p(x) = x2 – 1 and q (x) = 5 (x minus 1), which expression is equivalent to (p – q)(x)?

Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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A teacher, she is measuring the height of students, She gets data from 500 students, the visual displays is most appropriate is, Bar chart. So option A is correct.

Statistics is a process in which we collect, interpret, study and understand the data. We took a small sample from the large quantity and then we did study of the sample then according to results, we did our predictions for events which can happen in future.

Given that,

A teacher is measuring the height of students at her high school

She gets data from 500 students at her high school

Most appropriate visual displays by,

The bar graph,

because it will show result,

In rectangular columns and vertical height can represent the number of students,

Different  columns can represent the range of height

Hence, the appropriate choice is Bar chart

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The lateral surface area and total surface area of the given triangular prism are 252cm² and 348 cm² respectively.

The entirety of an object's sides, excluding its base and top, are referred to as the lateral surface. The size of the lateral surface is referred to as the lateral surface area. The total surface area, which includes the lateral surface area as well as the areas at the base and top, should be distinguished from this.

Total surface area of this prism = 3 × l × b + 2 × h × b

= 3 × 14 × 6 + 2 × 8 × 6

= 348 cm²

And lateral surface area =  3 × l × b

= 3 × 14 × 6

= 252cm²

Thus, the lateral surface area and total surface area of the given triangular prism are 252cm² and 348 cm² respectively.

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The expression 1500 to the square root of 3 to the square root is approximately equal to 44.7.

The expression 1500 to the square root of 3 to the square root can be simplified using exponent rules. Recall that [tex]( {a}^{b} )^{c} = {a}^{b \times c} [/tex] for any positive real numbers a, b, and c.

Therefore, the expression becomes,

[tex] {1500}^{ { \frac{1}{2} }^{ \frac{3}{2} } } [/tex] where the inner square root of 3 can be written as [tex] \frac{ {2}^{ \frac{3}{2} } }{2} [/tex].

Evaluating the expression, we have

[tex] {1500}^{ { \frac{1}{2} }^{ \frac{3}{2} } } = {1500}^{ {2}^{ \frac{1}{2} } } = {1500}^{1.41...} [/tex], where 1.41... is the square root of 2.

To the best of our approximation, the exact value of [tex] {1500}^{1.41...} [/tex] is approximately 44.7.

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answer: A survey

explanation: The manager of the restaurant is conducting a survey to determine which sandwich is more preferred by customers. He is taking a random sample of customers that have tried both sandwiches and asking them which sandwich they like best. The survey method is a statistical way of collecting data and it is a non-experimental design, because the manager is not controlling the variables that may affect the outcome. The outcome of this survey is based on the customers' preference of the sandwiches, and it is a way to gather data on their opinion

On solving the provided question, we can say that by percentage

20% of 1570 => 20/100 X 1570=314; rent = 1570 - 314 = $1256

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

A couple has a combined income of = $15,720 per year.

they spend 20%

by percentage

20% of 1570

20/100 X 1570

=314

rent = 1570 - 314 = $1256

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Therefore , as a result, there exist four complex numbers.√3, - √3, √15 i, and - √15 i  satisfy the following complex number sequence equations.

An grouping of numbers, or "terms," is called a sequence. Examples are 2, 5, and 8. Some sequences can be made to continue indefinitely by trying to take advantage of a particular pattern that they employ. Using the example of 2,5,8, add 3 to the sequence to continue it. There are equation that can be found in a string of words that indicate where to look. A sequence in mathematics is a group of objects that are ordered in some way (or events). 

Here,

Given:

The complex plane's reflection on the real line is referred to as complex conjugation. The complex conjugation of z can be represented by either Z or z. The complex conjugate has identical real and imaginary parts, but the imaginary part has the opposite sign.

It follows from z=a+ib, in other words.

There are four complex numbers. √3, - √3, √15 i, - √15 i  satisfy the following complex number sequence equations.

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Answer: I agree with both of them

Step-by-step explanation:

A dozen is 12

And a dozen cost $3.00,

To get how many mini muffins they can get for$1.00= 12/3 =4 mini muffins

Andre has $2.00 =2*4=8 he can get 8 mini muffins.

Elena wants 16 mini muffins.

She'll need $4.00

=16/4= $4.00

Answer:

20 feet

Step-by-step explanation:

6(3)=18

60/3=20

Answer: The building would be 20 feet tall

Step-by-step explanation: If the 6 foot man was casting a shadow of 18 feet you can figure out that 6 times 3 is 18 and then take 60 divided by three to get an answer of 20 feet.

Answer:

x = 76°

Step-by-step explanation:

given ∠ STR = ∠ SRT = 28°

∠ STR and ∠ STU are a linear pair and sum to 180° , that is

28° + 2x = 180° ( subtract 28° from both sides )

2x = 152° ( divide both sides by 2 )

x = 76°

The perimeter of the triangle is,

⇒ P = (4x + 9)

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The figure of triangle is shown.

All the sides are,

⇒ AB = x + 1

⇒ BC = x + 3

⇒ CA = 2x + 5

Now, Remember that the perimeter is the sum of all sides of a figure, so in this case would be;

⇒ P = (x + 1) + (x + 3) + (2x + 5)

       = 4x + 9

Thus, The simplified expression of the perimeter is,

⇒ P = (4x + 9)

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Answer:

20

Step-by-step explanation:

Let the number of days be [tex]d[/tex].

[tex]250=12d \\ \\ d=\frac{250}{12}=\frac{125}{6} \implies \lfloor d \rfloor=20[/tex]

Answer: 18 - 2 = ...

Step-by-step explanation:

Substitute 3 into n:

6 * 3 - 2

= 18 - 2

=  Solve this yourself :>

Answer: The value of 6n-2 when 4 is 3=16

Step-by-step explanation: Put value of n in the expression 6n - 2. The resulting expression will be 6(3)-2. We will multiply first and then subtract. 18-2 which equals 16.

Therefore , the solution of the given problem of quadrilateral comes out to be A.5 , B.2/3, C.-1/5 and D.2/3 .

A quadrilateral in geometry is a four-sided object with four corners and four corners. The term derives from the Latin terms quadri or latus (meaning "side"). Rectangles are two-dimensional shapes that have four corners, four corners, and four corners. There are essentially two types of concave and convex.

Here,

Given that

A(-4, -5), B(-3, 0), C(0, 2), and D are the quadrilateral ABCD's vertices (5, 1).

If ABCD is a trapezoidal or not is what we must ascertain.

We are aware that a trapezoidal is a quadrilateral by one set of parallel opposed sides. Furthermore, two parallel lines have equal slopes.

The slopes of sides AB, BC, CD, and DA will first be determined.

Ours has

The gradient for

AB =0+5/ -3+4

=>5/1 => 5, in step 1.

Step 2: BC's slope is

=> 2-0 / 0+3

=> 2/3.

Step 3: The gradient of CD is

=> 1-2 / 5-0, which equals -1/5.

Step 4: The gradient of DA is equal to

=>-5.1/-4.4/2.3

=>2/3.

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a. The tea that he needs to make 450ml of mint tea will be 4050 ml

b. The mint syrup that he needs to make 5.4 liters of mint tea will be 0.6 liters.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split

The tea that he needs to make 450ml of mint tea will be:

= 450ml ÷ 1/9

= 450 × 9

= 4050ml

The mint syrup that he needs to make 5.4 liters of mint tea will be:

= 5.4 ÷ 9

= 0.6 liters

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The digit in the  tens   place is the best place for the stem value of the data shown above.

====================================

Explanation:

Common convention with 2 digit numbers is to have the tens place as the stem, and the units digit as the leaf.

For example, the number 65 has a stem of 6 and leaf of 5.

Another example: The number 71 has 7 as the stem and 1 as the leaf.

--------

This is what the full stem-and-leaf plot looks like:

[tex]\begin{array}{r|l} \text{stem} & \text{leaf}\\\cline{1-2}4& 0\ 4\ 5\ 9\ \ \ \ \ \\ 5& 2\ 4\ 6\ 7\ \ \ \ \ \\ 6& 2\ 3\ 4\ 5\ 5\ 7\ 7\ 8\ 8 \\ 7& 1\ 4\ \ \ \ \ \ \ \\ 8& 7\ \ \ \ \ \ \ \ \end{array}[/tex]

[tex]\boxed{\text{Key: } 4|0 \ \text{means } 40}[/tex]

Answer:

Area: 107.625 feet squared

Step-by-step explanation:

A = 8+13/2 (10.25)

A = 21/2 (10.25)

A = 10.5 (10.25)

A = 107.625 feet squared

Answer:

The orthocenter of a triangle is the intersection point of the three altitudes of the triangle.

An altitude of a triangle is a line that goes from one vertex of the triangle to the opposite side, and is perpendicular to that side.

To find the orthocenter of a triangle, we can find the equation of each altitude by using the slope-point form.

The slope of the altitude from vertex X to side YZ is the negative reciprocal of the slope of line YZ.

The slope of line YZ is (3 - (-5)) / (9 - 1) = 8/8 =1

So the slope of the altitude from vertex X is -1

The equation of this altitude is y = -1x + b

We know that this line passes through the point X (-3, 3) so we can substitute this point in the equation and find the value of b

3 = -1(-3) + b

b = 6

So the equation of this altitude is y = -1x + 6

The orthocenter of angle XYZ is the point that is common to all three altitudes, we can find this point by finding the intersection point of all three altitudes.

So the coordinates of the orthocenter of angle XYZ are (1, -1)

To solve this problem, we need to know how much red paint Priya has. This information is not on the data card, so we need to know the amount of red paint Priya has in order to solve the problem.

Amount is a numerical value that can refer to the quantity of a particular item or resource. It can also refer to the sum of money due or owed for a product or service. In the context of mathematics, amount is often used to refer to a quantity, a measure, or a total. Amount can also be used to refer to the total value of a particular asset, such as a bank account or the total number of shares of a particular stock.

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Answer:

Choice B

(0.75) (0.90) (126)

Step-by-step explanation:

Original price of coat = $126

First note that
          25% ≡ 0.25 in decimal
           10% ≡ 0.10  in decimal

If she gets 25% off then the discount is 0.25(126)

The coat would then cost her 126-(0.25)(126) = 126(1-0.25) = (0.75)126

(In general if there is  a discount of d% where r = d/100 on sale price of S then the new price would be S(1-r))

On this discounted price she gets an additional 10%(0.10) off.

This means the already discounted price is reduced to 0.9 of its value

So the final discounted price is (0.90[126(0.75]

or (0.90)(0.75)(126)

which can be rewritten as

(0.75) (0.90) (126)

and corresponds to choice B

The other choices can be eliminated easily

A. Here the 10% discount is applied to the original price 126 not the discounted price

C. This is the total discount not the final price

D. This is attempting to find the final price but again the discount of 10% is being applied to 126

E. Does not make any sense. 0.25 x 0.10 = 0.025 and 126 - 0.025 = $125.975 which is practically no discount

Answer:

The question is incomplete, but the answer would just be 0.50 times the amount of students. Hope this helps.

Answer:

19 m^3

Step-by-step explanation:

nothing to factor

Answer:

Step-by-step explanation:

In the set-builder notation, the set C that contains the elements {-9, -6, -3, 3, 6, 9} can be written as:

C = {x | x ∈ Z and x ∈ {-9, -6, -3, 3, 6, 9}}

where "x" is a variable, "Z" represents the set of integers, and the expression "x ∈ {-9, -6, -3, 3, 6, 9}" specifies that x can only take on the values of -9, -6, -3, 3, 6, or 9.

Alternatively, we can write it as:

C = {-9, -6, -3, 3, 6, 9}

This notation is used to express a set of elements that have a common property or belong to a specific category, it makes it easy to understand and to read what the set consists of.

Answer: a) $10 per month b) the original runners

Step-by-step explanation: A) since runners cost $240, and you used them for a total of 2 years, which is 24 months. This means they cost 240/24 = $10 per month

b) The other pair costs $168 but you only have them for 2 months so they cost 168/2 = $84 per month which are more expensive.

The factors of this expression X⁴ - 2x + 1  is, (X - 1), (X - 1), (X + 1), (X + 1)

In mathematics, the factors are the algebraic expressions which divides the given expression evenly. After division there will be no remainder.

For example, x²-12x +12 =  (x-3)(x-4), (x-3) and (x-4) are the factors of the quadratic equation.

Given expression,

⇒ X⁴ - 2x + 1

⇒ X⁴ - 2x + 1⁴

by using identity,

(a + b)² = a² + 2ab + b²

Similarly,

⇒ (X²)² - 2×1²×X + (1²)²

⇒  (X² - 1)²

⇒  [(X - 1)(X + 1)]²

Hence, factors are (X - 1), (X - 1), (X + 1), (X + 1)

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The trebuchet projectile will reach 80 feet at 1.094 s later.

The height of the projectile at any given time "t" can be described by the function h(t) = -16t² + vt + h0, where h0 is the initial height and v is the initial velocity. In this case, h0 = 0 (the launch point) and v = 35 ft/s. So, the height function is h(t) = -16t² + 35t.

To find when the projectile first reaches 80 feet, solve the equation h(t) = 80. Plugging in the height function:

-16t² + 35t = 80

Solving for t:

-16t² + 35t - 80 = 0

This is a quadratic equation and can be solved using the quadratic formula or factoring. The two solutions are:

t = 4.069 s or t = -8.848 s

The negative solution is extraneous, as the time can't be negative. So, the first time the projectile reaches 80 ft is 4.069 s after launch.

To find when the projectile reaches 80 ft again, simply fill in the height and the velocity into the height function and solve for t. However, since the height function is a parabolic function, the projectile will reach the same height again at the maximum height, which is half of the time it takes for the projectile to reach its highest point.

Since the maximum height is reached at t = v/g = 35/(-16) = 2.188 s, the projectile will reach 80 ft again 2.188 s/2 = 1.094 s later.

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According to the solving we can say that the given expression is equivalent to = [tex]3f^3/g^2[/tex].

Expressions that seem different but perform the same way are referred to as equivalent expressions. If two algebraic expressions were equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

If two expressions could be written similarly or can be combined into a single, simpler phrase, then those two expressions are comparable. Additionally, you can tell if two expressions are equal if you substitute values for the variable in both and they get the same result.

√(900f⁶/100g⁴)

on simplifying this we get:

√(9f⁶/1g⁴)

Now removing the roots of the given expression we get:

= [tex]3f^3/g^2[/tex].

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Using substitution method to solve the system of linear equations, Brandy took care of 280 children and Adriana took care of 40 children.

A word problem is a type of mathematical problem that is presented in a natural language text, rather than in mathematical notation. These problems are designed to test a person's ability to understand and apply mathematical concepts and skills to real-world situations. They often involve describing a scenario, such as a situation involving money, time, or measurements, and then asking a question or series of questions about the scenario.

In this problem, we need to write equations to set up the variables.

a)

Let;

b)

x + y = 320 ...eq(i)

x = 7y ..eq(ii)

c)

Put equation (ii) into equation (i)

7y + y = 320

8y = 320

y = 40

Put y = 40 in equation (ii)

x = 7(40)

x = 280

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