Tim had 15 dollars. Paul had 6 dollars more than Tim. Rick had double Tim’s money. How much did they have ALTOGETHER?

The equation which is equivalent to the given simple interest formula is

[tex]P=\frac{A}{1+rt}[/tex].

What is an equivalent equation?

Equivalent equations are algebraic equations that have identical solutions.

According to the given question.

We have a simple interest formula.

[tex]A=P(1+rt)[/tex]

Now, the equivalent equation for the above formula can be given as

[tex]A=P(1+rt)[/tex]

⇒[tex]P=\frac{A}{1+rt}[/tex]

Hence, the equation which is equivalent to the given simple interest formula is [tex]P=\frac{A}{1+rt}[/tex].

Thus, option A is correct.

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The  airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let a represent the rate of the airplane with no wind. and b the rate of the wind, hence:

(a - b)3.2 = 640

a - b = 200   (1)

Also:

(a + b)2 = 640

a + b = 320    (2)

The solution to equation 1 and 2 is:

a = 260, b = 60

The  airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.

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Answer:

Ratio is 11 : 13

Step-by-step explanation:

We are given;

Time to develop estimate = 30 minutes

Time to do the job = 2 hours 45 minutes = (2 * 60) + 45 = 165 minutes

Total time to develop and do job = 165 + 30 = 195 minutes

Thus;

Ratio of time spent on job to total time = 165 : 195

Whrn this is broken further, we have; 11 : 13

Answer:

24 pounds of garlic

Step-by-step explanation:

if she spends 3$ per pound, you divide 72 by 3. the answer to that is 24, so if she spends 72 dollars on only garlic, she can buy 24 pounds.

Jennifer can buy 24 pounds of garlic

we see here, that if she spends 3$ per pound, you divide 72 by 3.

The answer would be 24, so if she spends 72 dollars on only garlic,

she can buy 24 pounds.

1: any of various units of mass and weight specifically: a unit now in general use among English-speaking peoples equal to 16 avoirdupois ounces or 7000 grains or 0.4536 kilogram — see Weights and Measures Table

2: the basic monetary unit of the United Kingdom.

In maths, a division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each

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Answer:

(x+9) and (x-4)

Step-by-step explanation:

The team can be formed in 420 different ways

This is a combination problem since we are to select a set of people from a group. Combination has to do with selection.

if r number of objects is to be selected from a pool of n objects, this can be done in nCr number of ways.

[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]

Now If A company has 8 male and 6 female employees, and needs to nominate 2 men and 2 women for the company bowling team, then this can be done in the following way;

[tex]_{8} C_{2}=\frac{8!}{2!6!} =28\\_{6} C_{2}=\frac{6!}{2!4!} =15[/tex]

[tex]_{8} C_{2}*_{6} C_{2}=28*15[/tex]

[tex]=420[/tex] teams

Hence, The team can be formed in 420 different ways

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Answer:

The third option.

Step-by-step explanation:

[tex](\frac{4xy^3}{x^2})^2\\\\=(\frac{4y^3}{x})^2\\\\=\frac{16y^6}{x^2}[/tex]

Hence the 3rd option.

The table is

x | 4 | 8 | 12
y |  1 | 2 | 3

The question is not understandable. The well-formatted question is

Complete the table for the given rule

Rule:

[tex]y=\dfrac{1}{4}x[/tex]

Table:

x | 4 | 8 | 12
y |  ? | ? | ?

Evaluation of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the provided number to replace the expression's variable before applying the sequence of operations to simplify the expression.

For instance

On evaluation of y= x+7  when x=3, and x=12

we get y(3) = 3 + 7 = 10 and y(12) = 12 + 7 = 19

The given equation is

[tex]y=\dfrac{1}{4}x[/tex]

So, the table is

x | 4 | 8 | 12
y |  1 | 2 | 3

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Answer:

0

12/4

1.75

in that order

Answer:

If it is assumed that the change was constant from 2009 and 2012 , then change of population is 142 .

Step-by-step explanation:

In the question, it is given that the population of a small town increased from 1442 to 1868 between 2009 and 2012 .

It is asked to find the change of population if it is assumed that the change was constant from 2009 and 2012 .

Step 1 of 2

Population in 2012 is given to be 1868 and

Population in 2009 is given to be 1442 .

Duration of year is given by 2012-2009 which is 3 years.

Change in population is given by 1868-1442 which is 426 .

Step 2 of 2

Change in population per year is given by dividing the change in population and the duration of years it took to happen the change.

Hence, change in population per year is

[tex]$\frac{426}{3}=142$[/tex]

Hence, the population was changed by 142 per year from 2009 to 2012 .

Answer:

LM

Step-by-step explanation:

Usually these problems would already be in order, so since PQ are the first 2 letters of polygon PQRS, then for LMNO, it's LM.

Step-by-step explanation:

it isnot looking well here so go on geogebra. org/calculator and you will see. have a nice day :))

Answer:

C on Edge 2022

Step-by-step explanation:

Just did it and got it right

Coterminal angles are angles that are made by the positive x-axis of the coordinate plane. The positive angle that is less than 2π and is coterminal with 14π/6 is  1/3π.

Coterminal angles are angles that are made by the positive x-axis of the coordinate plane.

The angle that 14π/6 makes from the positive x-axis is 1/3π, which is equal to 60°.

Hence, the positive angle that is less than 2π and is coterminal with 14π/6 is  1/3π.

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Answer:

Second graph

Step-by-step explanation:

See attached image.

dy/dx by implicit differentiation is cos(πx)/sin(πy)

Since we have the equation

(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.

So, [(sin(πx) + cos(πy)⁸ = 17]

d[(sin(πx) + cos(πy)⁸]/dx = d17/dx

d[(sin(πx) + cos(πy)⁸]/dx = 0

Let sin(πx) + cos(πy) = u

So, du⁸/dx = 0

du⁸/du × du/dx = 0

Since,

= dsin(πx)/dx + dcos(πy)/dx

= dsin(πx)/dx + (dcos(πy)/dy × dy/dx)

= πcos(πx) - πsin(πy) × dy/dx

So, du⁸/dx = 0

du⁸/du × du/dx = 0

8u⁷ × [ πcos(πx) - πsin(πy) × dy/dx] = 0

8[(sin(πx) + cos(πy)]⁷ ×  (πcos(πx) - πsin(πy) × dy/dx) = 0

Since 8[(sin(πx) + cos(πy)]⁷ ≠ 0

(πcos(πx) - πsin(πy) × dy/dx) = 0

πcos(πx) = πsin(πy) × dy/dx

dy/dx = πcos(πx)/πsin(πy)

dy/dx = cos(πx)/sin(πy)

So, dy/dx by implicit differentiation is cos(πx)/sin(πy)

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Answer:

B

Step-by-step explanation:

[] means the endpoints are inclusive. Therefore [2,7] is equivalent to 2 <= x <= 7. So [2,7] represents graph B.

If the salesman chooses highway route 1 he will arrive in the shortest time because the distance in route 1 is less than the distance in route 2.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Route 1:

The distance between A and D

Distance of AB:

[tex]\rm AB=\sqrt{(400-0)^2+(300-0)^2}[/tex]

AB = 500 mi

Distance between BD:

[tex]\rm BD=\sqrt{(1300-400)^2+(1500-300)^2}[/tex]

BD = 1500 mi

In route 1 the distance traveled by salesman:

AD = 500 + 1500 = 2000 mi

Route 2:

[tex]\rm AC=\sqrt{(800-0)^2+(1500-0)^2}[/tex]

AC = 1700 mi

[tex]\rm CD=\sqrt{(1300-800)^2+(1500-1500)^2}[/tex]

CD = 500 mi

AD(through C) = 1700 + 500 = 2200 mi

Thus, if the salesman chooses highway route 1 he will arrive in the shortest time because the distance in route 1 is less than the distance in route 2.

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Answer: 3

Step-by-step explanation:

By the intersecting chords theorem,

[tex](KM)(16)=(4)(12)\\\\KM=3[/tex]

Answer:

Step-by-step explanation:

Answer:

Answer A is correct

Step-by-step explanation:

Let us use completing square method for this.

[tex]x^{2} -5x -10=0\\\\x^{2} -5x=10\\\\x^{2} -5x+\frac{25}{4}=10+ \frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{10*4}{1*4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40}{4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40+25}{4} \\\\(x+\frac{5}{2}) ^{2} =\frac{65}{4} \\\\(x+\frac{5}{2}) = \±\sqrt{\frac{65}{2} }\\\\(x+\frac{5}{2}) =\±\frac{\sqrt{65}}{4}\\\\x=\±\frac{\sqrt{65}}{4}-\frac{5}{2}[/tex]

∴ [tex]x=-\frac{5}{2} \±\frac{\sqrt{65}}{4}[/tex]

Answer:

a.) 1003

Step-by-step explanation:

The formula to find the sum of an arithmetic sequence: Sn = n/2[2a + (n - 1)d], where a is the first term, n is the number of terms and d is the common difference.

1) Let's substitute the values into the formula.

S17 = 17/2[2(11) + (17 - 1)6]

S17 = 17/2[22 + (16)6]

S17 = 17/2[22 + 96]

S17 = 17/2[118]

S17 = 17/2 × 118

S17 = 1003

Therefore, the sum of the first 17 terms of this arithmetic sequence is 1003 (a).

Answer:

3300

Step-by-step explanation:

This can be worked out using PEMDAS:

First you solve in the PARENTHESIS:

(4 × 10³) – (7 × 10²)

Then, you look at the EXPONENTS:

(4 × 10³) = (4 × 1000)

(7 × 10²) = (7 × 100)

After that, look at the MULTIPLICATION:

(4000) - (700)

Since there is only subtraction left, subtract it:

3300

Answer:

Parenthesis:

4 *1000 = 4000

7*100= 700

4000-700=3300

Step-by-step explanation:

Answer:

19912/76000=0.262.000000

Answer:

Step-by-step explanation:

 19912 76000  

-152000 0.262  

  471200

 -456000

    152000

   -152000

         0

Answer:

Step-by-step explanation:

from the sign on the picture it is a rigth triangle

we use pythagoras

x² = 12² - 7²

x² = 144 - 49

x² = 95

x = √95

(x = 9.75)

Answer:

x = [tex]\sqrt{95}[/tex]

Step-by-step explanation:

In this problem, we need to use the Pythagorean theorem.

Pythagorean theorem is a theorem where you can find a side length in a right triangle.

The hypotenuse (The longest side) squared equals the other two side lengths added together after being squared.

In numbers, this will be: (12)^2 = (7)^2 + (x)^2.

144 = 49 + x^2.

95 = x^2

x = [tex]\sqrt{95}[/tex]

We cannot simplify [tex]\sqrt{95}[/tex], so that is the final answer.

Answer:

It must be probably √29

Step-by-step explanation:

[tex]distance = \sqrt{ { (- 4)}^{2} + {(5)}^{2} } [/tex]

hope it to be the correct...

The first graph is the exponential function.

The exponential function serves as the  positive-valued function with respect to real variable. and  the values denoted as X which is exponential is  all real numbers.

Analyzing the first graph, moving down the graph, we can see that  x value increases.

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Answer:

First Graph

Step-by-step explanation:

Edge

The false statement include:

This relationship between two variables involves them having a positive slope. This means that as volume increases, temperature also increases which isn't the case.

This cause and effect pattern also means that the volume doesn't have explanatory variables.

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Answer:

Volume is the explanatory variable

Step-by-step explanation:

because vanilla is better than chocolate

Since we know that <C is congruent to <E, we can say that: A. the two triangles are similar by SAS.

In Geometry, two triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Ratio = BC/AC = 6/3 = 2.

Ratio = FE/DE = 4/2 = 2.

Thus, the ratio of their corresponding sides are equal in magnitude i.e BC/AC ≡ FE/DE.

Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.

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Answer:

9.62 cm²

Step-by-step explanation:

 diameter = 7 cm

              r = 7 ÷2 = 3.5 cm

             Ф = 45°

  [tex]\sf \boxed{\text{\bf Area of sector = $\dfrac{\theta}{360}*\pi r^2$}}[/tex]  

                              [tex]\sf =\dfrac{45}{360}*3.14*3.5*3.5\\\\ = 4.81 \ cm^2[/tex]

Area of the given sectors = 2 *4.81

                                           = 9.62 cm²

Hello!

Let's solve this in step

Let's find the circular region to the left of the center:

  [tex]Area = \frac{45}{360}*Area_.formuka_.of_.Circle =\\ Area = \frac{45}{360}*\pi (radius)^2\\ Area = \frac{45}{360} *\pi (3.5)^2\\Area=4.81[/tex]

Now let's find the circular region to the right of the center

 ⇒ the angle 45° by the vertical angle theorem is equal to the angle  

      opposite it in the other circular region

     ⇒ has the same area as the left region

Total Area = 4.81 + 4.81 = 9.62 cm²

Answer: 9.62 square centimeters

Hopefully that helps!

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.