Find the measure of < 1.
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Answer: 184,500

Hope i could help

Answer:

182.91

Step-by-step explanation:

First multiply the cost of the meal by the sales tax percentage as a decimal (.14)

\(136.50*.14=19.11\)

Then multiply the cost of the meal before sales tax by the tip percentage

\(136.50*.2=27.30\)

Then add the tip and the sales tax on top of the cost of the meal to calculate the total cost

\(136.5+19.11+27.3=182.91\)

Answer:

I would pick C.

Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Answer:

\(\textsf{a)}\quad P(t)=310000(1.0085)^t\)

where P is the population, and t is the number of years after 500 BC.

b)   42,013,000

Step-by-step explanation:

\(\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}\)

Define the variables:

The population in 500 BC is the initial value (when t = 0), therefore if the population was 310,000 in 500 BC:

If the population increases by 0.85% each year then the growth rate in decimal form is:

Therefore, the function that models the given scenario is:

\(\boxed{P(t)=310000(1.0085)^t}\)

where P is the population, and t is the number of years after 500 BC.

To use the function to calculate the population in 80 AD, first calculate the number of years (value of t):

⇒ 80 AD - 500 BC = 580 years

Therefore, to find the population in 80 AD, substitute t = 580 into the function:

\(\implies P(580)=310000(1.0085)^{580}\)

\(\implies P(580)=42013142.9844236...\)

Therefore, the population in 80 AD is 42,013,000 (to the nearest thousand).

The two tanks differ in terms of Filling rates and initial volumes.

We can work with the equation for tank A, which represents a linear relationship between the volume of liquid in the tank (y) and the time it has been filling (x).

The equation y = 75x + 110 tells us that the tank A is filling at a constant rate of 75 units per minute, starting with an initial volume of 110 units.

To analyze the data for tank B, we would need to know the volumes of the tank at different times as it is being filled.

If the relationship for tank B is also linear, we could find the equation that represents it by using two points from the table and the slope-intercept form of a linear equation (y = mx + b). Once we have both equations, we can compare them to see how the two tanks differ in terms of filling rates and initial volumes.

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The constant of proportionality is 5

Answer:

I think it's B

Step-by-step explanation:

Answer:

The coordinates of the dillated vertices are \(A'(x,y) = (2,2)\), \(B'(x,y) = (4,4)\), \(C'(x,y) = (8,2)\) and \(D'(x,y) = (4,-2)\).

Step-by-step explanation:

From Linear Algebra, we define dilation by the following equation:

\(P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]\) (1)

Where:

\(O(x,y)\) - Center of dilation, dimensionless.

\(P(x,y)\) - Original point, dimensionless.

\(k\) - Scale factor, dimensionless.

\(P'(x,y)\) - Dilated point, dimensionless.

If we know that \(O(x,y) = (0, 0)\), \(k = 2\), \(A(x,y) = (1,1)\), \(B(x,y) = (2,2)\), \(C(x,y) = (4,1)\) and \(D(x,y) = (2,-1)\), then the dilated points are, respectively:

Point A

\(A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)]\) (2)

\(A'(x,y) = (0,0) + 2\cdot [(1,1)-(0,0)]\)

\(A'(x,y) = (2,2)\)

Point B

\(B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)]\) (3)

\(B'(x,y) = (0,0) + 2\cdot [(2,2)-(0,0)]\)

\(B'(x,y) = (4,4)\)

Point C

\(C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)]\)

\(C'(x,y) = (0,0) + 2\cdot [(4,1)-(0,0)]\)

\(C'(x,y) = (8,2)\)

Point D

\(D'(x,y) = O(x,y) + k\cdot [D(x,y)-O(x,y)]\)

\(D'(x,y) = (0,0) + 2\cdot [(2,-1)-(0,0)]\)

\(D'(x,y) = (4,-2)\)

The coordinates of the dillated vertices are \(A'(x,y) = (2,2)\), \(B'(x,y) = (4,4)\), \(C'(x,y) = (8,2)\) and \(D'(x,y) = (4,-2)\).

Answer:

  150 m²

Step-by-step explanation:

You want the total area of a figure consisting of a 12 m wide rectangle 5 m high with a triangle above that bringing the total height to 20 m.

The area of the rectangle is the product of its length and width:

  A = LW

  A = (12 m)(5 m) = 60 m²

The area of the triangle is half the product of its base and height.

  A = 1/2bh

  A = 12/(12 m)(20 -5 m) = 90 m²

The area of the whole figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 60 m² +90 m² = 150 m²

The area of the figure is 150 m².

__

Additional comment

Since you know a triangle's area is equivalent to the area of a rectangle that has half the height, the 15 m high triangle can be considered as a rectangle 7.5 m high. Adding that to the 5 m area of the rectangle already there gives the equivalent area as that of a rectangle 12 m wide and 5+7.5 = 12.5 m high: (12 m)(12.5 m) = 150 m².

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Answer:

(-5, -8)

Step-by-step explanation:

Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k).

x^2 + 10x = - 17

x^2+10x+17=0

x^2+2*5x+25 - 8=0

(x+5)^2-8=0

h=-5, k= -8

vertex is (-5, -8)

Answer:

176

Step-by-step explanation:

The unknown number is between 100 and 200

      H  T U;

By default, the hundred unit  = 1

  The tens unit is from 0-9

Given that the ten digit is 2 less than 9;

         Tens digit = 9-2 = 7

So,

   Hundred digit  = 1

    Tens digit  = 7

Unit digit  = 14 - (1+7)= 6

The number of 176

Answer:

665.3

Step-by-step explanation:

You start with a temperature of 62 degrees and add 612. You now have 674. You then subtract 8.7 from 674 to arrive at an answer of 665.3.

The evening temperature will be 665.3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can ais lso be used to indicate the logical syntax's order of operations and other features.

Given that Joaquin recorded a temperature of 62°F this morning for science class. The temperature increased to 612°F in the afternoon before decreasing to 8.7°F in the evening.

The evening temperature will be calculated as below:-

Start with a temperature of 62 degrees and add 612. You now have 674. You then subtract 8.7 from 674 to arrive at an answer of 665.3.

Evening temperature = 62 + 612 - 8.7

Evening temperature = 665.3 F

Therefore, the evening temperature will be 665.3.

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Answer:

1/12

Step-by-step explanation:

1+1=2

there are 24 hours in a day so, 2/24= 1/12

The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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Answer:

5 total hours

Step-by-step explanation:

3 ÷ 60% = 5

Alan worked 5 hours on the project.

A percentage is a proportion or value that may be expressed as a fraction of 100. Furthermore, the notation "%" is used to denote it.

Let H be the hours he worked on the model.

Alan spent 3 hours building a model for his science project. This was 60% of the total time he spent on the project.

To find the H;

we use the percentage property,

3 = H x 60 / 100

H = 300 /60

H = 5 hours.

Therefore, 5 hours he worked on the project.

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The given triangle has one angle of 90° and the other two are different thus, it will be the right scalene triangle so option (A) is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

The given triangle has been drawn below.

A right-scalene triangle is a right-angle triangle whose angles other than 90 degrees are not the same.

Since the given triangle it is not the same thus it will be a right scalene triangle.

Hence "The given triangle has one angle of 90° and the other two are different thus, it will be the right scalene triangle".

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Answer:

Step-by-step explanation:

Given that:

If C(x) =  the cost of producing x units of a commodity

Then;

then the average cost per unit is c(x)  = \(\dfrac{C(x)}{x}\)

We are to consider a given function:

\(C(x) = 54,000 + 130x + 4x^{3/2}\)

And the objectives are to determine the following:

a) the total cost at a production level of 1000 units.

So;

If C(1000) = the cost of producing 1000 units of a commodity

\(C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}\)

\(C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )\)

\(C(1000) = 54,000 + 130000 + 4(31622.7766)\)

\(C(1000) = 54,000 + 130000 + 126491.1064\)

\(C(1000) = $310491.1064\)

\(\mathbf{C(1000) \approx $310491.11 }\)

(b) Find the average cost at a production level of 1000 units.

Recall that :

the average cost per unit is c(x)  = \(\dfrac{C(x)}{x}\)

SO;

\(c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}\)

Using the law of indices

\(c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}\)

\(c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}\)

c(1000) =$ 310.49 per unit

(c) Find the marginal cost at a production level of 1000 units.

The marginal cost  is C'(x)

Differentiating  C(x) = 54,000 + 130x + 4x^{3/2} to get  C'(x) ; we Have:

\(C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}\)

\(C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}\)

\(C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}\)

\(C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}\)

\(C'(1000) = 319.7366596\)

\(\mathbf{C'(1000) = \$319.74 \ per \ unit}\)

(d)  Find the production level that will minimize the average cost.

the average cost per unit is c(x)  = \(\dfrac{C(x)}{x}\)

\(c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}\)

the production level that will minimize the average cost is c'(x)

differentiating \(c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}\) to get c'(x); we have

\(c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }\)

\(c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }\)

Also

\(c''(x)= \dfrac{108000}{x^3} -x^{-3/2}\)

\(c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0\)

\(x^2 = 27000\sqrt{x}\)

\(\sqrt{x} (x^{3/2} - 27000) =0\)

x= 0;  or  \(x= (27000)^{2/3}\) = \(\sqrt[3]{27000^2}\) = 30² = 900

Since  production cost can never be zero; then the production cost = 900 units

(e) What is the minimum average cost?

the minimum average cost of c(900) is

\(c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}\)

c(900) = 60 + 130 + 4(30)

c(900) = 60 +130 + 120

c(900) = $310 per unit

(a) Starting at 12 and making 1/2 revolution clockwise, the hand stops at 6.

(b) Starting at 2 and making 1/2 revolution clockwise, the hand stops at 8.

(c) Starting at 5 and making 1/4 revolution clockwise, the hand stops at 8.

(d) Starting at 5 and making 3/4 revolution clockwise, the hand stops at 11.

To determine where the hand of a clock will stop, we need to consider the fractions of a revolution made by the hand starting from different positions.

(a) If the hand starts at 12 and makes 1/2 of a revolution clockwise, it will stop at 6.

This is because a half revolution corresponds to the hand moving from 12 to 6 on the clock face.

(b) If the hand starts at 2 and makes 1/2 of a revolution clockwise, it will stop at 8.

Again, a half revolution corresponds to the hand moving from 2 to 8 on the clock face.

(c) If the hand starts at 5 and makes 1/4 of a revolution clockwise, it will stop at 8.

A quarter revolution corresponds to the hand moving from 5 to 8 on the clock face.

(d) If the hand starts at 5 and makes 3/4 of a revolution clockwise, it will stop at 11.

A three-quarter revolution corresponds to the hand moving from 5 to 11 on the clock face.

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Answer:

The answer to the question provided is option 2.

Answer:

−225x^6y^4

Step-by-step explanation:

If a manufacturer manufactures 5,000 dozen of sweaters, and sells 3,000 dozen of them only, then the total profit he/she earns from the these sweaters is [1000(3x - 5y)], assuming that the cost of manufacturing one sweater is "x" and the selling price of that sweater is "y".

As per the question statement, a manufacturer miscalculates the demand of the market and manufactures 5,000 sweaters, but sold only 3000 of them.

We are required to calculate the total profit earned by the manufacturer from the sale of the sweaters.

Since, no data about the manufacturing cost of the sweaters and their selling price is provided in the question statement, let us assume that the cost of manufacturing one sweater is "x" and the selling price of that sweater is "y". Solving with these variables will give us a generalized answer which we can use for any value.

Now, Since assumed that, manufacturing cost of one sweater is "x", then, manufacturing cost of 5000 sweaters will be \((5000*x)=5000x\).

Similarly assumed that, selling cost of one sweater is "y", and then, selling cost of 3000 sweater will be \([(3000*y)=3000y]\).

Now, we know that,

[Profit = (Total Selling Cosy) - (Total Manufacturing Cost)],

Therefore, in this case, total profit from the sale of 3000 sweaters

\(=(3000y-5000x)\\=1000(3y-5x)\).

Now, on using real integers or numbers in place of "x" and "y", if the value of Profit comes negative, it will mean, that for those values of "x" and "y", the manufacturer makes loss, not profit.

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1. The simplified expression for the area of the triangle is 10x²y²

2. The expression for the volume of the prism is 80x²y²

3. The area of the triangle 1440 cm² and the volume of the prism is 11520cm³

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The area of a triangle is expressed as

A = 1/2bh

where b is the base and h is the height.

base = 5x'y'

height = 4xy

A = 1/2 × 5xy × 4xy

A = 10x²y²

The volume of a prism is expressed as;

V = base area × height

height = 8cm

The expression for the volume = 10x²y² × 8

= 80x²y²

When x = 4 and y = 3

A = 10x²y² = 10 × 16 × 9

= 1440 cm²

Volume of the prism = 1440 × 8

= 11520 cm³

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Answer:

14 cm.

Step-by-step explanation:

The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

In this case, the width is 4 cm and the length is 3 cm.

P = 2(3) + 2(4)

P = 6 + 8

P = 14

So, the perimeter of the rectangle is 14 centimeters.

Answer: 14

Step-by-step explanation:

2 sides are 3

2 sides are 4

3x2 is 6

2x4 is 8

8+6 is 14

let's firstly move the decimal point to the right, thus leaving the recurring part to the right, and then assign the recurring part at right to some variable, let's proceed.

\(1.4\overline{55555}\implies \cfrac{14.\overline{55555}}{10}\qquad \qquad \stackrel{\textit{now let's make}}{x = 0.\overline{55555}} \\\\\\ \stackrel{\textit{so then we can say}}{\cfrac{14.\overline{55555}}{10}\implies \cfrac{14+0.\overline{55555}}{10}}\implies \cfrac{14+x}{10} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{so we can say that}~\hfill }{10x~~ =~~5.\overline{55555}}\implies 10x = 5+ 0.\overline{55555}\implies 10x = 5+x \\\\\\ 9x=5\implies x = \cfrac{5}{9}\)

well, now let's plug that into our fraction

\(\cfrac{14+x}{10}\implies \cfrac{14+\frac{5}{9}}{10}\implies \cfrac{~~\frac{131}{9}~~}{10}\implies \blacktriangleright\cfrac{131}{90}\implies 1\frac{41}{90} \blacktriangleleft\)

Answer:

25:15

Hope this helps :)

Step-by-step explanation:

5:3 so since there is 25 dogs we had to multiply 5 to the 5 in 5:3. We will have to multiply 5 to the 3 in 5:3 to get number of cats.

5:3 = 25:15

Answer:

\( = 15\)

Step-by-step explanation:

Taking that the ratio of dogs to cats is 5:3, then:

The number of dogs = 25, so:

\(5 = 25 \\ 3 = x \\ x= 25 \times 3 \div 5 \\ x = 15\)

Answer:

a= -858

Step-by-step explanation:

46 times -18 equals -846

-846-12 equals -858

Answer:

a=-858

Step-by-step explanation:

12+a=846

a=-846-12

a=-858

Answer: 14

Step-by-step explanation: