4

x=3

[tex]\frac{3+y}{2}[/tex]=-1

3+y=-2

y=-5

⇒x=3andy=-5

Hence, the fourth vertex of the parallelogram is (3,-5)

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The new function, g(x), will be stretched or compressed by a factor of two, making it equivalent to f(2x).

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. This specific sort of relationship is thus defined.

A function called f(x) is displayed in the coordinate plane.

The formula is g(x) = f. (2x)

It is the transformation of the f, as we can see in the new function g(x) (x).

Applying transformation is done as follows:

x → 2x (x is replaced by the twice of it) (x is replaced by the twice of it)

= f(x) (x)

= f(2x) (2x)

= g(x) (x)

In the given function, the factor is 2, thus the g(x) will be stretched or compressed in accordance with that factor. When the function is multiplied by a positive number, it will be compressed or stretched vertically according to that factor.

As a result, the new function g(x), which is equal to f(2x), will be expanded or contracted by a factor of 2.

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The initial payment for the first 3 years of an interest-only loan for a $141,000 5/130-year ARM at 5% would be $7050.

An ARM, or Adjustable Rate Mortgage, is a type of mortgage loan where the interest rate can change over time. The 5/1 in the loan term "5/130-year ARM" means that the initial rate is fixed for the first 5 years and can change once every year thereafter for the remaining life of the loan (in this case, 130 years).

For an interest-only loan, the borrower pays only the interest due on the loan for a set period of time, in this case, the first 3 years. The interest payment can be calculated as:

Interest payment = Loan amount * Interest rate

The loan amount in this case is $141,000 and the interest rate is 5%, so the interest payment is:

Interest payment = $141,000 * 0.05 = $7050

So, the initial payment for the first 3 years of an interest-only loan for a $141,000 5/130-year ARM at 5% would be $7050.

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1930.54 can be written in standard form as 1.93054 × 10³. Option D is correct.

A number can be written in standard form to make it simpler to read. It is frequently used for extremely high or extremely low figures. Mathematics and other science fields employ the use of standard form, which is similar to scientific notation.

When a decimal number is multiplied by a power of 10, it is said to be expressed in standard form.

Similar to scientific notation, standard form represents a number as a decimal number times a power of 10. (i.e a*10^b)

From the given information:

1930.54 can be written in standard form as 1.93054 × 10³

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The number of ways can a person toss a coin 12 times so that the number of heads is between 7 and 11 inclusive is 1585.

Combinations are methods for choosing elements from collections of objects. Unlike permutations, selection order is unimportant. The number of combinations can be counted in simpler situations.  

The formula for combinations is given by

Here we have

Number of tosses = 12 times

The number of heads is between 7 and 11 inclusive    

Number of ways of getting 7 heads and 5 tails

= 12! / (7!5!) = 792  

Number of ways of getting 8 heads and 4 tails

= 12!/(8!4!) = 495    

Number of ways of getting 9 heads and 3 tails

= 12!/(9!3!) = 220  

Number of ways of getting 10 heads and 2 tails

= 12!/ (10!2!) = 66

Number of ways of getting 11 heads and 1 tail

= 12! / (11!1!) = 12  

Total number of ways = 792 + 495 + 220 + 66 + 12

= 1585

Therefore,    

The number of ways can a person toss a coin 12 times so that the number of heads is between 7 and 11 inclusive is 1585.

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Answer:

Sarah purchased 2 first class tickets and 5 coach tickets.

Step-by-step explanation:

Let's call the number of first class tickets purchased "x".

The number of coach tickets purchased would be 7-x.

We know that the total spent on first class tickets was $1170 * x and the total spent on coach tickets was $320 * (7-x).

The total budget was $3940, so we can set up the following equation:

$1170 * x + $320 * (7-x) = $3940

Expanding the right side:

$1170 * x + $320 * 7 - $320 * x = $3940

Combining like terms:

$800 * x = $3940 - $320 * 7

Subtracting $320 * 7 from both sides:

$800 * x = $3940 - $2240

$800 * x = $1700

Dividing both sides by 800:

x = 2.125

Since x must be a whole number, Sarah purchased 2 first class tickets and 5 coach tickets.

Step 1: Calculate the volume of the water in the first container.

The volume of a cylinder is V = πr^2h, where r is the radius of the cylinder and h is the height of the cylinder.

Therefore, the volume of the water in the first container is V = πr^2 x 15 cm, where r is the given radius of the container.

Step 2: Calculate the height of the water in the second container.

The volume of the water in the second container is the same as the volume of the water in the first container, since the same quantity of water is being poured from one container to the other.

Therefore, the volume of the water in the second container is also V = πr^2 x 15 cm, where r is now 2r, the radius of the second container.

To find the height of the water in the second container, we can substitute the value of the radius into the equation for the volume and solve for h. This gives us h = (15 cm) / (π(2r)^2), which simplifies to h = 15 cm / 4πr^2.

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The area of a parallelogram with given sides and angle between them is equal to 19847 square foot.

Let us consider the two sides of a parallelogram be x feet  and y feet.

x = 270 feet

y = 470 feet

Angle between x and y is 9°

Diagonal divides the parallelogram into two congruent triangles

Area of a parallelogram = 2 × Area of a triangles

Area of triangle = ( 1/ 2) ( x × y × sin9° )

                          = (1/2) ( 270 × 470 × sin9° )

                          = ( 1/2) ( 270 × 470 × 0.1564 )

                          = 9923.58 square feet

Area of a parallelogram = 2 × 9923.58

                                        = 19847.16

                                        = 19847 square foot.

Therefore, the area of a parallelogram for the given measurements is equal to 19847 square foot.

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The percentage of No purchase is 26%, the computer is 59.9% and the printer is 22%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that he collected the following data during a recent week: 327 customers visited the store, 196 purchased computers, 72 purchased printers, and 87 made no purchase.

The percentage of No purchase is:-

P = 87 / 327

P = 26%

The percentage of computer purchases:-

P = 196 / 327

P = 59.9%

The percentage of printer purchases is:-

P = 72 / 327

P = 22%

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Answer: the answer is C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It's like connecting the dots

For example, BD. When you draw a line from B to D, you have to touch O at some point.

That happens for all of them except one, which is a.) AB.

When you connect points A and B, you never touch point O

Edit; What the other person said is right actually. I'm wrong. He gets my 5 stars.

Answer:  11/8 ( 1 3/8)

Step-by-step explanation: Look at the attachment below for the best experience. First, before we add we need to find the common denominator of the denominators (2, 4, 8) That'd be 8, because 2, 4, 8 . Look at the explanation for the best view.

The frequency tree will be:

Tree imagination attached as image below.

This question can be answered by calculating the ratio of boys to girls and the number of people with and without vouchers.

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Therefore , if we know the measures of the angles θ1 and θ2 in degrees, we can use equations (1) and (2) to find their difference, α - β.

An angle in Euclidean space is a shape made up of two poles that divide at the centre, or apex, of the structure. These beams are referred to as the sides or loops. When two rays are combined, there may be an inclination inside this surfaces where they are situated. Angles can also be created by combining two surface.

Here,

Since the two angles share the same terminal side, they are coterminal angles. This means that they differ by an integer multiple of 360 degrees or 2π radians.

Let the two angles be θ1 and θ2. Then we can express them as:

θ1 = k(360°) + α (1)

θ2 = k(360°) + β (2)

where k is an integer and α and β are the measures of the angles in degrees, such that 0° ≤ α, β < 360°.

Since the angles share the same terminal side, they must add up to 360 degrees or 2π radians. So we have:

θ1 + θ2 = k(360°) + α + k(360°) + β = 360° (3)

Simplifying equation (3), we get:

θ1 + θ2 = 2k(360°) + α + β = 360°

α + β = 360° - 2k(360°) = 360°(1 - 2k)

Therefore, the sum of the two angles α and β is equal to 360 degrees times an integer 1-2k.

To find the difference between the two angles, we can subtract equation (2) from equation (1):

θ1 - θ2 = (k(360°) + α) - (k(360°) + β) = α - β

Therefore, the difference between the two angles is equal to the absolute value of the difference between their measures in degrees:

|α - β| = |θ1 - θ2|

Note that since the angles are coterminal, their measures differ by an integer multiple of 360 degrees, so the difference between their measures can be found by subtracting one from the other and taking the result modulo 360. That is:

α - β = (θ1 - θ2) mod 360°

So if we know the measures of the angles θ1 and θ2 in degrees, we can use equations (1) and (2) to find their difference, α - β.

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