A shopkeeper buys 72 articles for $82.80. How much will he have to pay if he buys 150 such articles.​

Answer:

[tex]\boxed{\bf x = 23.5}[/tex]

Step-by-step explanation:

Using the law of sines.

[tex] \bf \cfrac{ \sin(A) }{a} = \cfrac{ \sin(B) }{b} [/tex]

[tex]\bf \cfrac{ \sin(42) }{22} = \cfrac{ \sin(x) }{12} [/tex]

[tex]\bf \cfrac{12}{22} \sin(42) = \sin(x) [/tex]

[tex] \bf \sin(x) = 0.4[/tex]

[tex]\bf x = 23.5[/tex]

[tex]a - 4 = ( \sqrt{a} - 2)( \sqrt{a} + 2)[/tex]

[tex] \frac{ \sqrt{a} - 2}{a - 4} = \frac{ \sqrt{a} - 2}{( \sqrt{a} - 2)( \sqrt{a} + 2) } = \frac{1}{ \sqrt{a} + 2 } [/tex]

Answer: r = 121.92 cm

              Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]

              7587404.65

Step-by-step explanation:

The radius is given. It's the distance from the center of the sphere to the end. The radius is 4 ft. 1 ft is 30.48cm so 4ft is 121.92cm  

(radius) r = 121.92 cm

Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]

             = 4/3 x 3.14 x 1812278.18

             = 4/3 x 5690553.49

             = 7587404.65

The trigonometry ratios are cos(θ) = -7/√58, sec(θ) = -√58/7 and cot(θ) = -7/3

The point on the terminal side is given as:

(x, y) = (-7, 3)

Start by calculating the hypotenuse using:

[tex]h= \sqrt{x^2 + y^2[/tex]

So, we have:

[tex]h= \sqrt{(-7)^2 + 3^2[/tex]

Evaluate

[tex]h= \sqrt{58[/tex]

The cosine is then calculated using:

cos(θ) = x/h

This gives

cos(θ) = -7/√58

The secant is then calculated using:

sec(θ) = 1/cos(θ)

This gives

sec(θ) = -√58/7

The cotangent is then calculated using:

cot(θ) = cos(θ)/sin(θ)

Where

sin(θ) = y/h

So, we have:

sin(θ) = 3/√58

So, we have:

cot(θ) = (-7/√58)/(3/√58)

This gives

cot(θ) = -7/3

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Answer:

Domain: all real numbers, or (-oo, oo)

Range: (3, oo).

Step-by-step explanation:

The domain is the set of x-values that work when plugged into a function. Here, all values when plugged in produce a real answer, so the answer is all real numbers, or (-oo, oo).

The range is the result of the domain, or the y-values. Since the x^2 will only produce positive numbers, the lowest y-value we can get is 3, and the highest y-value we can get is infinity. So, the answer is (3, oo).

Brainliest, please :)

Answer:

  $385.50

Step-by-step explanation:

The amount of commission is found by multiplying the commission rate by the value of the sale.

  1.5% × $25,700 = $385.50

A commission of $385.50 is made on an average car sold.

The number of customers I would have expected to win the prize is 6.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Based on the probability, the number of customers I would have expected to win: 0.18 x 300 = 36

How many more people I would have expected to win : 36 - 30 = 6

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Answer:

5/8

Step-by-step explanation:

5/8=0.6.25

0.625> all the other numbers

If the value of mean is 781.67, then the standard deviation will be 100. Then the correct option is C.

The complete question is given below.

Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan. The list represents the approximate number of megabytes of data Grace used each month.

700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750

What is the standard deviation of the data? Round to the nearest whole number.

65

75

100

130

It is a metric for statistical information dispersion. The degree of spread indicates how much the result varies.

Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan.

The list represents the approximate number of megabytes of data Grace used each month.

700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750

The mean of the data will be

Mean = (700 + 735 + 680 + ...... + 820 + 750) / 12

Mean = 781.67

Then the standard deviation will be

SD² = [(700 – 781.67)² + (735 – 781.67)² + ..... + (750 – 781.67)²] / 12

SD² = 10072.2222

SD = 100.36 ≈ 100

Then the correct option is C.

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The answer is (x+4) (x-2) =x.x

Square (Rug A) has area x times x = x^2 (All sides of square are equal)

x is the side of Rug A

For the Rectangle (Rug B) it mentioned that it has a length of that is 4 ft greater than the length of Rug A. The expression could be written as Length = (x+4)

It also mentions that the width of Rectangle is 2 ft less than Rug A. The expression could be written as Width = (x-2)

So, if you multiply (x+4) and (x-2), will give you the area of rectangle (Rug B)

The question mentions that the area of the rectangle and square are equal, so therefore the answer is (x+4) (x-2) =x.x

Hope it helps!

∠A ≅ ∠D , BC≅ EF , AC ≅   DF  , option B , C , F are the correct answer.

CPCTC stands for corresponding parts of congruent triangles are congruent .

This means when two triangles are congruent then the corresponding sides are also congruent.

In the given triangles , Δ ABC ≅ ΔDEF

∠A ≅ ∠D

BC≅ EF

AC ≅   DF

Therefore option B , C , F are the correct options

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The answers are as follow:

a) y'= -2x/y

b) y' = -4/y

The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y.

Given:

x²y+4y=8

On differentiation

applying product rule

2xy+ x²y'  = 0

2xy = - x²y'  

2y = -xy'

y'= -2x/y

b) equation of the tangent line to the graph when x = 2.

y' = -4/y

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The simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].

The given expression is [tex]\frac{4(3x^{2} y^{4} )^{3} }{(2x^{3} y^{5} )^{4} }[/tex].

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n".

We need to simplify the given expression.

Now, [tex]\frac{4(3^{3}x^{6} y^{12} )}{2^{4} x^{12}y^{20} }[/tex]

⇒[tex]\frac{108x^{6}y^{12} }{16x^{12} y^{20} }[/tex]

⇒[tex]\frac{27}{4x^{12} y^{8} }[/tex]

Therefore, the simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].

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The profit-maximizing price of​ e-books relating to​ do-it-yourself topics is $5.35 and the average total cost of producing​ e-books is $4.35.

​

a. Profit-maximizing price

The maximum that the firm can earn is $35,000 at a quantity of 35,000 copies

Fixed cost FC = $140,000

Variable cost vc=$0.35 per book

Total Revenue TR =P XQ

Total Revenue TR= P x 35,000

Total Cost TC = FC + VC XQ

Total Cost TC = 140,000 + (0.35×35,000)

Total Cost TC = 140,000 +$12,250

Total Cost TC = $152,250

Profit = TR- TE

35,000 = 35,000P- $152,250

35,000P=187,250

P=187,250/35,000 copies

P=$5.35

b. Average total cost

Average total cost=Total cost/Quantity

Average total cost= $152,250/35,000 copies

Average total cost=$4.35

Therefore the profit-maximizing price of​ e-books relating to​ do-it-yourself topics is $5.35 and the average total cost of producing​ e-books is $4.35.

​

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The complete question is:

A firm that sells​ e-books - books in digital form downloadable from the Internet​ - sells all​ e-books relating to​ do-it-yourself topics​ (home plumbing,​ gardening, and so​ on) at the same price. At​ present, the company can earn a maximum annual profit of ​$35,000 when it sells 35,000 copies within a​ year's time. The firm incurs a 35​-cent expense each time a consumer downloads a​ copy, but the company must spend ​$140,000 per year developing new editions of the​ e-books. The company has determined that it would earn zero economic profits if price were equal to average total​ cost, and in this case it could sell 40,000 copies. Under marginal cost​ pricing, it could sell 120,000 copies.

In the short​ run, to the nearest​ cent, what is the​ profit-maximizing price of​ e-books relating to​ do-it-yourself topics? ​

At the​ profit-maximizing quantity, to the nearest​ cent, what is the average total cost of producing​ e-books?

Answer:

D. 2√2

Step-by-step explanation:

x² = 8

x = √8

x = √4 x √2

x = 2√2

Step-by-step explanation:

[tex] x {?}^{2} \sqrt{2 \times 2 \times 2} \\ \\ x { }^{2} = 2 \sqrt{2} [/tex]

The complete statements are mathematically given as

Generally,  The transfer of money, products, or services in return for other goods and services in proportions that have been previously agreed upon and deemed acceptable is what is meant by the term "payment."

In conclusion, the amount borrowed= 88000

the annual interest rate= 6%

the number of payments per year= 12

The loan term= 18

the payment amount.=667*12

the payment amount.=8004

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Answer:

Second choice GD and GF with the LINE symbol over each

Step-by-step explanation:

Angle named DGF means that G ( in the middle) is the vertex so GD would be a line starting at G going out toward D and G F would be a line starting at G going out to F

The vertex of the absolute value function is (-7,-2)

The function is given as:

f(x) = 3|x + 7| - 2

The above function is an absolute value function.

An absolute value function is represented as:

f(x) = a|x - h| + k

Where:

Vertex = (h,k)

By comparison, we have:

(h,k) = (-7,-2)

Hence, the vertex of the absolute value function is (-7,-2)

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The domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

A carpet installer charges a flat rate of $40 and $1.50 per square foot for labor.

So the total cost for the labor depends on the amount of carpet installed, the relationship between the total cost for labor and the amount of corporate installed.

Then the domain of the relation is the range of the relation will be

Let y be the total amount and x be the number of square foot.

y = 1.5x + 40

Then the domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).

The graph is given below.

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Solution of 9x+8y=26 and 3x+2y=9 are given by (C)  [tex]\mathbf{x=\frac{10}{3},y=-\frac{1}{2}}[/tex].

We have to plot the graphs of the given two lines or curves, then we have to find the intersection point(s) of the curves or lines. That point is the solution for the system of the equations.

Given equations are,

9x+8y=26 .................(1)

3x+2y=9 ...................(2)

Now multiplying 3 with (2) and then subtracting (1) from that we get,

3(3x+2y)-(9x+8y)=3(9)-26

9x+6y-9x-8y=27-26

-2y=1

y=-1/2, on dividing both sides by -2

Substituting the value of y in (1) we get,

9x+8(-1/2)=26

9x-4=26

9x=26+4

9x=30

x=30/9=10/3

Also if we draw the graphs of the given equations by using graphing calculator we get,

Here in the graph we can see that the lines represented by the given equations intersects each other at point [tex]\left(\frac{10}{3},-\frac{1}{2}\right)[/tex].

Hence the solution is [tex]x=\frac{10}{3},y=-\frac{1}{2}[/tex].

Thus the correct option is (C).

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Answer:

-28x^3-28x^2+16x+15

Step-by-step explanation:-28x^3-28x^2+16x+15

The number of gallons of Jet fuel that is needed to fly for an hour is; 14400 gallons

We are given;

Number of gallons burned = 4 gallons

Time to burn 4 gallons = 3 seconds

Now, for 1 hour there are 3600 seconds and so;

Number of gallons that is burnt in 3600 seconds = 3600 * 4

Number of gallons that is burnt in 3600 seconds = 14400 gallons

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The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

a. Distribution

X ~ N (20 , 6)

b. P(x ≤24)

= P[(x - μ ) / σ  (24 - 20) / 6]

= P(z  ≤0.67)

=  0.74857

=0.7486

Hence:

Probability = 0.7486

c. P(21 < x < 26)

= P[(21 - 26)/ 6) < (x - μ  ) / σ   < (24 - 20) / 6) ]

= P(-0.83 < z < 0.67)

= P(z < 0.67) - P(z < -0.)

=  0.74857- 0.2033

= 0.54527

Hence:

Probability =0.54527

d. Using standard normal table ,

P(Z < z) = 66%

P(Z < 0.50) = 0.66

z = 0.50

Using z-score formula,

x = z×  σ +  μ

x = 0.50 × 6 + 20 = 23

23 Christmas cards

Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

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Based on the upper and lower quartiles of the box plots:

Range for Maths is 60 to 85

Range for Language arts is 60 to 80.

In a box plot, the about half of the data set lies between the upper quartile and the lower quartile which are represented at the beginning and the end of the edges of the box respectively. This makes up 50% of a data distribution.

Thus, for Maths, the Upper and lower quartiles are between 60 to 85, hike that for Language arts are between 60 to 80.

Therefore, 50% of Theos scores for Maths ranges from: 60 to 85, while for Language arts is: 60 to 80.

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The decimal expansion of 2 1/6 is 2.167

The expression is given as:

2 1/6

Rewrite the expression as:

2 + 1/6

Express 1/6 as decimal

2 + 0.167

Evaluate the sum

2.167

Hence, the decimal expansion of 2 1/6 is 2.167

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Answer:

[tex]\boxed {360 m^{3}}[/tex]

Step-by-step explanation:

Water needed to fill the pool = volume of pool

Volume :

Hence, 360 m³ of water has to be filled.

Answer:

360 m³

Step-by-step explanation:

The swimming pool can be modeled as a rectangular prism with the following dimensions:

To find how much water is needed to fill the pool, calculate the volume of the rectangular prism using the given dimensions:

[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf length \times width \times height\\\implies \textsf{Volume of pool} & = \sf 12 \times 6 \times 5 \\& = \sf 72 \times 5\\& = \sf 360 \:\: m^3\end{aligned}[/tex]

Therefore, 360 m³ of water is needed to fill the swimming pool.

Let h represent hamburgers and c represent cheeseburgers

h + c ≤ 100 - The number of burgers sold

3h + 3.5c ≥ 80 - Amount that each burger sells for

Answer:

No

Step-by-step explanation:

no because just muiltiplying 7.00 * 8 is 56 not inculuding the 99 cents it is already over 50. The answer is 63.92 so a reasonable estimate would be around $60

Answer:

Step-by-step explanation:

Use interest formula:

Substitute given values and calculate:

Answer:

$ 380

Step-by-step explanation:

We can use the below formula to find the simple interest.

Simple interest = P r t ÷ 100

Here,

P ⇒ Principal ⇒ $ 9500

r ⇒ rate ⇒ 2%

t ⇒ time ⇒ 2 years

Let us solve it now.

Simple interest = P r t ÷ 100

Simple interest = 9500 × 2 × 2 ÷ 100

Simple interest = 38000 ÷ 100

Simple interest = $ 380