The PRIDE club is selling school t-shirts and hoodies during football games. Two t-shirts and 2
hoodies will sell for $76.50. Five t-shirts and 3 hoodies will sell for $140.25. How much does
each shirt sell for?

Answer:

a. dS(t)/dt + [7S(t)/(300 - 5t)] = 1.2 with S(0) = 0.8

b. S(t) =   [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex]  -  16.34[tex]e^{-\frac{7t}{100}[/tex]

Step-by-step explanation:

a. Write an initial value problem for S(t), the amount of salt in the tank at time t. Do not solve the equation!!

The net mass flow rate of salt dS(t)/dt = mass flow in - mass flow out

mass flow in = concentration of flow in × flow rate in = 0.6 lb/gal × 2 gal/min = 1.2 lb/min

Let S(t) be the mass of salt in the tank at time, t. The concentration of salt in the tank at time, t, C(t) = S(t)/volume of tank at time t ,V

V = V₀ + (r - r')t where V₀ = initial volume of water in tank = 300 gal, r = volume flow rate in = 2 gal/min, r'= volume flow rate out = 7 gal/min and t = time

So, V = V₀ + (r - r')t

V = 300 + (2 - 7)t

V = 300 - 5t

So, C(t) = S(t)/V = S(t)/(300 - 5t) lb/gal

Now, mass flow rate out = concentration in tank × volume flow rate out = S(t)/(300 - 5t) lb/gal × 7 gal/min = 7S(t)/(300 - 5t) lb/min

So, dS(t)/dt = mass flow in - mass flow out

dS(t)/dt = 1.2 lb/min - 7S(t)/(300 - 5t) lb

dS(t)/dt = 1.2 - 7S(t)/(300 - 5t)

So, our differential equation is

dS(t)/dt + [7S(t)/(300 - 5t)] = 1.2 with S(0) = 0.8 since we initially have 0.8 lb of salt

b. Write an expression in terms of S for the amount of salt in the tank when the tank is one-quarter full.

When the tank is one-quarter full, V = volume of tank/4 = 400 gallons/4 = 100 gallons

We now solve our differential equation

dS(t)/dt + 7S(t)/100 = 1.2

Using the integrating factor method, I.F = [tex]e^{\int\limits{\frac{7}{100} \, dt } =[/tex]  [tex]e^{\frac{7t}{100} }[/tex]

[tex]e^{\frac{7t}{100}[/tex]dS(t)/dt +

d[[tex]e^{\frac{7t}{100}[/tex]S(t)]/dt = 1.2

d[[tex]e^{\frac{7t}{100}[/tex]S(t)] = [1.2

integrating both sides, we have

∫d[[tex]e^{\frac{7t}{100}[/tex]S(t)] = ∫[1.2

Let u = 7t/100. So, du/dt = 7/100 and dt = 100du/7

∫[1.2[tex]e^{\frac{7t}{100}[/tex]]dt = ∫[1.2 × 100[tex]e^{u}[/tex]]du/7 = (120/7)∫

[tex]e^{\frac{7t}{100}[/tex]S(t) =  [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex] + C

S(t) =   [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex] ÷ [tex]e^{\frac{7t}{100}[/tex]  +  [tex]e^{-\frac{7t}{100}[/tex]

S(t) =   [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex]  +  C[tex]e^{-\frac{7t}{100}[/tex]

From our initial condition, S(0) = 0.8. So,

S(0) =   [tex]\frac{120e^{\frac{7(0)}{100} } }{7}[/tex]  +  C[tex]e^{-\frac{7(0)}{100}[/tex]

S(0) =   [tex]\frac{120e^{\frac{0}{100} } }{7}[/tex]  +  C[tex]e^{-\frac{0}{100}[/tex]

S(0) =   [tex]\frac{120e^{0}}{7}[/tex]  +  C[tex]e^{0}[/tex]

0.8 =   [tex]\frac{120}{7}[/tex]   +  C

C = 0.8 - 120/7

C = 0.8 - 17.14

C = - 16.34

So,

S(t) =   [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex]  -  16.34[tex]e^{-\frac{7t}{100}[/tex]

Answer:

this may help you.look it once

Step-by-step explanation:

.

Answer:it can hold 23 passangers

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The equation is V=4/3 times Pi times radius^3

Answer:

answer: 85

Step-by-step explanation:

These add up to 360 and

85 + 85 + 95 + 95 = 360 so 85 is the answer.

Hope that helps!

Answer:

22.18

Step-by-step explanation:

c squared = a squared + b squared - 2ab cos c

or a instead of c in this case.

144+225-360(-0.342)

square root 492.12

9514 1404 393

Answer:

  x-intercept: (-5, 0)

  y-intercept: (0, 5)

Step-by-step explanation:

The x-intercept is where the graph crosses the x-axis. The x-value there is -5. The y-value of any point on the x-axis is 0, so the point coordinates are (-5, 0).

The y-intercept is where the graph crosses the y-axis. The y-value there is 5. The x-value of any point on the y-axis is 0, so the point coordinates are (0, 5).

Answer:

B. f (4) = 4 · [tex]20^{3}[/tex]

Step-by-step explanation:

I did the quiz too

Answer:

x=13

Step-by-step explanation:

18-5=13. You have to subtract 5 from 5 itself and then 18.

Answer:

A=wl=4·7=28 answer is 28

Step-by-step explanation:

Answer:

the answer is 28

Step-by-step explanation:

you do lengthh times width

the length is 7 the width is 4

so 7 times 4 is 28

Answer: It’s B.

Step-by-step explanation: Got it on edge

Answer:

Answer: It’s B.

Got it on edge

Step-by-step explanation:

Got it right on edge

Answer:

What type of line the picture represent

Answer:

here are the cordinates you need to mark :

Step-by-step explanation:

(1,15) : 1x,15y

(2,20) : 2x,20y

(3,35) : 3x,35y

(4,45) : 4x,45y

(5,70) : 5x,70y

Hope this helps :)

Answer:

B, C and F

Step-by-step explanation:

Negative numbers go farther and father to the left on a number line the higher in value they get.

Answer:

27 cents

Step-by-step explanation:

10% of 90= 9

9x3=27

Answer:

p x t x r / 100

90 x 10 x 3 / 100

=27

Answer:

I am almost postive it is B, D, E

Answer:

slope: 4

Y-intercept: -7

Step-by-step explanation:

you would have to solve for y so you subtract the 7 on both sides. then it is in slope-intercept form which is y=mx+b where m is slope and b is the y-intercept. the slope would be 4 and the y-intercept would be -7

Answer:

area = 5

Step-by-step explanation:

Answer:

12.327X + 452.084

45206.327

Step-by-step explanation:

The linear regression model obtained by fitting the data using technology is :

ŷ = 12.327X + 452.084

Where, 12.327 = slope ; 452.084 = Intercept ; X = appraised value ; y = Area

The estimated error variance which is the degree of variation between the actual and predicted value.

Error variance = ΣSSE /n-2

n = sample size = 15

ΣSSE = 587682.2638

Error variance = 587682.2638/13

Error variance = 45206.327

Answer:e

Step-by-step explanation:

-(5/3)=-5/3

Answer:

B= 43

Step-by-step explanation:

B=19+(6)(4)

B=19+24

B=43

Answer:

Hello! if Chris garden is a square shape then the answer is 40 7/10 in fraction form or 40.7 in decimal form

Answer:

0.75 = 75% probability that he will have to wait at a red light for more than 15 seconds

Step-by-step explanation:

At each second, the stoplight is equally likely to change, which means that we use the uniform probability distribution to solve this question.

Uniform probability distribution:

Has two bounds, a and b. The probability of finding a value higher than x is given by:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Red for 60 seconds

So when Jamal arrives it can change in any number of seconds between 0 and 60, that is, [tex]a = 0, b = 60[/tex]

Probability that he will have to wait at a red light for more than 15 seconds?

[tex]P(X > 15) = \frac{60 - 15}{60 - 0} = \frac{45}{60} = \frac{3}{4} = 0.75[/tex]

0.75 = 75% probability that he will have to wait at a red light for more than 15 seconds

Answer: 33

Step-by-step explanation: When a tangent and radius intersect (as in the diagram) they will always be perpendicular. And using the Triangle Sum Theorem that all angles add up to 180 when get that m<BCA must be 33 degrees.

Answer:

Pedro pagó $448

Step-by-step explanation:

Sea P el precio inicial de un objeto.

Si aplicamos un descuento del X%, entonces el nuevo precio del objeto es:

NP = P*(1 - X%/100%)

y lo que estamos ahorrando es:

P - NP

En este caso, primero tenemos un descuento del 30%, entonces:

NP = P*(1 - 30%/100%) = P*(1 - 0.3)

Luego tenemos otro descuento, esta vez del 20%, entonces:

NP' = NP*(1 - 20%/100%) = P*(1 - 0.3)*(1 - 20%/100%) = P*(1 - 0.3)*(1 - 0.2)

Lo que Pedro ahorra es igual a $352

entonces:

P - NP' = $352

P -  P*(1 - 0.3)*(1 - 0.2) = $352

P*(1 - (1 - 0.3)*(1 - 0.2)) = $352

P*(1 - 0.56) = $352

P = $352/(1 - 0.56) = $800

Esto significa que el precio original era $800.

Y lo que pedro pago esta dado por la ecuación:

NP' = P*(1 - 0.2)*(1 - 0.3) = $800*(1 - 0.2)*(1 - 0.3) = $448.

Answer:

true

true

false

Answer:

The test statistic is [tex]z = -0.28[/tex]

Step-by-step explanation:

First, before finding the test statistic, we need to understand the central limit theorem and difference between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A random sample of children in two different schools found that 16 of 40 at one school

This means that:

[tex]p_1 = \frac{16}{40} = 0.4, s_1 = \sqrt{\frac{0.4*0.6}{40}} = 0.0775[/tex]

13 of 30 at the other had this infection.

This means that:

[tex]p_2 = \frac{13}{30} = 0.4333, s_2 = \sqrt{\frac{0.4333*0.5667}{30}} = 0.0905[/tex]

Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other.

At the null hypothesis, we test if there is no difference, that is:

[tex]H_0: p_1 - p_2 = 0[/tex]

And at the alternate hypothesis, we test if there is difference, that is:

[tex]H_a: p_1 - p_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]p = p_1 - p_2 = 0.4 - 0.4333 = -0.0333[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0775^2+0.0905^2} = 0.1191[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.0333 - 0}{0.1191}[/tex]

[tex]z = -0.28[/tex]

The test statistic is [tex]z = -0.28[/tex]

Answer:

shhdhd

Step-by-step explanation:

Oh wow great marks