How to find the average collection period

Reason:

Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.

You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.

Answer:

 Numbers are 5 , 7

Step-by-step explanation:

  Let the two consecutive odd numbers be (2x + 1) and (2x + 3)

         Their product = 35

(2x + 1)(2x + 3) = 35

Use FOIL method.

       2x*2x + 2x*3  + 1*2x + 1*3 = 35

              4x² + 6x  + 2x + 3       = 35

      Combine like terms

                            4x² + 8x  + 3    = 35

                         4x² + 8x + 3 - 35 = 0

                            4x² + 8x  - 32   = 0

 Solving:

                 4x² + 8x - 32 = 0

Divide the entire equation by 2

                [tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]

                  2x² + 4x - 16 = 0

Sum = 4

Product = -32

Factors = 8 , (-4)

When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.

Rewrite the middle term

2x² + 8x - 4x  - 16 = 0

 2x(x + 4) - 4(x + 4) = 0

   (x + 4) (2x - 4) = 0

2x - 4 = 0   {Ignore x +4 = 0  as it gives negative number}

2x = 4

   x = 4/2

   x= 2

2x + 1 = 2*2 + 1 = 5

2x + 3 = 2*2 +3 = 7

   The numbers are 5 , 7

[tex]~~~~~~~\cos^2 \left(34^{\circ}\right) - \sin^2 \left( 34^{\circ} \right)=\cos A\\\\\implies \cos \left( 2 \cdot 34^{\circ} \right) = \cos A~~~~~~~~~~~~~;[\cos 2x = \cos^2 x -\sin^2 x]\\\\\implies \cos \left(68^{\circ}\right) = \cos A\\\\\implies A = 68^{\circ}[/tex]

Answer: Commutative property

Answer:

The answer is C: (2x +3, 2y)

Step-by-step explanation:

When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.

Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.

(x, y) -----> (2x, 2y)

Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.

Translation 2 units right:

(2x, 2y) -----> (2x +3, 2y)

−9x^4−18x^4y+27x^2y^2

Answer:

=−18x^4y−9x^4+27x^2y^2

Step-by-step explanation:

(−9x^2)(x^2+2x^2y−3y^2)

=(−9x^2)(x^2+2x^2y+−3y^2)

=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)

=−9x^4−18x^4y+27x^2y^2

=−18x^4y−9x^4+27x^2y^2

---

Hope I helped! Have a great day :)

Answer: C

Step-by-step explanation:

[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]

Answer:

The bottom right line plot.

Step-by-step explanation:

In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.

Answer:

[tex]p = 3\\\\q= 1[/tex]

Step-by-step explanation:

[tex]x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1[/tex]

To solve these types of problems:

 ⇒ just solve like a regular algebraic equation

     ⇒ with an inequality sign in the middle

Let's solve:

           [tex]-3p + 2 > 5\\-3p > 3[/tex]

                ⇒ must change the inequality sign to face the other direction

            [tex]-3p > 3\\p < -1[/tex]

Answer: p < -1

Hope that helps!

Answer:

p < -1

Step-by-step explanation:

-3p + 2 > 5

subtract 2 from both sides

-3p + 2 - 2 > 5 - 2

-3p > 3

divided both sides by -3 to get p alone

-3p / -3 > 3 / -3           reverse the inequality

p > -1

Step-by-step explanation:

we are missing the inequality sign in step 3.

step 1 and step 2 are correct.

step 4 is wrong.

the correct step 3 looks like

3x <= -3

if your original step 3 says the same, then the first wrong step is step 4.

if your original step 3 does not say the same, then the first wrong step is step 3.

Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,

sin²(x) + cos²(x) = 1

we always take the positive square root when solving for either sin(x) or cos(x).

Given that cos(α) = √11/7 and sin(β) = √11/4, we find

sin(α) = √(1 - cos²(α)) = √38/7

cos(β) = √(1 - sin²(β)) = √5/4

Now, recall the sum identity for cosine,

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

It follows that

cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

Pythagorean Theorem

[tex]c^2 = a^2 + b^2[/tex]

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]

Now let's factorize to get solutions for x.

[tex]0 = x(x-20)[/tex]

First solution:

[tex]x = 0[/tex]

Second solution:

[tex]x - 20 = 0\\x = 20[/tex]

Since a side of a triangle has to be a positive number, x is equal to 20.

Now let's just substitute x back to get side lengths. From the question the lengths are in inches.

longer leg: x = 20 in

shorter leg: x - 5 = 20 - 5 = 15 in

hypotenuse: x + 5 = 20 + 5 = 25 in

The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.

From the information, we are told to convert 2 litres into ml. This will be:

= 1000 × 2

= 2000ml

The number of eggs that will be bought to make 500 muffins will be:

= 500 × 2

= 1000 eggs.

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The theorem that verifies that the two right angled triangles are similar is HA.

Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.

Analysis:

From the diagrams KL = OQ ( hypotenuse)

∠L is equal to ∠Q which are acute.

so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.

In conclusion, the HA theorem verifies that the two triangles are similar.

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Answer:

  68 texts per day

Step-by-step explanation:

The description of the variables in the equation tells you that you want to find t (texts sent per day) for the given value of 'a' (age in years).

__

Substitute the number (15) for the variable (a) and do the arithmetic:

  t = -1.63a +92.14

  t = -1.63(15) +92.14 = -24.45 +92.14

  t = 67.69

Keiko's trend line estimates a 15-year-old would send about 68 texts per day.

let me answer the last one first

compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.

hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.

hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.

now let's do the others

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]

Using proportions, it is found that the number of chaperones that the school needs is given by:

B. 8.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 2 chaperones are needed for every 25 students. How many are needed for 100 students? The rule of three is given by:

2 chaperones - 25 students

n chaperones - 100 students

Applying cross multiplication:

25n = 2 x 100

n = 200/25

n = 8.

Hence option B is correct.

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By solving a quadratic equation, we will see that the length is 10m and the width is 6.5m

For a rectangle of width W and length L, the area is:

A = W*L

In this case, we know that the area is 65m² and that the length is 3 meters less than 2 times the width, so:

L = 2*W - 3m

Then we can write:

65m² = (2*W - 3m)*W = 2*W² - 3m*W

This is a quadratic equation:

2*W² - 3m*W - 65m² = 0.

The solutions are given by the Bhaskara's formula:

[tex]W = \frac{3 \pm \sqrt{(-3)^2 - 4*2*(-65)} }{2*2} \\\\W = \frac{3 \pm 23 }{4}[/tex]

We only care for the positive solution, which is:

W = (3m + 23m)/4 = 26m/4 = 6.5m

Then the length is:

L = 2*6.5m - 3m = 10m

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Answer:

x = 6, -3

Step-by-step explanation:

. . . . . . . . . . . . . . . . .

Answer:

your answer is 4 my friend

Step-by-step explanation:

Step-by-step explanation:

Reflection in the x axis (x,y)—>(x,-y)

(-4,-3)—>(-4,3)

The exercise is designed to test the students knowledge of prepositions. The correct answer thus is (Option D) Yo estudio (which translates) "I study".

To understand the answer, you need to know what a preposition is. A preposition, in simple terms, is a word or group of words that comes before a noun.

The function of a preposition (much like an adjective) is to give clarity to the noun that it precedes.

Let us complete the Preposition phrase to give meaning to it:

"I study Mathematics". Where;

"Mathematics" is the noun;

"I Study" is the prepositional phrase. Hence the correction answer to the question above is Option D.

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The probability of drawing a black ball on the second draw will be 3/5.

From the information given, the total number of balls will be:

= 2 + 3 = 5 balls.

When the first ball is black and the second is red. This will be:

= 2/5 × 3/4

= 3/10

When the first is red and the second is black, this will be:

= 3/5 × 2/4

= 3/10

Therefore, the probability of drawing a black ball on the second draw will be:

= 3/10 + 3/10

= 3/5.

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B. x^9

just simplify

Answer:

4x^2 - 4x - 3

Step-by-step explanation:

f(x) = 2x - 1

g(x) = x^2 - 4

g(f(x)) = ?

[substitute the x of g(x) with f(x)]

g(x) = x^2 - 4

g(f(x)) = (2x - 1)^2 - 4

[solve]

[binomial * binomial = quadratic equation]

[use FOIL method (first, outer, inner, last)]

g(f(x)) = (2x - 1)(2x - 1) - 4

g(f(x)) = (2x*2x) + (-2x) + (-2x) + (1) - 4

[combine like terms]

g(f(x)) = 4x^2 - 2x - 2x + 1 - 4

g(f(x)) = 4x^2 - 4x - 3

(4)

1. 11.444 repeater

2. 0.58333 repeater

3. 6.7333 repeater

4. 27.5454 repeater (on both 5 and 4)

5. 1.482517482517 (482517 repeater)

6. 2.285714285714 (285714 repeater)

7. 7.5666 repeater

8. 60.60606060 (60 repeater)

(5)

1. 0.666 (repeater)

2. 0.3666 (repeater)

3. 1.1818181818 (18 repeater)

4. 0.418181818 (18 repeater)