Consider the relationship 7r+4t=14. a. Write the relationship as a function r=f(t).

I hope this helps you...

Answer:

Step-by-step explanation:

let $p, $c and $d represents the costs of popcorn, candy and a drink respectively. If the popcorn was three times as  expensive as the candy then;

p = 3c.... 1

If the drink was  twice as expensive as the candy then d = 2c .... 2

If Eva spent a  total sum of $10.50 at the movies, the equation that represents the situation will be p + c + d = $10.50 .... 3

Substituting equation 1 and 2 into 3;

3c + c + 2c = $10.50

6c = $10.50

Hence the equation to represent the situation is 6c = $10.50 where c represents the cost of the candy.

b) To get c from the equation 6c = $10.50, we will simply divide both sides by the coefficient of c i.e 6 as shown

6c/6 = $10.50/6

c = $1.75

Hence the value of c is $1.75

c) The equation representing Eva's drink in terms of the candy is expressed as d = 2c

Substituting c = $1.75 into the equation will give;

d = 2(1.75)

d = 3.5

Hence the cost of Eva's drink is $3.50

Answer

[tex]a=0[/tex], [tex]b=2[/tex]

[tex]g_1(x)=\frac{5x}{2}[/tex],  [tex]g_2(x)=7-x[/tex]

Step-by-step explanation:

Given that

[tex]\int \int Df(x,y)dA=\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy+\int_5^7\int_0^{7-y} f(x,y)dxdy\; \cdots (i)[/tex]

For the term  [tex]\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy[/tex].

Limits for [tex]x[/tex] is from [tex]x=0[/tex] to [tex]x=\frac {2y}{5}[/tex] and for [tex]y[/tex] is from [tex]y=0[/tex] to [tex]y=5[/tex]  and the region [tex]D[/tex], for this double integration is the shaded region as shown in graph 1.

Now, reverse the order of integration, first integrate with respect to [tex]y[/tex] then with respect to [tex]x[/tex] . So, the limits of [tex]y[/tex] become from [tex]y=\frac{5x}{2}[/tex] to [tex]y=5[/tex] and limits of [tex]x[/tex] become from [tex]x=0[/tex] to [tex]x=2[/tex] as shown in graph 2.

So, on reversing the order of integration, this double integration can be written as

[tex]\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx\; \cdots (ii)[/tex]

Similarly, for the other term  [tex]\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy[/tex].

Limits for [tex]x[/tex] is from [tex]x=0[/tex] to [tex]x=7-y[/tex] and limits for [tex]y[/tex] is from [tex]y=5[/tex] to [tex]y=7[/tex]  and the region [tex]D[/tex], for this double integration is the shaded region as shown in graph 3.

Now, reverse the order of integration, first integrate with respect to [tex]y[/tex] then with respect to [tex]x[/tex] . So, the limits of [tex]y[/tex] become from [tex]y=5[/tex] to [tex]y=7-x[/tex] and limits of [tex]x[/tex] become from [tex]x=0[/tex] to [tex]x=2[/tex] as shown in graph 4.

So, on reversing the order of integration, this double integration can be written as

[tex]\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy=\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx\;\cdots (iii)[/tex]

Hence, from equations [tex](i)[/tex], [tex](ii)[/tex] and [tex](iii)[/tex] , on reversing the order of integration, the required expression is

[tex]\int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx+\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx[/tex]

[tex]\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\left(\int _ {\frac {5x}{2}}^5 f(x,y)+\int _5 ^ {7-x} f(x,y)\right)dydx[/tex]

[tex]\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^{7-x} f(x,y)dydx\; \cdots (iv)[/tex]

Now, compare the RHS of the equation [tex](iv)[/tex] with

[tex]\int_a^b\int_{g_1(x)}^{g_2(x)} f(x,y)dydx[/tex]

We have,

[tex]a=0, b=2, g_1(x)=\frac{5x}{2}[/tex] and [tex]g_2(x)=7-x[/tex].

The required values are,

[tex]a=0\\b=2\\g_1(x)=\frac{5x}{2} \\g_2(x)=7-x[/tex]

Double integral is mainly used to find the surface area of a 2d figure, and it is denoted using ‘ ∫∫’. We can easily find the area of a rectangular region by double integration.

Given function is,

[tex]\int \int_Df(x,y)dA=\int_{0}^{5}\int_{0}^{2y}f(x,y)dxdy+\int_{5}^{7}\int_{0}^{7-y}f(x,y)dxdy[/tex]

We can write the double integral as a single term by reversing the order as,

[tex]\int_{a}^{b}\int_{g_1(x)}^{g_2(x)}f(x,y)dydx=\int_{0}^{2}\int_{\frac{5x}{2}}^{7-x}f(x,y)dydx)[/tex]

The region D is attached below.

Hence, we get the values,

[tex]a=0\\b=2\\g_1(x)=\frac{5x}{2} \\g_2(x)=7-x[/tex]

Learn more about the topic Double Integral:

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Answer:

420 in^2

Step-by-step explanation:

The area of the rectangle before removing the circles is

A = l*w

A = 24*22

   =528

The area of one of the circles is

A = pi r^2

The diameter is 6 so the radius is 6/2 = 3

  = 3.14 * ( 3) ^2

  =28.26

There are 4 circles

4* 28.26

113.04

Subtract the area of the 4 circles from the rectangle

528-113.04

414.96

415 in ^2

The best estimate is 420

Answer:

a + 50

Step-by-step explanation:

Step 1: Translate word into math

sum = +

fifty = 50

a = a

Step 2: Combine

a + 50

Answer:

a + 50

Step-by-step explanation:

Step 1: Translate word into math

sum = +

fifty = 50

a = a

Step 2: Combine

a + 50

Answer:

Step-by-step explanation:

1/x + 1/y =9/11 (x+y)/x.y=9/11 11x+11y=9x.y

F(x)=11x/(9x-1)

Answer:

Step-by-step explanation:

(-5,-3) (1,0)

(0+3)/(1+5)= 3/6 = 1/2

y - 0 = 1/2(x - 1)

y = 1/2x - 1/2

Answer:

4x+10+2x-1=9x-15;

6x+9=9x-15;

6x-9x=-15-9;

-3x=-24;

3x=24;

from which

x=24:3=8

Then:

DF=9x-15=(9×8)-15=72-15=57

Was this helpful

Answer:

≈ 2.8 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (3, - 3)

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

   = [tex]\sqrt{2^2+(-2)^2}[/tex]

  = [tex]\sqrt{4+4}[/tex]

  = [tex]\sqrt{8}[/tex] ≈ 2.8 ( to the nearest tenth )

Answer: The answer is 2.8

Step-by-step explanation:

(1,-1)(3,-3)          (those are the points shown in the graph)

The formula for finding distance is  √(x2-x1)^2+(y2-y1)^2

= √(3-1)^2+(-3-(-1)^2

= √(2)^2+(-3+1)^2

= √4+(-2)^2

= √4+4

= √8

=2.828427125    (to the nearest tenth)

Answer:

1 no. answer is -21

Step-by-step explanation:

According to BODMAS

12 + 8 / 2 * 3 - (42 + 3)

= 12 + 8 / 2 * 3 - 45

= 12 + 4 * 3 - 45

= 12 + 12 - 45

= 24 - 45

= -21

Leila's fish tank has 18 liters of water in it. She plans to add 5 liters per minute until the tank has more than 58 liters. What are the possible numbers of minutes Leila could add water? Use t for the number of minutes.

Write your answer as an inequality solved for t.

58<18+5t

40<5t

8

JUST LIKE THIS U CAN SOLVE...

ITS BETTER TO NOT GIVE STRAIGHT ANSWERS

Answer:

For y(-7) =6.4

        The  largest interval  is  between  

                                       [tex]-\infty \to -5[/tex]

For   y(-2.5) = -0.5.

          The  largest interval  is  between  

                                        [tex]-5 \to 5[/tex]

For  y(0) = 0

          The  largest interval  is  between  

                                        [tex]-5 \to 5[/tex]

For y(4.5) = -2.1.

            The  largest interval  is  between  

                                        [tex]-5 \to 5[/tex]

For y(14)= 1.7.

                          The  largest interval  is  between  

                                        [tex]9 \to \infty[/tex]        

Step-by-step explanation:

From m the question we are told that

     The first order differential equation is   [tex]\frac{y' - t}{ t^2 -25} = \frac{e^t}{t-9}[/tex]

Now the first step is to obtain the domain of the differential equation

Now to do that let consider the denominators

  Now generally

                           [tex]t^2 - 25 \ne 0[/tex]                                           side calculation

                   =>     [tex]t\ne \pm5[/tex]                                                      [tex]t^2 - 25 = 0[/tex]

                                                                                          [tex]t = \pm 5[/tex]

Also              [tex]t-9\ne 0[/tex]                                                     [tex]t -9 = 0[/tex]

        =>          [tex]t\ne 9[/tex]                                                            [tex]t= 9[/tex]    

This means that this  first order differential equation is discontinuous at

       [tex]t = -5 , \ \ t = 5 \ \ t = 9[/tex]

  [tex]This \ is \ illustrated \ below \ \\ ------------------\\\. \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ |\\. \ -5 \ \ \ \ \ \ \ \ \ \ \ \ 5 \ \ \ \ \ \ \ \ \ \ \ \ \ 9[/tex]

So

For y(-7) =6.4

        The  largest interval  is  between  

                                       [tex]-\infty \to -5[/tex]

For   y(-2.5) = -0.5.

          The  largest interval  is  between  

                                        [tex]-5 \to 5[/tex]

For  y(0) = 0

          The  largest interval  is  between  

                                        [tex]-5 \to 5[/tex]

For y(4.5) = -2.1.

            The  largest interval  is  between  

                                        [tex]-5 \to 5[/tex]

For y(14)= 1.7.

                          The  largest interval  is  between  

                                        [tex]9 \to \infty[/tex]        

Step-by-step explanation:

If x is the number of hours, then:

48 = 10x + 7

41 = 10x

x = 4.1

Complete question :

A : 2.7, 3.7, 5.6, 2.6, 2.7

B : 5.1, 4.0, 3.9, 3.8, 5.2

Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73B. 1.21C. 1.32D. 1.89

Answer: A.1.73

Step-by-step explanation:

Given the data:

A : 2.7, 3.7, 5.6, 2.6, 2.7

B : 5.1, 4.0, 3.9, 3.8, 5.2

Difference betweenA and B (A - B) :

Xd = (A - B) = - 2.4, -0.3, 1.7, - 1.2, - 2.5

Sum of (A - B) = Σ Xd = (-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5) = - 4. 7

Md = ΣXd / n = - 4.7 / 5 = - 0.94

Xd - Md = (-2.4 + 0.94), (-0.3 + 0.94), (1.7 + 0.94), (-1.2 + 0.94), (-2.5 + 0.94)

(Xd - Md) = - 1.46, 0.64, 2.64, - 0.26, - 1.56

(Xd - Md)^2 = (-1.46)^2 + 0.64^2 + 2.64^2 + (-0.26)^2 + (-1.56)^2

Σ(Xd - Md)^2 = (2.1316 + 0.4096 + 6.9696 + 0.0676 + 2.4336) = 12.012

Standard deviation = √[Σ(Xd - Md)^2 / (n-1)]

Standard deviation= √12.012 / 4

Standard deviation = 1.7329

Standard deviation= 1.73

Answer:

  a

Step-by-step explanation:

There are no like terms here, hence no "common like term."

__

The terms have a greatest common factor of 'a', so the expression could be written as ...

  a(11av -12b^2)

The greatest common factor is 'a'.

Answer:

4x^2+12x+9

Step-by-step explanation:

(2x+3)(2x+3)

Multiply 2x by 2x first.

then 2x by 3

and then repeat that step and you add like terms

then recieve your answer.

Answer:

4x^2 + 12x + 9

Step-by-step explanation:

Actually, you are to find (2x + 3)^2, which is "the square of 2x + 3."

2x + 3 is a binomial.  There is a formula for the square of a binomial:

(a + b)^2 = a^2 + 2ab + b^2

Following this pattern,

(2x + 3)^2 becomes:

[2x]^2 + 2[2x][3] + [3^2], or

4x^2 + 12x + 9

Answer:

210

Step-by-step explanation:

Answer:

(-∞,∞)

Step-by-step explanation:

This would form a roughly parabolic shape that extends infinitely along the x-axis.  It would reach a height of ³√2 on the y-axis.  Because it extends infinitely left and right, it would have an infinite domain.  In interval notation, this would be (-∞,∞)

Answer:

a

  [tex]P(G) =  0.69[/tex]

b

  [tex]P(S | G) = 0.81[/tex]

c

  [tex]P(M|G') =  0.26[/tex]

Step-by-step explanation:

From the question we are told the

   The probability of getting into getting into graduated school if you receive a strong recommendation is  [tex]P(G |S) = 0.80[/tex]

   The probability of getting into getting into graduated school if you receive a moderately good recommendation is  [tex]P(G| M) =  0.60[/tex]

   The probability of getting into getting into graduated school if you receive a weak recommendation is  [tex]P(G|W) =  0.05[/tex]

   The probability of getting a strong recommendation is  [tex]P(S) =  0.7[/tex]

     The  probability of receiving a moderately good recommendation is [tex]P(M) =  0.2[/tex]

       The probability of receiving a weak recommendation is [tex]P(W) =  0.1[/tex]

      Generally  the probability that you will get into a graduate program is mathematically represented as

     [tex]P(G) =  P(S) *  P(G|S) + P(M) *  P(G|M) + P(W) *  P(G|W)[/tex]

=>   [tex]P(G) =  0.7 * 0.8 +  0.2 *  0.6 + 0.1 *  0.05[/tex]

=>   [tex]P(G) =  0.69[/tex]

Generally  given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation is mathematically represented as

      [tex]P( S|G) =  \frac{ P(S) *  P(G|S)}{ P(G)}[/tex]

=>    [tex]P(S|G) =  \frac{ 0.7 * 0.8 }{0.69}[/tex]

=>     [tex]P(S | G) = 0.81[/tex]

Generally given that you didn't receive an offer to attend a graduate program  the probability that you received a moderately good recommendation is mathematically represented as

        [tex]P(M|G') =  \frac{ P(M) *  (1- P(G|M))}{(1 - P(G))}[/tex]

         [tex]P(M| G') =  \frac{ 0.2 *  (1- 0.6)}{ (1 - 0.69)}[/tex]

         [tex]P(M|G') =  0.26[/tex]

Answer:

False

Step-by-step explanation:

All you want to do is times 5.71 by 0.8. Once you do that, you'll get 4.568. Then you times 3.26 by 1.45 which gets you 4.727, 4.568 does not = 4.727 which makes the statement false.

Answer:

Just a

Step-by-step explanation:

8+(-8) they cancel each other out so 0+a = a

Answer:

a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.

The  average height for turkeys at the 90th percentile for weight is 34.554

Of the turkeys at the 90th percentile for weight, roughly the percentage that  would  be taller than 28 inches 79.37%

Step-by-step explanation:

Given that:

For a population of turkeys at a farm, the correlation found between the weights and heights of turkeys is r = 0.64

the average weight in pounds [tex]\overline x[/tex] = 17

the standard deviation of the weight in pounds [tex]S_x[/tex] = 5

the average height in inches [tex]\overline y[/tex] = 28

the standard deviation of the height in inches [tex]S_y[/tex] = 8

Also, given that the weight and height both roughly follow the normal curve

For this study , the slope of the regression line can be expressed as :

[tex]\beta_1 = r \times ( \dfrac{S_y}{S_x})[/tex]

[tex]\beta_1 = 0.64 \times ( \dfrac{8}{5})[/tex]

[tex]\beta_1 = 0.64 \times 1.6[/tex]

[tex]\beta_1 = 1.024[/tex]

To the intercept of the regression line, we have the following equation

[tex]\beta_o = \overline y - \beta_1 \overline x[/tex]

replacing the values:

[tex]\beta_o = 28 -(1.024)(17)[/tex]

[tex]\beta_o = 28 -17.408[/tex]

[tex]\beta_o = 10.592[/tex]

However, the regression line needed for this study can be computed as:

[tex]\hat Y = \beta_o + \beta_1 X[/tex]

[tex]\hat Y = 10.592 + 1.024 X[/tex]

Recall that;

both the weight and height roughly follow the normal curve

As such, the weight related to 90th percentile can be determined as shown below.

Using the Excel Function at 90th percentile, which can be computed as:

(=Normsinv (0.90) ; we have the desired value of 1.28

∴

[tex]\dfrac{X - \overline x}{s_x } = 1.28[/tex]

[tex]\dfrac{X - 17}{5} = 1.28[/tex]

[tex]X - 17 = 6.4[/tex]

X = 6.4 + 17

X = 23.4

The predicted height [tex]\hat Y = 10.592 + 1.024 X[/tex]

where; X = 23.4

[tex]\hat Y = 10.592 + 1.024 (23.4)[/tex]

[tex]\hat Y = 10.592 + 23.9616[/tex]

[tex]\hat Y = 34.5536[/tex]

Now; the probability of predicted height less than 34.5536 can be computed as:

[tex]P(Y < 34.5536) = P( \dfrac{Y - \overline y }{S_y} < \dfrac{34.5536-28}{8})[/tex]

[tex]P(Y < 34.5536) = P(Z< \dfrac{6.5536}{8})[/tex]

[tex]P(Y < 34.5536) = P(Z< 0.8192)[/tex]

From the Z tables;

P(Y < 34.5536) =0.7937

Hence,  a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.

The  average height for turkeys at the 90th percentile for weight is :

[tex]\hat Y = 10.592 + 1.024 X[/tex]

where; X = 23.4

[tex]\hat Y = 10.592 + 1.024 (23.4)[/tex]

[tex]\hat Y = 10.592 + 23.962[/tex]

[tex]\mathbf{\hat Y = 34.554}[/tex]

Of the turkeys at the 90th percentile for weight, roughly what percent would you estimate to be taller than 28 inches?

i.e

P(Y >28) = 1 - P (Y< 28)

[tex]P(Y >28) = 1 - P( Z < \dfrac{28 - 34.554}{8})[/tex]

[tex]P(Y >28) = 1 - P( Z < \dfrac{-6.554}{8})[/tex]

[tex]P(Y >28) = 1 - P( Z < -0.8193)[/tex]

From the Z tables,

[tex]P(Y >28) = 1 - 0.2063[/tex]

[tex]\mathbf{P(Y >28) = 0.7937}[/tex]

= 79.37%

Answer : 180 degrees

2 units left

5 units down

Your welcome ❤️

Answer:

The first transformation is a rotation of 180

degrees.

The second transformation is a translation that moves  

2 units left and 5 units down.

Step-by-step explanation:

Answer:

C :) try the box method! it always works for alot of people but i prefer diatrubuative method

Answer:

The 45 in snake is the shorter one.

Step-by-step explanation:

Which is shorter, 45 in or 4 1/2 ft?

                                                                                        12 in

Convert 4 1/2 ft into inches by multiplying 4 1/2 ft by --------- = 54 in.

                                                                                          1 ft

Thus, the 45 in snake is shorter than the 54 in one and should b e V's first choice.

The shorter snake will be a corn snake. Then she will get a corn snake.

Conversion means to convert the same thing into different units.

Vivian is getting a pet snake. She is choosing between the ball python and the corn snake. The ball python is 4 1/2 feet long and the corn snake is 45 inches long.

Convert inches into feet. Then the length of a corn snake will be

45 inches = 45/12 feet

45 inches = 3 3/4 feet

Vivian wants the shorter snake.

Thus, the shorter snake will be a corn snake. Then she will get a corn snake.

More about the conversion link is given below.

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Answer:

t = 8/9

Step-by-step explanation:

There are many possible solutions that could be expressed as equivalent to the equation 10t - 4t + 3t = 8.  With that being said, here is a simplified form, solved for t.

10t - 4t + 3t = 8

6t + 3t = 8

9t = 8

t = 8/9

Each of these form's is an equivalent equation to the one written by Mrs. McAlister.

If you can provide the table of student answers, we could answer which students were correct or wrong.  Without the table, we can only guess.

Cheers.

Answer:

9t=8

Step-by-step explanation:

Answer:

(Kq_1q_2/F)^(1/2).

Step-by-step explanation:

Coulomb's law is a fundamental tenet of several branches of physics, including electromagnetic, electrostatics, and electronics, and it holds true for both positive and negative charges.

The electrostatic force that exists between two charged particles is described by Coulomb's law, a basic tenet of physics. It asserts that the force between two point charges is inversely proportional to the square of the distance between them and directly proportional to the product of their charges.

Coulomb's law can be expressed mathematically as follows:

F = k(q₁q₂)/r²

Where q₁ and q₂ are the charges' magnitudes, r is the distance between them, and k is the Coulomb constant, F denotes the force acting between the two charges.

The electrostatic constant, commonly referred to as the Coulomb constant, is a proportionality constant that establishes the magnitude of the electrostatic force. Its worth is roughly 8.99 x 109 Nm2/C2.

More about Coulomb's law link is given below:

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Answer:

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write expression

(7.5 + 2) - 5

Step 2: Parenthesis

9.5 - 5

Step 3: Subtract

4.5

Answer:

4.5

Step-by-step explanation:

Order of operations rules dictate that we do the operation within the parentheses first:  7.5 + 2 = 9.5.

Then we have 9.5 - 5, or 4.5.