Ingrid is buying a pair of pants with an original cost of c dollars. The pants are on sale for 15% off their original cost. which two calculations could Ingrid perform in order to find the amount she needs to spend?​ Please explain how it the answer is found

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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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.

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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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]

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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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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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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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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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:

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]

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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Answer:

19 m^3

Step-by-step explanation:

nothing to factor

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°

Answer:

a)  Alternate interior angles

b)  Same-side interior angles

c)  Alternate exterior angles

d)  None

e)  Supplementary

Step-by-step explanation:

Alternate interior angles

When two lines are intersected by a transversal, the angles that are interior to the two lines and are on opposite sides of the transversal line are called "alternate interior angles".

Same-side interior angles

When two lines are intersected by a transversal, the angles that are interior to the two lines and on the same side of the transversal line are called "same-side interior angles".

Alternate exterior angles

When two lines are intersected by a transversal, the angles that are exterior to the two lines and are on opposite sides of the transversal line are called "alternate exterior angles".

Supplementary angles are two angles whose measures sum to 180°.

They do not need to be adjacent to be supplementary.

As ∠9 and ∠11 form a linear pair, they are supplementary angles.

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

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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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

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 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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The distance between the two towers and the building is 50 ft.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that The height of a tower is 55 ft and the height of a building is 25 ft. If the angle of elevation from the top of the building to the top of the tower is 30.9°.

The distance will be calculated as,

Distance = 30 / tan(30.9)

Distance = 50 ft

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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.

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:

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

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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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.

The commission paid to the salesperson would be $1110.

What is a commission?

A commission is a fee or percentage of the value of a sale that is paid to a salesperson as a form of compensation for their work in making the sale.

In this case, the commission paid to the salesperson at Kings Park Auto Giant is based on the profit of the sale and is determined by the piecewise function c(p), where p is the profit. To determine the commission for a specific sale, you would need to use the profit of that sale in the piecewise function and perform the calculations.

In the case provided, the car was purchased for $32,090 and sold for $33,200. The profit would be the difference between these two prices, which is $33,200 - $32,090 = $1,110. With this information, the commission that would be paid to the salesperson can be determined by plugging the profit, $1,110, into the commission function c(p) and performing the calculations.

Hence, the commission paid to the salesperson would be $1110.

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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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