A clinic treated 536 children over a 4month period how many children did the clinic treat in 1month

Answer:

a(n)= a(n+1)+4

Step-by-step explanation:

The first terms of this sequence are: 4,0, -4, -8, -12

Let 4 be a0 and 0 a1.

● a1-a0 = 0-4

●a1-a0 = -4

●a1 = -4+a0

So this relation links the first term with the second one.

replace 1 in a1 with n.

0 in a0 will be n-1

● an = -4+a(n-1)

Add one in n

● a(n+1) = a(n)-4

● a(n) = a(n+1)+4

Answer:  B.  

Four students won 12, 13, 14, 15, 16, or 17 prizes

Answer:

Four students won 12, 13, 14, 15, 16, or 17 prizes!

Step-by-step explanation:

Answer:

(x – 4)^2 + (y + 7)^2 = 16

Step-by-step explanation:

The formula of a circle is:

(x – h)^2 + (y – k)^2 = r^2

(h, k) represents the coordinates of the center of the circle

r represents the radius of the circle

If you plug in the given information, you get:

(x – 4)^2 + (y – (-7))^2 = 4^2

which simplifies into:

(x – 4)^2 + (y + 7)^2 = 16

Step-by-step explanation:

angle A = angle B( Corresponding angles)

so,

5x - 5 = 3x + 13

=> 5x - 3x = 13 + 5

=> 2x = 18

=> x = 9

angle B = 3x + 13 = (3×9) + 13 = 27 + 13 = 40

Answer:

x=9, ∠B=40

Step-by-step explanation:

In this case, ∠A≅∠B, as they are corresponding angles. Therefore, if you set up the equation to be 5x-5=3x+13,

2x=18, x=9

∠B=3(9)+13=27+13=40

Answer:

0.992774 ≅ .993

Step-by-step explanation:

a²+b²=c²

a=x

b=3

c=3.16

x²+3²=3.16²

x²+9=9.9856

x²=.9856

x=0.992774

x≅0.993

Answer:

D

Step-by-step explanation:

this is the only one inside the overlapping inequalitlies

Answer:

30 years

Step-by-step explanation:

let the age of Ezekiel be x years

Given

Lily is 14 years older than her little brother Ezekiel

Age of Lily = x + 14 years

Next condition

after 8 years\

age of Ezekiel = x+8

age of Lily = x + 8 +14 = x + 22 years

Given

. In 8 years, Lily will be twice as old as Ezekiel will be then.

Thus,

x + 22 = 2(x+8)

=> x + 22 = 2x + 16

=> 22-16 = 2x -x

=> x = 6

Thus, age of  Ezekiel = 8 years

age of lily = 8+14 = 22 years

sum of their age = 22 + 8 = 30 years      answer.

Answer:

0.76 or 19/25

Step-by-step explanation:

Convert 4/10 so that it has a common denominator with 36/100.

4/10 x 10/10 = 40/100

Now that the denominator is the same, just add the top values.

40/100 + 36/100 = 76/100

We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.

Answer:

Step-by-step explanation:

[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]

[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]

[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]

Answer:

x ≥ 4 AND  x + y ≤ 10

Step-by-step explanation:

If you need up to 10 volunteers, then you can take 10 or less. If we add y and x, we'll get the total amount of people, therefore making the inequality:

x + y ≤ 10.

Now, he needs no fewer than 4 females, so he can take 4 or greater. This means that x should be greater than or equal to 4.

x ≥ 4.

Nothing was mentioned about how many males he needed (y) so these two inequalities match the situation.

Hope this helped!

Answer:

Yes the sample data   indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years

Step-by-step explanation:

From the question we are told that

   The sample size is  [tex]n = 51[/tex]

    The sample mean is  [tex]\= x = 2.03[/tex]

    The sample standard deviation is  [tex]\sigma = 0.82[/tex]

    The population mean is  [tex]\mu = 1.75[/tex]

    The level of significance is  [tex]\alpha = 0.01[/tex]

The null hypothesis  is  

      [tex]H_o : \mu = 0.82[/tex]

The alternative hypothesis is

     [tex]H_a : \mu >1.75[/tex]

The critical value of the the level significance [tex]\alpha[/tex] obtained from the critical value table for z-value is [tex]z_\alpha = 2.33[/tex]

 Now the test statistic is mathematically evaluated as

          [tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]

substituting values  

           [tex]t = \frac{ 2.03 - 1.75 }{\frac{0.82}{\sqrt{51} } }[/tex]

           [tex]t = 2.44[/tex]

From that calculated and obtained value we see that the critical value of the level of significance is less than the test statistics so we  reject the null hypothesis

Hence there sufficient evidence to proof that the sample data indicates that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years

Hey there! :)

Answer:

m = 4.

Step-by-step explanation:

We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)

Where 'm' is the slope and 'b' is the y-intercept. Therefore:

y = -5 + 4x becomes y = 4x - 5

The 'm' value is equivalent to 4, so the slope of the equation is 4.

Answer:

4

Step-by-step explanation:

because of y= mx + b where m is the slope

m= 4 in the equation

Answer:

3rd

Step-by-step explanation:

i got it right on khan academy

Answer:

x=0

Step-by-step explanation:

If the slope is undefined, the line is vertical

vertical lines are of the form

x =

Since the point is (0,6)

x=0

Answer:

The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.

Step-by-step explanation:

Convert to a mixed number:

209/8

Divide 209 by 8:

8 | 2 | 0 | 9

8 goes into 20 at most 2 times:

| | 2 | |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

8 goes into 49 at most 6 times:

| | 2 | 6 |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 |  

Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:

| | 2 | 6 | (quotient)

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 | (remainder)

The quotient of 209/8 is 26 with remainder 1, so:

Answer: 26 1/8° C

Answer:

2.01m; 0.41m + 2.10m + 3.52m = 6.03 6.03/3= 2.01

Step-by-step explanation:

0.41m + 2.10m + 3.52m = 6.03 6.03/3= 2.01

The average height of the three trees is 2.01 meters.

Given that,

The heights of the three trees are 0.41m, 2.10m and 3.52m.

To find the average height of the three trees,

Use the formula for calculating the mean

Add up their heights and then divide by the total number of trees.

So, we have:

Average height = (0.41 m + 2.10 m + 3.52 m) ÷ 3

We can simplify this expression:

Average height = 6.03 m ÷ 3

Average height = 2.01 m

Therefore, the average height of the three trees is 2.01 meters.

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Answer: c(x) = $50*x + $24

Step-by-step explanation:

First, this situation can be modeled with a linear equation like:

c(x) = s*x + b

where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)

Then we know that:

The company charges $50 per cubic yard, so the slope is $50

A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.

Then our equation is:

c(x) = $50*x + $24

This is:

"The cost of buying x cubic yards of mulch"

Answer:

The slope is -4.

Step-by-step explanation:

The values -2 and -6 are 4 values apart.

The values -4 and -3 are 1 value apart.

Since the second coordinate is lower than the first one, the slope of this is negative.

4 / 1 = 1

Negating 1 gets us -1.

Hope this helped!

Answer:

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

Step-by-step explanation:

[tex]x = ( - 3) - ( - 4) = 1[/tex]

[tex]y = ( - 6) - ( - 2) = - 4[/tex]

Answer:

A) cooling constant =  0.0101365

B) [tex]\frac{df}{dt} = k ( 60 - F )[/tex]

c)  F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]

D)137.46 ⁰

Step-by-step explanation:

water temperature = 60⁰F

temperature of Bar after 20 seconds = 120⁰F

temperature of Bar after 60 seconds = 100⁰F

A) Determine the cooling constant K

The newton's law of cooling is given as

= [tex]\frac{df}{dt} = k(60 - F)[/tex]

= ∫ [tex]\frac{df}{dt}[/tex] = ∫ k(60 - F)

= ∫ [tex]\frac{df}{60 - F}[/tex] = ∫ kdt

= In (60 -F) = -kt - c

       60 - F = [tex]e^{-kt-c}[/tex]

      60 - F = [tex]C_{1} e^{-kt}[/tex]       ( note : [tex]e^{-c}[/tex] is a constant )

after 20 seconds

[tex]C_{1}e^{-k(20)}[/tex] = 60 - 120 = -60  

therefore [tex]C_{1} = \frac{-60}{e^{-20k} }[/tex] ------- equation 1

after 60 seconds

[tex]C_{1} e^{-k(60)}[/tex] = 60 - 100 = - 40  

therefore [tex]C_{1} = \frac{-40}{e^{-60k} }[/tex] -------- equation 2

solve equation 1 and equation 2 simultaneously

= [tex]\frac{-60}{e^{-20k} }[/tex] = [tex]\frac{-40}{e^{-60k} }[/tex]

= 6[tex]e^{20k}[/tex] = 4[tex]e^{60k}[/tex]

= [tex]\frac{6}{4} e^{40k}[/tex] = In(6/4) = 40k

cooling constant (k) = In(6/4) / 40 = 0.40546 / 40 = 0.0101365

B) what is the differential equation  satisfied

substituting the value of k into the newtons law of cooling)

60 - F = [tex]C_{1} e^{0.0101365(t)}[/tex]  

F(t) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

The differential equation that the temperature F(t) of the bar

[tex]\frac{df}{dt} = k ( 60 - F )[/tex]

C) The formula for F(t)

t = 20 , F = 120

F(t ) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

120 = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

[tex]C_{1} e^{0.0101365(20)}[/tex] = 60

[tex]C_{1} = 60 * 1.291[/tex] = 77.46

C1 = - 77.46⁰ as the temperature is decreasing

The formula for f(t)

= F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]

D) Temperature of the bar at the moment it is submerged

F(0) = 60 + 77.46[tex]e^{0.01013659(0)}[/tex]

F(0) = 60 + 77.46(1)

     = 137.46⁰

Answer:

79.67%

Step-by-step explanation:

To find the percentage correct, take the number correct over the total

98/123

.796747967

Change to a percent by multiplying by 100 %

79.6747967%

Round to the nearest hundredth

79.67%

Answer:

79.67%

Step-by-step explanation:

percent = part/whole * 100%

percent = 98/123 * 100%

percent = 79.67%

Answer:

   sqrt( 146)

Step-by-step explanation:

To find the distance, we use the following formula

d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)

    sqrt( ( -9-2) ^2 + ( 0-5) ^2)

  sqrt( ( -11) ^2 + ( -5) ^2)

   sqrt( 121+25)

   sqrt( 146)

Answer:

Hey there!

The line can be expressed into y intercept form, y=3x+1.

Thus, in y=mx+b form, m is the slope, and we see that 3 is the slope of the line.

Let me know if this helps :)

Answer:

The first part is of permutations.

We are selecting 3 elements from three different elements {1,2,3}

Points given:

We permit overlapped elements for the sequence. Here "overlapped elements" indicates that repetition is allowed.

So when repetition is allowed and order matters, we use permutations.

Formula to compute permutation is:

Lets say n is the three elements {1,2,3}

We have to select 3 elements so r = 3

Total number of selections using permutations = [tex]n^{r}[/tex] =  n × n × n

                                                                    = 3³ = 3 * 3 * 3

                                                                    = 27

This means if we have 3 different elements then we have have 3 choices each time for making a sequence.

Hence  If we make a sequence selecting three elements from three different elements  {1, 2, 3} and we permit overlapped elements for the sequence, then the total  number of sequences is 27.

Step-by-step explanation:

The second part indicates combinations.

This is because the statement of the question:  If we do not take into account the order.

When the order does not matter, we use combinations.

So when the order does not matter and repetition is allowed we use the following formula:

Total number of selections using combinations = (r + n - 1)! / r! (n - 1)!

                                                                                = (3 + 3 - 1) ! / 3! (3 - 1)!

                                                                                = (3 + 2) ! / 3! (2!)

                                                                                = 5! / 3! 2!

                                                                                = 5*4*3*2*1 / (3*2*1 ) (2*1)

                                                                                = 120 / 6 * 2

                                                                                = 120 / 12

                                                                                = 10

So these are the number of combinations of 3 elements taken 3 at a time with  repetition.

The total number that will be selected in the permutations is 27.

Based on the information given, the total number of permutations will be:

= n³

= 3 × 3 × 3

= 27

Also, the total number of selection using combination will be:

= (3 + 3 - 1)! / 3!(3 - 1)!

= 120 / (6 × 2)

= 120/12

= 10

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Answer:

the amount of space occupied by a three-dimensional solid object

Step-by-step explanation:

Volume is a measure of the space in a 3D solid object enclosed by the closed surfaces of the solid object.

By using the definition of volume, we can see that the correct option is the last one:

"The amount of space occupied by a three-dimensional solid object"

Volume is defined as a 3-dimensional metric derived from longitude, that measures a region in the space. So, each region that "takes space" has a volume.

With that in mind, the option that correctly describes volume is the last option:

"The amount of space occupied by a three-dimensional solid object"

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Answer:

1. k=0

2. yes, result is still a polynomial.

3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)

Step-by-step explanation:

1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)

for k=0 any polynomial f(x) will reduce f(k) to the constant term.

2. If we multiply a polynomial by a constant, is the result a polynomial?

Yes, If we multiply a polynomial by a constant, the result is always a polynomial.

3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?

Yes.  

If

deg(f+g) < deg(f) and

deg(f+g) < deg(g)

then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.

Answer:

see explanation

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides

6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )

- 7a₁ + 30d = 156d ( subtract 30d from both sides )

- 7a₁ = 126d ( divide both sides by - 7 )

a₁ = - 18d

Now

a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required

Answer:

Your answer is B

Step-by-step explanation:

rotating about/around the origin taking a shape and rotating it with the same values but around the point (0,0). so rotating your shape ABC around (0,0) with the same value would give you the shape A'B'C'

Answer:

I got 45, but I may be wrong.

Step-by-step explanation:

When a number is even, the number must end in an even number. Here, the even numbers are 4 and 6, so the numbers we are going to create are all going to end in 4 and 6.

To answer this question, we just have to find as many possible combinations following the guidelines provided.

334

344

354

364

374

434

444

454

464

474

534

544

554

564

574

634

644

654

664

674

336

346

356

366

376

436

446

456

466

476

536

546

556

566

576

636

646

656

666

676

736

746

756

766

776

Answer:

9.06×10 to the power of 8(8 is superscript above 10)

Answer:

9.06 x 10^8

Step-by-step explanation:

906000000 = 9.06 x 10^8

8 decimal places in

Answer:

x=1

Step-by-step explanation:

1+1+2x+2x= 6

1+1=2

2x+2x=4x

2+4x=6

x=1

Answer:

(26+92)+17 = 26 + ( 92+17)

Step-by-step explanation:

The associative property of addition is

a + (b + c) = (a + b) + c

We want to move the parentheses

(26+92)+17 = 26 + ( 92+17)