Billy purchased $100$ shirts at a cost of $\$15$ each and planned to resell them. The first week he sold some of them for $\$25$ each. The second week he sold the rest for $\$20$ each. If his total profit was $\$600$, how many shirts did he sell the first week?

Answer:

B

Step-by-step explanation:

first of all articles are perfect and there is . sign at the last of the sentence

Answer:

376.8 cm²

Step-by-step explanation:

Given:

Surface area = 2πrh + 2πr²

[Where "r" and "h" represents the radius and the height respectively]

Let's substitute the height and the radius in the formula and simplify it.

[tex]\implies 2\pi rh + 2\pi ^{2}[/tex]

[tex]\implies 2\pi (4)(11) + 2\pi (4)^{2}[/tex]

[tex]\implies 2\pi (44) + 2\pi (16)[/tex]

[tex]\implies 88\pi + 32\pi[/tex]

We can factor π out of the expression. Therefore, we get:

[tex]\implies 88\pi + 32\pi[/tex]

[tex]\implies \pi (88 + 32)[/tex]

Now, simplify the expression inside the parentheses.

[tex]\implies \pi (88 + 32)[/tex]

[tex]\implies \pi (120)[/tex]

The value of π, we are given, is 3.14. When substituted, we get:

[tex]\implies \pi (120)[/tex]

[tex]\implies 3.14(120) = 31.4(12) = \boxed{376.8 \ \text{cm}^{2} }[/tex]

Therefore, the surface area of the cylinder is 376.8 cm².

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Answer: 20

Step-by-step explanation:

    Box plots give us the median just by looking at them. See attached.

Answer:

[tex]a_n=3n-2[/tex]

Step-by-step explanation:

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

Create expressions for the 4th and 6th terms:

[tex]\implies a_4=a+(4-1)d=a+3d[/tex]

[tex]\implies a_6=a+(6-1)d=a+5d[/tex]

The ratio of the 4th term to the 6th term is 5:8, therefore:

[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]

[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]

[tex]\implies 8(a+3d)=5(a+5d)[/tex]

[tex]\implies 8a+24d=5a+25d[/tex]

[tex]\implies 8a-5a=25d-24d[/tex]

[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

The sum of the first 7 terms of an arithmetic progression is 70:

[tex]\implies S_7=70[/tex]

[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]

[tex]\implies 2a+6d=20[/tex]

[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]

Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:

[tex]\implies a+3(3a)=10[/tex]

[tex]\implies a+9a=10[/tex]

[tex]\implies 10a=10[/tex]

[tex]\implies a=1[/tex]

Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:

[tex]\implies 3(1)=d[/tex]

[tex]\implies d=3[/tex]

Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:

[tex]\implies a_n=1+(n-1)3[/tex]

[tex]\implies a_n=1+3n-3[/tex]

[tex]\implies a_n=3n-2[/tex]

Answer:

$1431

Step-by-step explanation:

If Stan pays a 10% deposit, he pays $159. 10% of $1590 is simply 0.1 * 1590 = 159. Assuming this is the only amount he pays, he then simply needs to pay the full price minus $159. We can find this by simply subtracting 159 from 1590 to get 1431. Stan still needs to pay $1431.

Step-by-step explanation:

First, use the Pythagorean theorem to find cos x.

[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]

[tex] (\frac{7}{9} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]

[tex] \cos {}^{2} (x) = 1 - \frac{49}{81} [/tex]

[tex] \cos {}^{2} (x) = \frac{32}{81} [/tex]

[tex] \cos(x) = \frac{4 \sqrt{2} }{9} [/tex]

Now, use the quotient identity

[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]

[tex] \tan(x) = \frac{ \frac{7}{9} }{ \frac{4 \sqrt{2} }{9} } [/tex]

[tex] \tan(x) = \frac{7}{4 \sqrt{2} } [/tex]

[tex] \tan(x) = \frac{7 \sqrt{2} }{8} [/tex]

The answer is A

Answer:

Option 2

Step-by-step explanation:

Evaluating the options :

Option 1

Option 2

Option 2 is the right answer.

Answer:

Domain = x ≥ 0

Range = f( x ) ≥ 1

Step-by-step explanation:

The graph starts from 0 in the x - axis and 1 in the y hence the given domain and range.

Answer: 56°

Step-by-step explanation:

Answer: b=840

Step-by-step explanation:

edge 2022

do good on your tests !!

There are 840 ways can he arrange his family members into a row of five seats if Jose must sit in the first seat

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Since, the order matters, we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

ⁿPₓ = n! / (n - x)!

In this question:

The first seat is Jose's.

The remaining four are organized among the other 7 members. So

There is no difference. So, 7 people can be sit in different ways as;

ⁿPₓ = n! / (n - x)!

⁷P₄ = 7! / (7 - 4)!

     = 7! / 3!

     = 840

So, the correct answer is, 840

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Inequalities help us to compare two unequal expressions. Wyatt needs to sell at least 17 keychains.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given Wyatt bought $40 worth of materials to make braided keychains. Also, it is given that Wyatt Sells his keychains for $2.50 each. Therefore, the minimum number of keychains he should sell to make a profit are,

Number of keychains>(40/2.50)

Number of keychains > 16

Thus, Wyatt needs to sell at least 17 keychains.

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Answer:

Step-by-step explanation:

17

Answer:

C=98°

Step-by-step explanation:

125°- 27°

=98°

Answer:

D

Step-by-step explanation:

4x + 3y = 6

-4x + 2y = 14

0 + 5y / 5 = 20/ 5 = 4 = y

4x + 3(4) = 6

4x + 12 - 12 = 6 - 12

4x / 4 = -6 / 4 = -3 / 2 =x

Answer: they are all correct congrats!

Step-by-step explanation:

Answer:

Area of the triangle is 6

Step-by-step explanation:

The formula for the area of a triangle is the base x height / 2. This means we can just plug in the variables and solve

A = b x h/2

A= 4 x 3/2

A= 12/2

A= 6

Answer: 6

Step-by-step explanation:

Step-by-step explanation:

this is the answer

hope it help

Answer:

[tex]\huge{\purple {r= 2\times\sqrt[3]3}}[/tex]

[tex]\huge 2\times \sqrt [3]3 = 2.88[/tex]

Step-by-step explanation:

Answer:

Your answers are below ↓

Step-by-step explanation:

Given ↓

A) 2x-3y = 5 and 3x+4y = 6  ( The method this has to be solved in is the elimination method. )

Now using these,

(1)×3 - (2)×2 = 6x + 9y - 6x - 8y = 15 - 12

therefore,

y = 3

putting the value of y in eqn. (1)

2x + 6 = 5

therefore,

x = -1/2

B)  y=x^2 - 2x and y = 2x -3  ( The method this has to be solved in is the substitution method. )

Reduce the greatest common factor on both sides of the equation:
[tex]\left \{ {{4x-y=9} \atop {xy=-2}} \right.[/tex]

Rearrange like terms to the same side of the equation:

[tex]\left \{ {{-y=9-4x} \atop {xy=-2}} \right.[/tex]

Divide both sides of the equation by the coefficient of the variable:

[tex]\left \{ {{y=-9+4x} \atop {xy=-2}} \right.[/tex]

Substitute the unknown quantity into the elimination:

[tex]x(-9+4x)=-2[/tex]

Apply Multiplication Distribution Law:

[tex]-9x+4x^2=-2[/tex]

Reorder the equation:

[tex]4x^2-9x=-2[/tex]

Divide the equation by the coefficient of the quadratic term:

[tex]\frac{1}{4}(4x^2)+\frac{1}{4}(-9x)=\frac{1}{4}*(-2)\\[/tex]

Calculate:

[tex]x^2-\frac{9x}{4}=-\frac{1}{2}[/tex]

Add one term in order to complete the square:

[tex]x^2-\frac{9x}{4}+(\frac{9}{4}*\frac{1}{2})^2=-\frac{1}{2}+(\frac{9}{4}*\frac{1}{2})^2[/tex]

Calculate:

[tex]x^2-\frac{9x}{4}+(\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]

Factor the expression using [tex]a^2$\pm$2ab+b^2=(a$\pm$b)^2[/tex]:

[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]

Simplify using exponent rule with the same exponent rule: [tex](ab)^n=a^n*b^n[/tex]

[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +\frac{9^2}{8^2}[/tex]

Calculate the power:

[tex](x-\frac{9}{8} )^2=-\frac{1}{2}+\frac{81}{64}[/tex]

Find common denominator and write the numerators above the denominator:

[tex](x-\frac{9}{8} )^2=\frac{-32+81}{64}[/tex]

Calculate the first two terms:

[tex](x-\frac{9}{8} )^2=\frac{49}{64}[/tex]

Rewrite as a system of equations:

[tex]x-\frac{9}{8} =\sqrt{\frac{49}{64} }[/tex] or [tex]x-\frac{9}{8} =-\sqrt{\frac{49}{64} }[/tex]

Rearrange unknown terms to the left side of the equation:

[tex]x=\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]

Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:

[tex]x=\frac{\sqrt{49} }{\sqrt{64} } +\frac{9}{8}[/tex]

Factor and rewrite the radicand in exponential form:

[tex]x=\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]

Simplify the radical expression:

[tex]x=\frac{7}{8} +\frac{9}{8}[/tex]

Write the numerators over the common denominator:

[tex]x=\frac{7+9}{8}[/tex]

Calculate the first two terms:
[tex]x=\frac{16}{8}[/tex]

Reduce fraction to the lowest term by canceling the greatest common factor:

[tex]x=2[/tex]

Rearrange unknown terms to the left side of the equation:

[tex]x=-\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]

Rewrite the expression using [tex]\sqrt[n]{a} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:

[tex]x=-\frac{\sqrt{49} }{\sqrt{64} }+\frac{9}{8}[/tex]

Factor and rewrite the radicand in exponential form:
[tex]x=-\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]

Simplify the radical expression:

[tex]x=-\frac{7}{8} +\frac{9}{8}[/tex]

Write the numerators over common denominator:

[tex]x=\frac{-7+9}{8}[/tex]

Calculate the first two terms:

[tex]x=\frac{2}{8}[/tex]

Reduce fraction to the lowest term by canceling the greatest common factor:

[tex]x=\frac{1}{4}[/tex]

Find the union of solutions:

[tex]x=2[/tex] or [tex]x=\frac{1}{4}[/tex]

Substitute the unknown quantity into the elimination:

[tex]y=-9+4*2[/tex]

Calculate the first two terms:

[tex]y=-9+8[/tex]

Calculate the first two terms:

[tex]y=-1[/tex]

Substitute the unknown quantity into the elimination:

[tex]y=-9+4*\frac{1}{4 }[/tex]

Reduce the expression to the lowest term:

[tex]y=-9+1[/tex]

Calculate the first two terms:

[tex]y=-8[/tex]

Write the solution set of equations:
[tex]\left \{ {{x=2} \atop {y=-1}} \right.[/tex] or [tex]\left \{ {{x=\frac{1}{4} } \atop {y=-8}} \right.[/tex]   -------> Answer

C)   y=x^2 - 2x and y = 2x -3 ( This method this has to be solved in is the substitution method. )

Step 1: We start off by Isolating y in y = 2x - 3

y=2x-3 ----------> ( Simplify )

y+(-y)=2x-3+(-y)   ---- > ( Add (-y)on both sides)

0=-3+2x-y

y/1 = 2x-3/1 --------> (Divide through by 1)

y = 2x - 3

We substitute the resulting values of y = 2x - 3 and y = x^2 - 2x

(2 * x - 3) = x^2 - 2x ⇒ 2x -3 = x^2 - 2x ---->   ↓

                                               (Substituting 2x - 3 for y in y = x^2 -2x )

Next: Solve (2x - 3 = x^2 - 2x) for x using the quadratic formular method

2x - 3 = x^2 - 2x

x = -b±b^2-4ac/2a  Step 1: We use the quadratic formula with  ↓

                                                                                         a = -1,b=4,c= - 3

x = -4±(4)^2-4(-1)(-3)/2(-1) Step 2: Substitute the values into the Quadratic  Formular

x = -4± 4/ - 2         x = 1 or x = 3        Step 3: Simplify the Expression & Separate Roots

x = 1 or x = 3  ------- ANSWER

Substitute 1 in for x in y = 2x - 3 then solve for y

y = 2x - 3

y = 2 · (1)  - 3 (Substituting)

y = -1 (Simplify)

Substitute 3 for in y = 2x - 3 then solve for y

y = 2x - 3

y = 2 · (3) - 3 (Substituting)

y =  3   (Simplify)

Therefore, the final solutions for y = x^2 -2x; y = 2x - 3 are

x₁ = 1, y₁ = -1

x₂ = 3, y₂ = 3              

Answer:

I am clueless. Take care though.

Step-by-step explanation:

Answer:

x = 25.84

Step-by-step explanation:

Secx = hyp /adj

Secx = 30/27

x = ArcSec(30/27)

x = 25.84

The 200 random customers is the group in which he surveys to determine which colour of shirt will have the greatest number sold, option third is correct.

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

We have:

Jeff sells shirts at a store in the mall.

The selecting the colour of the shirts is subjective.

It also depends on that how many colours that store sell.

Female customers cannot be an option because men also buy shirts and affect the result of the survey.

Customers who are wearing blue data only tells that how many blue shirts sold.

200 random customers. 200 is a sample from a population, so it will give appropriate results about the colour of shirt will have the greatest number sold

Thus, the 200 random customers is the group in which he surveys to determine which colour of shirt will have the greatest number sold, option third is correct.

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Set of ordered pairs is {(-9,0),(2,5)(-3,8),(11,10)

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

Given:

h(x)=(0,-9),(5,2)(8,-3),(10,11)

The inverse of anything interchange the position of variables or numbers or etc.

In ordered set the inverse will be x- coordinate become y- coordinate and y- coordinate become x- axis.

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Answer:

560

Step-by-step explanation:

16 times 5 times 4=320

6 times 16 divide 2 then multiple 5

[tex] \frac{1}{x} + \frac{3}{x} = 16 \\ [/tex]

[tex] \frac{4}{x} = 16 \\ [/tex]

[tex]16x = 4[/tex]

[tex]x = \frac{4}{16} \\ [/tex]

[tex]x = \frac{1}{4} \\ [/tex]

[tex] \begin{gathered}\\ \large\implies\sf{ \frac{1}{x} + \frac{3}{x} = 16} \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\implies\sf{ \frac{4}{x } = 16 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\implies\sf{ x = 16 \times 4 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \implies \orange{\underline{\boxed{\large\frak \pink{x = 64 }}}} \\ \end{gathered}[/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Step-by-step explanation:

Given that Cooper answered 28 questions correctly and 7 incorrect answers, If the total number of questions is x,

therefore X = 28+7

= 35

R =

[tex] \frac{28}{35} [/tex]

=

[tex] \frac{4}{5} [/tex]

therefore, the ratio is 4:5

5/6 or 0.83 boxes of raisins

Answer:

The correct answer is:

P(nuts)=7/9

Step-by-step explanation:

The experimental probability that the next sundae sold will have nuts is

7/9

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]

where, [tex]P_e(E)[/tex]  is denoting the experimental probability of occurrence of E.

We are given that At Frosty Freeze, 14 of the last 18 sundaes sold had nuts.

Therefore,

Probability that the next sundae has nuts is 14/18 = 7/9.

Thus, Probability that the next sundae does not have nuts = 2/9

P(nuts)=7/9

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Answer:

  1, 5, 10, 10, 5, 1

Step-by-step explanation:

The coefficients for the expansion of the 5th power of a binomial are found on the 5th row of Pascal's triangle. They are ...

  1, 5, 10, 10, 5, 1

__

Algebraically, they are computed using the formula for 5 things taken k at a time:

  5!/(k!(5-k)!)

Answer:

3 cm

Step-by-step explanation:

Formula :

Given :

Solving :