What is the decay factor in the exponential decay function y=a (1-r) t

Answer: 7.142857142857143

Step-by-step explanation: all you have to do is divide 28.5 by 3.99

The cost per ounce of shampoo is 7.15 ounce.

Assume that the cost per ounce of shampoo is ${x}.

Total cost of bottle of a dog shampoo is $3.99.

Amount of shampoo in the bottle is 28.5 ounces.

So, we can write the cost per ounce of shampoo as

x = 28.5/3.99

x = 7.15 ounce

The cost per ounce of shampoo is 7.15 ounce.

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Answer:

First Term = 6

Common Ratio = 3

Step-by-step explanation:

According to the Question,

Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .

Now, on solving  [tex]\frac{S_{8} }{S_{4} }[/tex]  we get,

[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]  

[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]

[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )

So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .

Answer:

70

Step-by-step explanation:

the fraction 7/10 turns into 70% which means 70 out of 100 tickets were sold.

Answer:

70 tickets sold

Step-by-step explanation:

Multiply the number of tickets by the fraction of tickets sold

100 *7/10

Rewriting

100/10 * 7

10*7

70

Answer:

The Number of Zeroes In The Results is Always equal To the Powers of 10.

Step-by-step explanation:

Example:-

345*[tex]10^{2}[/tex] = 34500

345*[tex]10^{5}[/tex] = 34500000

345*[tex]10^{7}[/tex] = 3450000000

345*[tex]10^{8}[/tex] = 34500000000

(In the Above examples, There is All The Numbers of Zeroes In The Results is equal To the Powers of 10)

Step-by-step explanation:

In interval form, the domain of f is (−∞,∞).

Answer:

CNBD

Step-by-step explanation:

From the diagram, we can see that:

[tex]\displaystyle BL\parallel CA[/tex]

Then by Alternate Interior Angles:

[tex]\angle LBA\cong \angle CAB\text{ and } \angle BLC\cong \angle ACL[/tex]

From vertical angles, we also know that:

[tex]\displaystyle \angle BKL\cong \angle AKC[/tex]

This is all we can gather from the given image. Knowing only three pairs of angles cannot prove congruence, as proving congruence requires at least one side.

Congruence cannot be determined.

Answer:

Cannot be determined

Step-by-step explanation:

With BL and AC being parallel, we can deduce that the two triangles in question share all three of their angles. However, there is no information given that implies any of the sides are equal. AAA (Angle-Angle-Angle) is a proof of similarity, but not congruence, therefore the two triangles cannot be determined to be congruent.

Answer:

x=3

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

There are a couple of useful facts about parallelograms that can be used here.

1) The diagonals bisect each other.

2) Opposite sides are parallel, so each diagonal can be considered a "transversal" with respect to parallel lines. That means all of the angle relationships involving parallel lines apply.

__

The two marked sections of diagonal GIE are congruent, so you have ...

  3x +1 = 10

  3x = 9 . . . . subtract 1

  x = 3 . . . . . divide by 3

__

Angles IEH and IGF are "alternate interior" angles, so are congruent.

  angle IEH = 61°

__

Angles IHE and IFG are "alternate interior" angles, so are congruent.

  angle IHE = 35°

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{1}{6} + \frac{1}{6} + \frac{1}{6} =\frac{1}{2}[/tex]

Answer:

[tex]7,500[/tex]

Step-by-step explanation:

Let's solve this problem step-by-step. The library had 1,500 books in 2011. The ratio of books in 2011 and in 2012 is 1:2. Therefore, let the number of books in 2012 be [tex]x[/tex].

We have the following proportion:

[tex]\frac{1}{1,500}=\frac{2}{x},\\x=2\cdot 1,500=3,000[/tex]

Therefore, there were 3,000 books in 2012. The ratio of books in 2012 and in 2013 is 2:5. Let the number of books in 2013 be [tex]y[/tex].

We have:

[tex]\frac{2}{3,000}=\frac{5}{y},\\2y=5\cdot 3,000,\\2y=15,000\\y=\boxed{7,500}[/tex]

Therefore, there were 7,500 books in 2013.

Answer:

7,500 books

Step-by-step explanation:

Answer: Apply for loans

Step-by-step explanation:

I just took the quiz off gradpoint :) trust me its right!!!!

Answer:

The value of x is 9.

Step-by-step explanation:

55°

(3 x + 23)

75°

The sum of all the angles of triangle is 180°.

55 + 3 x + 23 + 75 = 180

3 x = 27

x = 9

So, the value of x is 9.

Answer:

Step-by-step explanation:

FORMULA= P(A)=

NUMBER OF FAVORABLE OUTCOMES

-------------------------------------------------------------

NUMBER OF POSSIBLE OUTCOMES

GIVEN: 12 Guitars, 10 Bass, 9 Drums, 12 Keyboards

WANT: The probality a seventh grader chosen at randome will play drums

add all the instruments

12+10+9+12=33

there are 9 drums

FOLLOW THE FORMULA

9 3

---- = ---- SIMPLIFIES FORM

33 11

Answer:

Everything is correct except for the second one and the ones you checkmarked.

Step-by-step explanation:

Answer:

140 degrees

Step-by-step explanation:

Answer: The measure of angle 4 is 95 degrees.

Step-by-step explanation:

Knowing that the lines are parallel that means the alternate exterior angles are congruent. The alternate exterior angle of the angle marked with 95 degrees is angle 1. That means angle one is 95 degrees. Angle 1 and Angle 4 are vertical angles. All vertical angles are congruent so this mean angle 4 is also 95 degrees.

Answer:

20 % increase in Area

Step-by-step explanation:

1.  Original Rectangle Area = 150cm ²

2. 20% of 15 is 3

3. Increased length is equal to 18

4. Increased Rectangle Area = 180cm ²

5. Ten percent of 150 = 15.

6. 15x2(ten percent) = 30. Which give us 150+30 equal to 180.

7. 2 ten percent equals 20%

8. Answer is 20%.

Answer:

to use the money when in an emergency

Answer:

15 is larger than -4

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

15 ÷ (-4) = -3.75

Answer:

Step-by-step explanation:

We could use the Law of Sines if we only knew what angle A was. It just so happens that by the Triangle Angle-Sum Theorem, angle A is equal to

180 - B - C. Therefore,

angle A = 180 - 11 - 75 so

angle A = 94. And the Law of Sines is

[tex]\frac{sin94}{a}=\frac{sin11}{600}[/tex] and cross multiply to get

600sin94 = asin11 and solve for a:

[tex]a=\frac{600sin94}{sin11}[/tex] gives you that

a = 3136.85

In the second quadrant, both cos and tan are negative while only sin is positive.

To find tan, we will use the following property below:

[tex] \large \boxed{ {tan}^{2} \theta = {sec}^{2} \theta - 1}[/tex]

Sec is the reciprocal of cos. If cos is a/b then sec is b/a. Since cos is 2/3 then sec is 3/2

[tex] \large{ {tan}^{2} \theta = {( - \frac{3}{2}) }^{2} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - \frac{4}{4} \longrightarrow \frac{5}{4} } \\ \large{tan \theta = \frac{ \sqrt{5} }{ \sqrt{4} } } \\ \large \boxed{tan \theta = \frac{ \sqrt{5} }{2} }[/tex]

Since tan is negative in the second quadrant. Hence,

[tex] \large{ \cancel{ tan \theta = \frac{ \sqrt{5} }{2} } \longrightarrow \boxed{tan \theta = - \frac{ \sqrt{5} }{2} }}[/tex]

Answer

Answer:

1. = x^2 -5x+6

Step-by-step explanation:

2. = 2x^2 +5x+3

3. =2x^2 +(x-1) +((x)/x^2 -x+6)

Answer:

To convert a meter measurement to a foot measurement, multiply the length by the conversion ratio. The length in feet is equal to the meters multiplied by 3.28084.

Step-by-step explanation:

Answer:

47.01 ft

Step-by-step explanation:

answer in photo above

Answer with Step-by -step explanation:

Sequence A;4,7,10,13,16

[tex]a_2-a_1=7-4=3[/tex]

[tex]a_3-a_2=10-7=3[/tex]

The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.

Common difference, d=3

a=4

[tex]a_n=a+(n-1)d[/tex]

[tex]a_6=a+5d=4+5\times 3=19[/tex]

[tex]a_7=a+6d=4+6(3)=22[/tex]

[tex]a_8=a+7d=4+7(3)=25[/tex]

Sequence B: 5,10,20,40,80,...

[tex]a_1=5,a_2=10,a_3=20[/tex]

[tex]\frac{a_2}{a_1}=\frac{10}{2}=2[/tex]

[tex]\frac{a_3}{a_2}=\frac{20}{10}=2[/tex]

The ratio  of two consecutive terms is equal. Therefore, it forms geometric sequence.

Common ratio, r=2

a=5

[tex]a_n=a r^{n-1}[/tex]

[tex]a_6=ar^5=5(2)^5=160[/tex]

[tex]a_7=ar^6=5(2^6)=320[/tex]

[tex]a_8=ar^7=5(2^7)=640[/tex]

Sequence C:2,5,10,17,26,..

a1=2

[tex]a_2=5=2+3=a_1+3[/tex]

[tex]a_3=10=5+5=a_2+5[/tex]

[tex]a_4=17=10+7=a_3+7[/tex]

[tex]a_5=26=17+9=a_4+9[/tex]

From the following pattern

We can get

[tex]a_6=a_5+11=26+11=37[/tex]

[tex]a_7=a_6+13=37+13=50[/tex]

[tex]a_8=a_7+15=50+15=65[/tex]

Answer:

[tex]= \frac{2x-3\sqrt{x} }{x-1}[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}[/tex]

Expand

[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}\\= \frac{x+2\sqrt{x}+1+(x-2\sqrt{x} +1) }{x-1}- \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1}{x-1} - \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1-(3\sqrt{x} +1)}{x-1}\\= \frac{2x-3\sqrt{x} +1-1}{x-1}\\= \frac{2x-3\sqrt{x} }{x-1}[/tex]

This gives the simplified form

Answer:

hundredths

Step-by-step explanation:

Numbers after the decimal start with

tenth

hundredth

Answer:

y = mx + by= mx+ b

Step-by-step explanation:

since we know the two points on the line. we use the two points formed to find its equation. the final equation.the slope intercept form ,y=mx+by = mx+b