Directions: Simplify by combining like terms in each of the following expressions.

1. 1s2 + 10s2 - 21st =

2. 5st - st - t2 =

3. x^{2} + x^{2} + x^{3} =

4. 6x - 4x + 2=

5. 9x - 3s - 2t=

6. 87x + 8x - 1 =

7. 3x + 6x - 2 =

8. 8s - 4s + 3s =

9. 12 + x - 11x =

10. 12x + 24x - 3x - 4 =

11. 14t + 8t - 12t =

12. 17g + 14g - 6g + g =

13. 13 + 12 - 12 + 13x =

14. 17s - 3s + 3s =

15. 14t - 12t + t =

Mnemonic expressions can be useful for remembering mathematical concepts, formulas, and equations.

PEMDAS: This acronym stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It is used to remember the order of operations in mathematical calculations.

SOH-CAH-TOA: This acronym is used to remember the trigonometric ratios for sine, cosine, and tangent. SOH stands for Sine = Opposite/Hypotenuse, CAH stands for Cosine = Adjacent/Hypotenuse, and TOA stands for Tangent = Opposite/Adjacent.

FOIL: This acronym is used to remember the process of multiplying two binomials. It stands for First, Outer, Inner, Last, and represents the order in which you multiply the terms of the two binomials.

Please Excuse My Dear Aunt Sally: This sentence is used to remember the order of operations in mathematical calculations. It stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

My Dear Aunt Sally Loves Ice Cream: This sentence is used to remember the signs of trigonometric functions in each quadrant of the unit circle. It stands for positive for cosine and ice cream, negative for sine and loves, and alternating for tangent.

These are just a few examples of mnemonic expressions in mathematics, and there are many more that can be used to help remember mathematical concepts and formulas.

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Answer: B. y= 6x -4 and C. 12x -2y=-4

Step-by-step explanation:

I got it wrong on nearpod. but luckily nearpod shows you the correct answer after submitting the answer choices. So these are the actual answers.

The line should cross over the x-axis at the point (0.5,). The line should cross over the y-axis at the point (0,2). To show this on the graph, like the question is asking, you can place one point at (0,2) and another point at (1,-2).

So the shaded region represents 30% of the whole. Each individual square on the grid must represent 1/100 of the whole.

A grid is a network of horizontal and vertical lines that intersect at regular intervals to form a pattern of squares, rectangles, or other shapes. It is commonly used as a tool for visualizing and organizing information, such as in maps, charts, graphs, and other types of diagrams. A grid can be simple or complex, depending on its purpose and the level of detail required. Simple grids may consist of only a few lines, while complex grids may have many lines and sub-divisions. In many cases, grids are labeled with coordinates or numbers to facilitate navigation or data analysis.

Here,

If the grid represents 1 in a grid of 100 squares, then each individual square on the grid must represent 1/100 of the whole.

The shaded region covers 30 squares out of the 100 squares in the grid. So the shaded region represents a fraction of the whole that can be calculated by dividing the number of shaded squares by the total number of squares:

30/100

This fraction can be simplified to:

3/10

Therefore, the shaded region represents three-tenths (3/10) of the whole. Alternatively, we can also express this as a percentage by multiplying the fraction by 100:

(3/10) x 100 = 30%

So the shaded region represents 30% of the whole.

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The required volume of the given cuboid is (B) 3/2 inches³.

A cuboid is a solid shape or a three-dimensional shape in geometry.

A cuboid is a convex polyhedron that has six rectangular faces, eight vertices, and twelve edges.

Another name for a cuboid is a rectangular prism.

A cube is a cuboid with six square faces.

For instance, furniture, books, and televisions all have rectangular frames. It is a cuboid shape.

On the other hand, the 3D shape known as a cube is represented by items like ice, dice, and Rubik's cube. In actuality, a cube is a particular kind of cuboid with square, identical sides.

So, the volume of cuboid:
V= l*w*h

V = 1*1.5*1

V = 1.5

V = 1/5 = 3/2

Therefore, the required volume of the given cuboid is (B) 3/2 inches³.

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Theoretically, there is a probability of 23.1%, or about 0.231, chance that a face card will be drawn at random from a deck of playing cards.

Each of the four suits hearts, diamonds, clubs, and spades in a conventional deck of playing cards, which has 52 cards total, has 13 cards (Ace, 2-10, Jack, Queen, and King). Among these 52 cards, there are 12 face cards (Jacks, Queens, and Kings). So the number of face cards is 12, and the total number of cards is 52.

The probability of selecting a face card can be calculated by dividing the number of face cards by the total number of cards:

[tex]P_{face card}[/tex] = [tex]\frac{number of face cards}{total number of cards}[/tex]

= 12 / 52

= 3 / 13

≈ 0.231 or 23.1%

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The complete question is:

Find the theoretical probability of randomly selecting a face card​ (J, Q, or​ K) from a standard deck of playing cards

If Zanele realized that the questiοnnaire is nοt suitable, it cοuld be fοr variοus reasοns, such as:

What is yοur name?

Name may nοt be needed tο prοvide advice οn taking a gap year.

Why dο yοu think that it is wise tο take a gap year after schοοl?

Taking a gap year after schοοl can prοvide students with a break frοm academic studies, help them gain life experience, and give them time tο explοre their interests befοre cοmmitting tο a university degree.

The benefits οf taking a gap year include persοnal and academic grοwth, increased indeοendence, cultural exοοsure, and the οοοοrtunity tο gain valuable wοrk οr vοlunteer exοerience.

Sοme students chοοse tο delay taking a gap year tο οursue a university degree first sο that they can stay οn track with their academic and career gοals. Others may want tο save mοney οr avοid interruοting their academic mοmentum.

The best way tο spend a gap year deοends οn yοur interests and gοals. Sοme pοpular gap year activities include traveling, vοlunteering, interning, wοrking, learning a new language οr skill, οr pursuing a passiοn prοject.

If Zanele realized that the questiοnnaire is nοt suitable, it cοuld be fοr variοus reasοns, such as:

The questiοns may nοt be relevant tο her specific situatiοn οr gοals.

The questiοns may nοt prοvide enοugh infοrmatiοn οr οptiοns tο help her make an infοrmed decisiοn.

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Answer:

Step-by-step explanation:

We are given that Lisa's age plus Sean's age is 17 years and Sean is 11 years old .

We need to find the age of Lisa.

Let's assume age of Lisa be x years.

A/q Lisa's age plus Sean's age is 17

[tex] \longrightarrow \: x + Sean's \: age = 17 \\ \\ \longrightarrow \: x + 11 = 17 \\ \\ \longrightarrow \: x = 17 - 11 \\ \\ \longrightarrow \: x = 6 \\ \\ [/tex]

Hence, Lisa is 6 years old.

Answer:

70% watched less than an hour.

Step-by-step explanation:

Less than 1 hour -- 3 people

Number of people 10

3/10 -- 30% of people watch less than 1 hour.

The Tortillas in 2 Packages from Given Data is 14

To determine how many tortillas are in 2 packages, we can use the given data to find the relationship between the number of packages and the number of tortillas.

From the table, we can see that there is a linear relationship between the two variables, with each package containing 7 tortillas.

Therefore, we can calculate the number of tortillas in 2 packages by multiplying 2 by 7,

So, we have

Packages = 2 * 7

Packages = 14

The answer of 14 tortillas in 2 packages.

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Complete question

A grocery store sells packages of fresh tortillas. The table shows the relationship between the number of packages and the number of tortillas. How many tortillas are in 2 packages?

Number of Packages   Number of Tortillas

5                                 35

7                                 49

15                             105

Answer:

Starting unpaid balance = $5942.00

On April 1st: Starting unpaid balance = $5942.00

On April 10th: $124.00 purchase is made, so the new balance becomes $5942.00 + $124.00 = $6066.00

On April 22nd: $1000.00 payment is made, so the new balance becomes $6066.00 - $1000.00 = $5066.00

On April 28th: $628.00 purchase is made, so the new balance becomes $5066.00 + $628.00 = $5694.00

Therefore, the ending balance on Jerry's credit card statement at the end of April is $5694.00.

Step-by-step explanation:

It would cost $13.02 to buy a Rectangle type frame for the painting.

What exactly is a rectangle?

A rectangle is a two-dimensional geometric shape that is characterized by having four sides and four right angles. It is a type of quadrilateral.

The opposite sides of a rectangle are parallel and equal in length, and the adjacent sides are perpendicular to each other. This means that the opposite sides of a rectangle have the same distance apart throughout their entire length. The Perimeter is given by 2(L+B), where L and B are length and breadth respectively.

Now,

The painting measures 1 meter by 2 meters, so the perimeter of the painting (the total length of its sides) is:

P = 2 x (1 + 2) = 2 x 3 = 6 meters

To frame the painting, we need to buy a wooden frame with a perimeter of 6 meters. The frame shop charges $2.17 per meter for the wooden frame, so the cost of the frame would be:

Cost = 6 x $2.17 = $13.02

Therefore, it would cost $13.02 to buy a frame for the painting.

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Answer:

Step-by-step explanation:

From the property of logarithm the input cannot be negative.

Therefore Z should be negative

As from the given question both sides have the (ln)
operator thus we can remove it.

-5Z=z^2-7Z

2Z=Z^2

Z^2=2Z

Z=2

The outcome that is most likely to occur after rolling the cube 100 times is that an even number would be rolled around 50 times.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

A fair number cube labeled with the numbers 1 - 6 is equally likely to land on any of its faces when rolled.

Therefore, we can use probability to determine which outcome is most likely to occur after rolling the cube 100 times.

"The number 6 would never be rolled." This outcome is highly unlikely, but not impossible.
If the cube is fair, each number has an equal probability of being rolled, so the probability of rolling a 6 on any given roll is 1/6.

The probability of rolling a non-6 on any given roll is 5/6. The probability of not rolling a 6 in 100 rolls is (5/6)¹⁰⁰, which is approximately 0.0001. So, while it is very unlikely that the number 6 would never be rolled, it is not impossible.

"All the numbers rolled would be odd." This outcome is even less likely than the first one.

The odd numbers on the cube are 1, 3, and 5, each with a probability of 1/2.

The probability of rolling an odd number on any given roll is 1/2.

The probability of rolling an odd number on 100 rolls is (1/2)¹⁰⁰, which is an extremely small number, approaching zero.

"An even number would be rolled 50 times." This outcome is more likely than the first two.

The even numbers on the cube are 2, 4, and 6, each with a probability of 1/2.

The probability of rolling an even number on any given roll is 1/2.

If we assume that each roll is independent of the others, the probability of rolling an even number exactly 50 times in 100 rolls can be calculated using the binomial distribution and is approximately 0.0796.

This means that this outcome is not very likely, but still possible.

"The number 7 would be rolled at least once."

This outcome is impossible since the cube is only labeled with the numbers 1 through 6.

Therefore, the number 7 cannot be rolled.

Hence, Based on the above analysis, the outcome that is most likely to occur after rolling the cube 100 times is that an even number would be rolled around 50 times.

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Answer:

To find the resultant of two forces, you can use the following formula:

R^2 = F1^2 + F2^2 + 2F1F2cosθ

Where R is the resultant force, F1 and F2 are the magnitudes of the two forces, θ is the angle between the two forces, and cosθ is the cosine of the angle.

Plugging in the given values, we get:

R^2 = (500 kg)^2 + (875 kg)^2 + 2(500 kg)(875 kg)cos(100 deg)

R^2 = 250000 + 765625 + 767321.98

R^2 = 1788946.98

R = sqrt(1788946.98) ≈ 1337.3 kg

So the magnitude of the resultant force is approximately 1337.3 kg.

To find the angle that the resultant force makes with the smaller force, we can use the following formula:

tanθ = (F2sinθ)/(F1 + F2cosθ)

Where θ is the angle between the resultant force and the smaller force.

Plugging in the given values, we get:

tanθ = (875 kg sin(100 deg))/(500 kg + 875 kg cos(100 deg))

tanθ = 0.768

θ = tan^-1(0.768) ≈ 36.2 deg

So the angle that the resultant force makes with the smaller force is approximately 36.2 degrees.

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Answer:

The 99% confidence interval for the population proportion is between (0.4526, 0.4960). The interpretation is that we are 99% sure that the true proportion of adults who have started paying bills online in the last year is between these two values.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\dfrac{\pi (1-\pi )}{n} }[/tex]

In which

z is the z-score that has a p-value of [tex]1-\dfrac{\alpha }{2}[/tex].

For this problem, we have that:

In a survey of 2954 ​adults, 1401 say they have started paying bills online in the last year. This means that [tex]n=2954, \ p=\dfrac{1401}{2954} =0.4743[/tex]

99% confidence level

So [tex]\alpha =0.01[/tex], z is the value of Z that has a p-value of [tex]1-\dfrac{0.01}{2} =0.995[/tex], so [tex]Z=2.575[/tex].

The lower limit of this interval is:

[tex]\pi -z\sqrt{\dfrac{\pi (1-\pi)}{n} } =0.4743-2.575\sqrt{\dfrac{0.4743\times0.4408}{2954} } =0.4526[/tex]

The upper limit of this interval is:

[tex]\pi -z\sqrt{\dfrac{\pi (1-\pi)}{n} } =0.4743+2.575\sqrt{\dfrac{0.4743\times0.4408}{2954} } =0.4960[/tex]

The 99% confidence interval for the population proportion is between (0.4526, 0.4960). The interpretation is that we are 99% sure that the true proportion of adults who have started paying bills online in the last year is between these two values.

Answer:

Step-by-step explanation:

Three and one-half times one and two-thirds is equal to 35/6 or 5 5/6.

Given the statement in the question; "three and one-half times one and two-thirds"

First, we can be written as a fraction:

Three and one-half → 3 1/2 = 7/2

One and two-thirds → 1 2/3 = 5/3

So, we have:

(7/2) × (5/3)

To multiply these fractions, we multiply the numerators together and the denominators together:

( 7 × 5 ) / ( 2 × 6 )

35/6

5 5/6

Therefore, the simplified form is 35/6 or 5 5/6.

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According to your query I am defining you multiply in simple manner.

The term multiply refers to the mathematical operation of repeatedly adding a number to itself a certain number of times. The result of this operation is known as the product. Multiplication is an essential arithmetic operation that is used in various fields, including science, engineering, and economics.

Multiplication is typically represented by the symbol "×" or "*", and the numbers being multiplied are called factors. For example, if we multiply 2 and 3, we get the product 6, which can be written as 2 × 3 or 2 * 3.

Multiplication has several important properties, including the commutative property, which states that the order of the factors does not affect the product. For example, 2 × 3 is equal to 3 × 2.

Another important property of multiplication is the distributive property, which states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each of the individual numbers. For example, 2 × (3 + 4) is equal to (2 × 3) + (2 × 4), which simplifies to 14.

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According to your query when you multiply in simple manner and it simplifies to 7/5.

The term multiply refers to the mathematical operation of repeatedly adding a number to itself a certain number of times. The result of this operation is known as the product. Multiplication is an essential arithmetic operation that is used in various fields, including science, engineering, and economics.

Multiplication is typically represented by the symbol "×" or "*", and the numbers being multiplied are called factors. For example, if we multiply 2 and 3, we get the product 6, which can be written as 2 × 3 or 2 * 3.

For the given question:

11/7 × 49/5

= 539/35

= 7/5

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The complete question is as follows:

By evaluating the linear function in different values of x, we will get the complete table:

x         f(x)

-3         -6

-2         -16/3

0            -4

3             -2

6              0

Here we have a table of x and f(x) and we want to complete it, to do so, we only need to evaluate the function in different  values of x and then put that in the correspondent places.

if x = -2

f(-2) = (2/3)*-2 - 4

      = -4/3 - 4 = -4/3 - 12/3 = -16/3

if x = 0

f(0) = (2/3)*0 - 4 = -4

if x = 3

f(3) = (2/3)*3 - 4 = 2 - 4 = -2

if x = 6

f(6) = (2/3)*6 - 4 = 0

Then putting these in the table, we will get:

x         f(x)

-3         -6

-2         -16/3

0            -4

3             -2

6              0

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(a) The size of angle x will be 90°.

(b) The theorem that helped to solve this problem is, the angle between the tangent and the radius at a point on a circle is 90°.

What is a circle's radius?

The radius of a circular is the separation between any two points on its circumference. R or r is typically used to indicate it. This amount is significant in practically all formulae involving circles. A circle's radius may also be used to calculate its surface area and circumference. Circle circumference equals two.

What are diameter and radius?

The circle's center is where a straight line called the diameter lies. Half of the size makes up the radius. It originates with a point circle and finishes at the circle's center.

Due to the fact that the angle between the tangent and the radius at a point on a circle is 90°.

As a result, angle x = 90°.

(b)The circle theorem that allows the calculation of angle is:

The angle between the tangent and the radius at a point on a circle is 90°.

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For the given equation, the values of X and Y are X=4 and Y=-2, respectively.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=).

To find the values of X and Y, we need to separate the real and imaginary parts of the complex number on the right-hand side of the equation.

We have:

X + Yi = 3Y - 2Xi + 4i

Separating the real and imaginary parts, we get:

X = -2Y + 0

Y = 3Y + 4

Simplifying the second equation, we have:

-2Y = 4

Dividing by -2, we get:

Y = -2

Substituting this value of Y into the first equation, we have:

X = -2(-2) = 4

Therefore, the values of X and Y are X=4 and Y=-2, respectively.

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Since there are 12 face cards (4 J, 4 Q, 4K) those represent 12/52.  The nonface cards excluding aces (4 twos through 4 tens) represent 36/52.

The expected value is then:

(12/52)($3)+(36/52)(-$2)= -$36/52 or -$0.69 but rounding to one decimal would be -$0.70

Answer: Y=10

Step-by-step explanation: please label me brainiest if I'm right

Therefore , the solution of the given problem of angles comes out to be  the detour via Town P is approximately 3.05 km longer .

The largest and smallest walls of a skew are determined by the point at which the lines that make up its ends meet. At a junction, it's possible that two routes will cross. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.

Here,

We can determine the length of the road from B to P using the rule of cosines:

=> BP² = AB² + AP² - 2AB(AP)cos(20°)

=>  BP² = x² + 4² - 2x(4)cos(20°)

We can determine the length of the detour via town P by using the rule of cosines once more:

y² = AP² + BP² - 2(AP)(BP)cos(110°)

y² = 4^2 + BP² - 2(4)(BP)cos(110°)

y² = 16 + BP² + 8BP(0.342)

y² = 16 + x² + 16 - 8x(cos(20°))(0.342) + 8(4)(0.342)(BP)

y²= 32 + x² - 2.75x + 1.368BP

=> BP² = x²+ 4² - 2x(4)cos(20°)

=> BP² = x² + 16 - 8x(cos(20°))

=> BP² = sqrt(x² + 16 - 8x(cos(20°)))

=> y² = 32 + x²- 2.75x + 1.368(sqrt(x^2 + 16 - 8x(cos(20°))))

=>  y - x = √(y²) - x

=>  y - x = √(32 + x² - 2.75x + 1.368(√x² + 16 - 8x(cos(20°))))) - x

With the aid of a computer, we can determine that y - x is roughly 3.05 km.

Consequently, the detour via Town P is approximately 3.05 km longer .

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Answer:

Step-by-step explanation:

Solve for the variable. Determine if there is one solution, infinitely many solutions, or no solution.

-6x – 12 = 5(-2x – 3)

Let's start by simplifying the right side of the equation:

5(-2x – 3) = -10x - 15

Substituting this back into the original equation, we get:

-6x - 12 = -10x - 15

Next, we can simplify this equation by adding 10x to both sides:

4x - 12 = -15

Finally, we can add 12 to both sides:

4x = -3

Dividing both sides by 4 gives us:

x = -3/4

Therefore, there is one solution, and x equals -3/4.

The length of the rectangular lot is 30m

The formula for calculating the perimeter of a rectangle is expressed as;

P =2(l + w)

Such that the parameters are;

From the information given, we have that;

Length = 5 + w

Now, substitute the values

110 = 2( 5 + w+ w)

collect the like terms

110 = 2(5 + 2w)

expand the bracket

110 = 10 + 4w

4w = 100

Divide both sides by the coefficient of w

w = 25

Then, the length = 30m

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