Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?

Answer:

Solution : [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]

Step-by-step explanation:

[tex]-3\left[\cos \left(\frac{-\pi }{4}\right)+i\sin \left(\frac{-\pi \:}{4}\right)\right]\:\div \:2\sqrt{2}\left[\cos \left(\frac{-\pi \:\:}{2}\right)+i\sin \left(\frac{-\pi \:\:\:}{2}\right)\right][/tex]

Let's apply trivial identities here. We know that cos(-π / 4) = √2 / 2, sin(-π / 4) = - √2 / 2, cos(-π / 2) = 0, sin(-π / 2) = - 1. Let's substitute those values,

[tex]\frac{-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)}{2\sqrt{2}\left(0-1\right)i}[/tex]

=[tex]-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)[/tex] ÷ [tex]2\sqrt{2}\left(0-1\right)i[/tex]

= [tex]3\left(-\frac{\sqrt{2}i}{2}+\frac{\sqrt{2}}{2}\right)[/tex] ÷ [tex]-2\sqrt{2}i[/tex]

= [tex]\frac{3\left(1-i\right)}{\sqrt{2}}[/tex]÷ [tex]2\sqrt{2}i[/tex] = [tex]-3-3i[/tex] ÷ [tex]4[/tex] = [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]

As you can see your solution is the last option.

Answer:

a.  k = -0.01014 s⁻¹

b.  [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]

c.  [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]

d.  y(t) = 130.485°F

Step-by-step explanation:

A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.

(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)

We are to determine :

a.  Determine the cooling constant k. k = s−1

By applying the new law of cooling

[tex]\dfrac{dT}{dt} = k \Delta T[/tex]

[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]

[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]

Taking the integral.

[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]

㏑ (T -60) = kt + C

T - 60 = [tex]e^{kt+C}[/tex]

[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]

After 20 seconds, the temperature of the bar submersion is 120°F

T(20) = 120

From equation (1) ,replace t = 20s and T = 120

[tex]120 = 60 + C_1 e^{20 \ k}[/tex]

[tex]120 - 60 = C_1 e^{20 \ k}[/tex]

[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]

After 1 min i.e 60 sec , the temperature  = 100

T(60) = 100

From equation (1) ; replace t = 60 s and T = 100

[tex]100 = 60 + c_1 e^{60 \ t}[/tex]

[tex]100 - 60 =c_1 e^{60 \ t}[/tex]

[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]

Dividing equation (2) by (3) , we have:

[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]

[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]

[tex]-40 \ k = In (\dfrac{3}{2})[/tex]

- 40 k = 0.4054651

[tex]k = - \dfrac{0.4054651}{ 40}[/tex]

k = -0.01014 s⁻¹

b. What is the differential equation satisfied by the temperature y(t)?

Recall that :

[tex]\dfrac{dT}{dt} = k \Delta T[/tex]

[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]

Since y is the temperature of the body , then :

[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]

(c) What is the formula for y(t)?

From equation (1) ;

where;

[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]

Let y be measured in degrees Fahrenheit

[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]

From equation (2)

[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]

[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]

[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]

[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]

[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]

[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]

(d) Determine the temperature of the bar at the moment it is submerged.

At the moment it is submerged t = 0

[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]

[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]

y(t) = 60 + 70.485

y(t) = 130.485°F

Answer: E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)

Step-by-step explanation:

According to the combinations: Number of ways to choose r things out of n things = C(n,r)

Given word: "georgianna"

It is a sequence of 10 letters with 2 a's , 2 g's , 2 n's , and one of each e, o,r, i.

If we think 10 blank spaces, then in a sequence we need 2 spaces for each of g.

Number of ways = C(10,2)

Similarly,

1 space for 'e' → C(8,1)

1 space for 'o' → C(7,1)

1 space for 'r' → C(6,1)

1 space for 'i' → C(5,1)

1 space for 'a' → C(4,2)

1 space for 'n' → C(2,2)

Required number of different sequences  = C(10,2) ×C(8,1)× C(7,1)× C(6,1)×C(5,1)×C(2,2).

Hence, the correct option is E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)

Answer: Transitive property.

Step-by-step explanation:

First, for the equality we have:

Reflexive:

  For all real numbers x, x = x.

Symmetric:  

 For all real numbers x, y

 if x= y, then y = x.

Transitive:

 For reals x, y and z.

 if x = y, and y = z, then x = z.

Now, let's talk about inequalities.

first, the reflexive property will say that:

x > x.

This has no sense, so this property does not work for inequalities.

Now, the reflexive.

If x > y, then y > x.

Again, this has no sense, if x is larger than y, then we can never have that y is larger than x. This property does not work for inequalities.

Not, the transitive property.

if x > y, and y > z, then x > z.

This is true.

x is bigger than y, and y is bigger than z, then x should also be bigger than z.

x > y > z.

And this also works for the inverse case:

x < y and y < z, then x < z.

So the correct option is transitive property.

Answer:the one area < with line underneath then -4

St-by-step explanation: I’m pretty sure this is correct

Answer:

Step-by-step explanation:

[tex] \mathrm{16x - 7 \leqslant - 71}[/tex]

Move constant to Right hand side and change its sign

[tex] \mathrm{16x \leqslant - 71 + 7}[/tex]

Calculate

[tex] \mathrm{16x \leqslant - 64}[/tex]

Divide both sides of the equation by 16

[tex] \mathrm{ \frac{16x}{16} \leqslant \frac{ - 64}{16} }[/tex]

Calculate

[tex] \mathrm{x \leqslant - 4}[/tex]

Hope I helped!

Best regards!

Answer:

80

Step-by-step explanation:

linear pair = 180

Now,

100 + 80 = 180

Answer:

Step-by-step explanation:

[tex]distance = 15 miles\\time = 0.1 hours\\\\Speed = \frac{Distance}{time}\\ Speed = \frac{15}{0.1}\\ Speed =150[/tex]

Answer:

[tex]150mph[/tex]

Step-by-step explanation:

Given:

s=15miles

t=0.1hours

Required:

v=?

Formula:

[tex]v = \frac{s}{t} [/tex]

Solution:

[tex]v = \frac{s}{t} = \frac{15m}{0.1h} = \frac{150m}{1h} = 150mph[/tex]

Hope this helps ;) ❤❤❤

Answer:

9x -9

9(x - 1)

4(3x-3) - 3x + 3

Step-by-step explanation:

4(2x + x-3) - 3x + 3

Combine like terms

4(3x-3) - 3x + 3

Distribute

12x -12 -3x+3

Combine like terms

9x -9

Factor out 9

9(x-1)

Answer:

9

18

Step-by-step explanation:

x = 2:

4(4 + 2 - 3) - 6 + 3 = 12 - 6 + 3 = 9

x = 3:

4(6 + 3 - 3) - 9 + 3 = 24 - 9 + 3 = 18

Answer:

y = 2(x - 3)² + 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 5), thus

y = a(x - 3)² + 5

To find a substitute (1, 13) into the equation

13 = a(1 - 3)² + 5 ( subtract 5 from both sides )

8 = 4a ( divide both sides by 4 )

a = 2, then

y = 2(x - 3)² + 5 ← equation of parabola in vertex form

Step-by-step explanation:

83P (E)=17-17P (E),

P (E)=17/100=0.17

Answer:

The Width = 28 inches

The Height = 21 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3

Using Pythagoras Theorem

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 35²

We are given ratio: 4:3 as aspect ratio

Width = 4x

Height = 3x

(4x)² +(3x)² = 35²

= 16x² + 9x² = 35²

25x² = 1225

x² = 1225/25

x² = 49

x = √49

x = 7

Hence, for the 35 inch tv set

The Width = 4x

= 4 × 7

= 28 inches.

The Height = 3x

= 3 × 7

= 21 inches

Answer:

102

Step-by-step explanation:

We have the sum for k = 1 to 4 of 3 ^ ( k-1)  * ( k-1)

k =1   3 ^ (1-1) * ( 1-1) = 3^0 * 0 = 0

k =2   3 ^ (2-1) * ( 2-1) = 3^1 * 1 = 3

k =3   3 ^ (3-1) * ( 3-1) = 3^2 * 2 = 9*2 = 18

k =4   3 ^ (4-1) * ( 4-1) = 3^3 * 3 = 27 *3 = 81

Add these together

0+3+18+81 =102

━━━━━━━☆☆━━━━━━━

▹ Answer

102

▹ Step-by-Step Explanation

Convert the notation into a sum and substitute values from 1-4:

(3¹⁻¹ *(1 - 1)) + (3²⁻¹ * (2 - 1)) + (3³⁻¹ * (3 - 1)) + (3⁴⁻¹ * (4 - 1))

0 + 3 + 18 + 81

= 102

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Explanation:

We have 4 options for the first choice and 3 options for the next. So there are 4*3 = 12 different combos possible. The tree diagram below shows 12 different paths to pick from. For instance, the right-most path has us pick the number 4 and the color yellow.

Answer:

9.488

Step-by-step explanation:

The critical value is found by first assessing which statistical test should be used.

We are interested in investigating relationship between social activity and education so chi-square test would be appropriate.

We have 3 rows and 3 columns. The degree of freedom for chi-square critical value is (r-1)(c-1)=(3-1)(3-1)=2*2=4

Chi-square critical value(0.05,4)= 9.488

Answer:

0.14

Step-by-step explanation:

The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14

The area under the curve shaded is 1 to 2 is 0.14

Probabilities are used to determine the chances of an event

The shaded region represents the probability of the z-scores

The shaded region 1 to 2 is represented as:

P(1 < z < 2) =

Using the probability of z-score, we have the formula

P(1 < z < 2) = P(z < 2) - P(z < 1)

From the given standard normal table:

P(z < 2) = 0.9772

P(z < 1) = 0.8413

So, we have:

P(1 < z < 2) = 0.9772 - 0.8413

P(1 < z < 2) = 0.1359

Approximate

P(1 < z < 2) = 0.14

Hence, the area under the curve shaded is 1 to 2 is 0.14

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Answer:

Part a ) The degrees of freedom for the given two sample non-pooled t test is 24

Part b ) The degrees of freedom for the given two sample non-pooled t test is 30

Part c ) The degrees of freedom for the given two sample non-pooled t test is 30

Part d ) The degrees of freedom for the given two sample non-pooled t test is 25

Step-by-step explanation:

Degrees of freedom for a non-pooled two sample t-test is given by;

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Now given the information;

a) :- m = 12, n = 15, s₁ = 4.0, s₂ = 6.0

we substitute

Δf =  {[ 4²/12 + 6²/15 ]²} / {[( 4²/12)²/12-1] + [(6²/15)²/15-1]}

Δf  = 30184 / 1241

Δf  = 24.3223 ≈ 24 (down to the nearest whole number)

b) :- m = 12, n = 21, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/12 + 6²/21 ]²} / {[( 4²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 56320 / 1871

Δf = 30.1015 ≈ 30 (down to the nearest whole number)

c) :- m = 12, n = 21, s₁ = 3.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 3²/12 + 6²/21 ]²} / {[( 3²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 29095 / 949

Δf = 30.6585 ≈ 30 (down to the nearest whole number)

d) :- m = 10, n = 24, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/10 + 6²/24 ]²} / {[( 4²/10)²/10-1] + [(6²/24)²/24-1]}

Δf = 1044 / 41  

Δf = 25.4634 ≈ 25 (down to the nearest whole number).

Answer:

The values is  

Step-by-step explanation:

From the question we are told that

  The population mean is  [tex]\mu = 2.45[/tex]

    The  standard deviation is  [tex]\sigma = 0.35 \ mi[/tex]

     The random value is  [tex]x = 2.03[/tex]

The standardized score for a binding site position of 2.03 microns is mathematically represented as

       [tex]z-score = \frac{x - \mu}{ \sigma }[/tex]

=>      [tex]z-score = \frac{2.03 - 2.45}{ 0.35}[/tex]

=>    [tex]z-score = -1.2[/tex]

Answer:

[tex]f(x) = x^{4}[/tex], [tex]g(x) = x-1[/tex]

Step-by-step explanation:

Let be [tex]F(x) = f\circ g (x) = (x-1)^{4}[/tex], then expression for [tex]f(x)[/tex] and [tex]g(x)[/tex] are, respectively:

[tex]f(x) = x^{4}[/tex] and [tex]g(x) = x-1[/tex]

Answer:

10,000

Step-by-step explanation:

There are 2970 positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

A number system is defined as a system of writing to express numbers.

We need to find

positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

Let all 9 numbers ae

a+b+c+d+e+f+g+h+9=13

a+b+c+d+e+f+g+h=13-9

a+b+c+d+e+f+g+h=4

Then we use combinations

(n+k-1)Ck

¹¹C₄

11!/(11-4)!4!

11!/7!4!

330

Three hundred thirty times of nine is two thousand nine hundred seventy.

Now 330 ×9=2970

Hence there are 2970  positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

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Answer:

Step-by-step explanation:

To find the value of y when x = 7 we must first find the relationship between them.

The statement

y varies directly with x is written as

y = kx

where k is the constant of proportionality

From the question

when y = - 11.7

x = - 3

We have

- 11.7 = -3k

Divide both sides by - 3

k = 3.9

So the formula for the variation is

When x = 7

y = 3.9(7)

Hope this helps you

Answer: 27.3

Step-by-step explanation:

Joint Variation

Answer:

The balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?

Answer:

6 months

A function is a relationship between inputs where each input is related to exactly one output.

x = 5,

f(5) = [tex]2^5\\[/tex] = 32

g(5) = 4 x 5 + 12 = 20 + 12 = 32

x = 6,

f(6) = [tex]2^6[/tex] = 64

g(6) = 4 x 6 + 12 = 24 + 12 = 36

At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = [tex]2^{x}[/tex]

g(x) = 4x + 12

x = number of months

Now,

x = 3,

f(3) = 2³ = 8

g(3) = 4 x 3 + 12 = 12 + 12 = 24

x = 4,

f(4) = [tex]2^4[/tex] = 16

g(4) = 4 x 4 + 12 = 16 + 12 = 28

x = 5,

f(5) = [tex]2^5\\[/tex] = 32

g(5) = 4 x 5 + 12 = 20 + 12 = 32

x = 6,

f(6) = [tex]2^6[/tex] = 64

g(6) = 4 x 6 + 12 = 24 + 12 = 36

We see that,

At x = 6,

f(5) = 64

g(5) = 36

Thus,

At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.

Learn more about functions here:

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Answer:

90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Here is the equation

[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]

In the order of operations parentheses go first so we get

[tex]20+3\times11+5+2\times16[/tex]

Next we do the multiplication

[tex]20+33+5+32\\[/tex]

And finally we add them all up

[tex]20+33+5+32=90\\[/tex]

Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]

Answer:

3 · |x+6|

Step-by-step explanation:

Write out what you see. "Three times" is 3 · something; "the absolute value of the sum of a number and 6" is |number + 6|. We'll use x for our number. Put it all together and you get 3 · |x+6|

The expression of the statement, Three times the absolute value of the sum of a number and 6 is  [tex]\[3\left| n+6 \right|\][/tex] .

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Answer:

5328 cups.

Step-by-step explanation:

Given that 333 gallons

We know that

1 gallons = 16 cups

1 cups = 0.0625 gallons

Therefore,from the above conversion we can say that

Now by putting the values in the above conversion

333 gallons = 16 x 333 cups

333 gallons = 5328 cups

So , we can say that 333 gallons is equal to 5328 cups.

Thus the answer will be 5328 cups.

Answer:

48 cups(BTW he meant 33 galons, IVE had this before). lol you need to put the double number line image. first u have to divide 64/4 to get 16, Then it says "How many cups are in 3 gallons". There fore, U multiply 16 to 3 to get ur answer "48".

Answer:

True

Step-by-step explanation:

We assume that is true for the nth case and prove it for the n+1 case

and show that it is true for the case when n=1

a. y = 2.5x + 2000

b. The variable x represents the domain because the domain is the range of the possible x values.

c. x ≥ 0

d. The variable y represents the range because the range is the range of the possible y values.

e. y ≥ 2000

f. y = 2.5(25) + 2000

  y = 62.5 + 2000

  y = $2062.50

g. 2500 = 2.5x + 2000

   2.5x = 500

   x = 200

h. I am sorry I cannot make the graph but hopefully you can figure out how to make it using the info I have given in the above parts of the problem :)

Answer:

−  1049

Step-by-step explanation:

-13.62-(27.9)

primero haremos los paréntesis y después las demás multiplicaciones de izquierda a derecha.

-13.62-243

-806-243

Finalmente tenemos −  1049

Espero te ayude :)

Answer:

-41.52

Step-by-step explanation:

When you subtract from a negative, the answer will be smaller than the starting number:

Therefore, the answer is -41.52.

Answer:

4i.

Step-by-step explanation:

To find the flux through the square, we use the divergence theorem for the flux. So Flux of F(x,y) = ∫∫divF(x,y).dA

F(x,y) = hxy,x - yi

div(F(x,y)) = dF(x,y)/dx + dF(x,y)dy = dhxy/dx + d(x - yi)/dy = hy - i

So, ∫∫divF(x,y).dA = ∫∫(hy - i).dA

= ∫∫(hy - i).dxdy

= ∫∫hydxdy - ∫∫idxdy

Since we are integrating along the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1, then

∫∫divF(x,y).dA = ∫₋₁¹∫₋₁¹hydxdy - ∫₋₁¹∫₋₁¹idxdy

= h∫₋₁¹{y²/2}¹₋₁dx - i∫₋₁¹[y]₋₁¹dx

= h∫₋₁¹{1²/2 - (-1)/2²}dx - i∫₋₁¹[1 - (-1)]dx

= h∫₋₁¹{1/2 - 1)/2}dx - i∫₋₁¹[1 + 1)]dx

= 0 - i∫₋₁¹2dx

= - 2i[x]₋₁¹

= 2i[1 - (-1)]

= 2i[1 + 1]

= 2i(2)

= 4i  

Answer:

Interquartile range is the distance between the first and third of a data.

Step-by-step explanation:

Hope it will help you :)