Mr. Santos purchased pizza and soda. Each pizza cost $14.50. He spent $127 on the soda. If he spent $315.50, use the equation 14.50p + 127 = 315.50 to determine how many pizzas, p, he purchased. *

The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

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There was 4 dollar of discount on the total amount.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.

At the counter, he received a discount. If he only paid 22 dollars total, then

Total cost 11 + 15 = 26

But 26 - 22 = 4

Therefore, the discount was 4 dollar.

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The market research department of a Company recommends that the Company to manufacture and market a new transistor radio after suitable test. The marginal cost of the company is 7000 - 2X  and marginal revenue is 10X - X/250.

Marginal cost is an extra cost per unit incurred when an extra unit of output produced or service rendered. Or in other words it can be said that marginal cost is an element of additional unit cost that incurred due to production of goods or services. Some time it is also considering as relevant cost or variable cost.

So in order to compute the transistor manufacturing company's marginal cost, marginal revenue and marginal profit of the company one shall equated the derivative function between them.

In micro economics technical relationship between the said marginal terms is written through derivative function:

Revenue = Price × Quantity Demanded,

Profit Maximize Point where Marginal cost is equal to marginal revenue;

MR = MC,

The marketing department also presents the following demand equation:

X = 5,000 - 500 P

P = 10 - (X ÷ 500), where P is Price and X is quantity demand.

Furthermore, the financial department provides the following cost equation:​

C(X) = 7, 000 + 2x

So the revenue function by the help of substitution method:

X = 5,000 - 500 P

Revenue = Price × Quantity Demanded,

Revenue =  10 - (X ÷ 500) × X

               =  10X - X^2 ÷ 500

Marginal Revenue! = 10X - !2X/500 = 10X - X/250

Marginal Cost =  7, 000 + 2 (5,000 - 500 P)

= 7000 + 10000 - 1000 P

= 17000 - 1000 ( 10 - (X ÷ 500))

= 17000 - 10000 - 2X

= 7000 - 2X

Therefore marginal revenue is revenue or additional earning made by a seller by selling an extra unit. Revenue is earned when extra unit is being sold.

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If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

option c is correct,

as they are correspondence angles their values are same so,

x + 25° = 55°

→ x = 55° - 25°

→ x = 30° ans

hope this answer helps you dear...take care and may u have a great day ahead!

Answer:

O corresponding angles ;x=30

Answer:

At the time the ball was thrown, it was 8 feet above the ground.

h'(x) = -32x + 64 = 0, so x = 2

The ball reaches its maximum height after 2 seconds.

Answer:

6/12

Step-by-step explanation:

there is a total of 12 boxes and six are colored so 6/12

PLEASE RATE!!

Answer:

  (a)  5/12

Step-by-step explanation:

The product of the fractions is the portion of the figure that is "doubly-colored." We notice the top half of the figure is colored yellow; the left 5/6 of the figure is colored blue. The 5 of 12 rectangles at upper left are green, indicating a combination of yellow and blue coloring.

The product is shown as 5/12.

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)

because,

Diameter = 2R

R = 3m

Diameter = 2×3

= 3m.

Answer:

the answer is 6

Step-by-step explanation:

the answer is 6

The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

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Using the concept of profit, it is found that the function is:

\(P(s) = -s^2 + 75s - 2000\)

Profit is revenue subtracted by cost, that is:

\(P(s) = R(s) - C(s)\)

The revenue function is:

\(R(s) = 100s - s^2\)

Fixed cost of $2,000 thus $25 for each sneaker, thus, the cost function is:

\(C(s) = 2000 + 25s\)

Then, the profit function is:

\(P(s) = R(s) - C(s)\)

\(P(s) = 100 - s^2 - (2000 + 25s)\)

\(P(s) = -s^2 + 75s - 2000\)

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Answer:

x=4

Step-by-step explanation:

f(x) = 12 and f(x) = 3x

f(x) = 12 =  3x

12=3x

12/3=x

4=x

Answer:

F

Step-by-step explanation:

Andrew, Blake, Jamal, Ernesto

Answer:

Step-by-step explanation:

 Both the triangles will be congruent by AAS property of congruence.

  It has been given in the question,

Property of congruence A-A-S (Angle-Angle-Side) states,

     "If two angles and a non-included side of one right triangle are equal to the corresponding angles and side of other triangle, then triangles will be congruent."

   Therefore, by the property of AAS property of congruence, given right triangles will be congruent.

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Length of bike route A is 12(65)=780 and length of bike route B is 65.

Two or more expressions with an Equal sign is called as Equation.

Given that the Bike route A is 12 times as long as bike route B.

Let x be the length of the bike route B.

12x be the  length of the bike route B.

The total length of the bike trails is 845 miles

12x+x=845

13x=845

Divide both sides by 13

x=65

Length of bike route A is 12(65)=780 and length of bike route B is 65.

Hence, Length of bike route A is 12(65)=780 and length of bike route B is 65.

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Answer: 250 $3 tickets and 100 $2 tickets were sold.

Answer:

16 and 9

Step-by-step explanation:

16 × 19 using the distributive property

16 × 10 + 16 × 9

Step-by-step explanation:

5th - 13

6th - 20

7th - 27

8th - 34

‍♂️

Answer:

what’s 2/3 x 7?

Step-by-step explanation:

Answer:150?

Step-by-step explanation:

Answer:

2x ( -3x + 14)

Step-by-step explanation:

Distribution property is used in a format like a ( b + c ). To simplify these kinds of expressions, we multiply the outside term by each of the inside terms. So in this instance, a ( b + c ) is equal to ab + ac.

3x ( 2x - 8 ) + 4x

Let's use what we learned above, and multiply the outside term (-3x) by each of the inside terms.

-3x · 2x + (-3x) · (-8) +4x

Simplify by multiplication:

-6x² + 24x +4x

Finally, we add:

-6x² +28x

Now, to simplify further, we can look for terms that show up in numbers.

We can see that the variable x is present in each of the terms, so we can factor that out, removing it from the term as follows:

x ( -6x + 28)

We can look and see that 2 is also a common factor between the two terms, so we can take that out too.

2x ( -3x + 14)

This is the most simplified it can get.

The volume of the rectangular prism is 208cm³

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width

length = 2cm

width = 13 cm

height = 8cm

base area = 13× 2 = 26cm²

Volume of the prism = 26× 8 = 208cm³

Therefore the volume of the rectangular prism is 208cm³.

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Answer:

The researcher will conclude that there is a correlation between the number of hours worked out and the amount of pounds lost by people on the exercise program

Step-by-step explanation:

Here, we want to state what the conclusion of the researcher should be:

From the last part of the question, we can see that the test statistic is greater than the critical value

So what do we do in a case like this?

We can see that the researcher is trying to see if there is a correlation between hours worked out and the number of pounds lost over a specific period of time.

Now, let us form the null hypothesis;

The null hypothesis here H0 is that we do not have a correlation between number of hours spent working out and the amount of pounds lost

The alternative hypothesis here H1 is that there is a correlation between the number of hours spent working out and the amount of pounds lost

Since we have the value of the test statistic greater than the critical value, we reject the null hypothesis and accept the alternative hypothesis

So therefore, the researcher will conclude that there is a correlation between the number of hours worked out and the amount of pounds lost by people on the exercise program

Step 1

We are given a homogenous rod in a cubic curve shape having two free ends, upper end B

and lower end x

The distance of the upper end from x

axis is 1m

and from y axis is 2m.

The rod is bent in a cubic curve shape between two ends and the equation for the rod is given by

\(y=2 x^3\)

Here, \($\bar{x}_1$\)and \($\bar{y}_1$\)are the centroidal distances of the strip element from \(x$and $y$\) axes respectively.

Step 3

The given equation of the homogenous rod is,

\(\begin{gathered}y=2 x^3 \\\frac{d y}{d x}=6 x^2\end{gathered}\)

The given equation of the homogenous rod is,

\begin{aligned}

\(& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}\)

\(& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}\)

\(& L=\int_{x=0}^{x=1 \mathrm{~m}} d L \\& L=\int_{x=0}^{x=1 \mathrm{~m}} \sqrt{1+36 x^4} \cdot d x \\\)

\(& L=6 \times \int_{x=0}^{x=1 \mathrm{~m}} \sqrt{\left(x^2\right)^2+\frac{1}{36}} \cdot d x \\\)

\(& L=6 \times\left[x^2 \sqrt{x^4+\frac{1}{36}}+\frac{1}{36} \ln \left|\left(x^2+\sqrt{x^4+\frac{1}{36}}\right)\right|\right]_0^{1 \mathrm{~m}}\end{aligned}\)

Substituting the values in the above expression and solving,

\(& \int_L y \cdot d L=\left[\frac{\left(36 \times(1 \mathrm{~m})^4+1\right)^{\frac{3}{2}}}{108}\right]-\left[\frac{\left(0+1 \mathrm{~m}^4\right)^{\frac{3}{2}}}{108}\right] \\& \int_L y \cdot d L=\frac{224.062}{108} \mathrm{~m}^2 \\& \int_L y \cdot d L=2.075 \mathrm{~m}^2\)

Now according to the formula for the center of gravity of a curve, the expression for the center of gravity of the homogenous rod is given by,

\(& \bar{y}=\frac{\int_L \bar{y}_1 \cdot d L}{\int_L d L} \\& \bar{y}=\frac{2.075 \mathrm{~m}^2}{2.42 \mathrm{~m}} \\& \bar{y}=0.857 \mathrm{~m}\)

Therefore, the center of gravity of the given homogeneous rod is

0.857 m above the horizontal axis

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Answer:

There is no x are we soppouse to name the triangle bc if so it would be isoclated

Step-by-step explanation:

Answer:62%

Step-by-step explanation: if you divide the amount spent by the amount made you get the percentage

Answer:

20 questions

Step-by-step explanation:

12/15 can be reduced to 4/5

you can create a ratio like the following:

4/5 = x/25

cross-multiply to get:

5x = 100

x = 20

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)