need help please full question in image

Answer:

Step-by-step explanation:

From the given information:

[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]

Given that the solution is pumped at a slower rate of 4gal/min

Then:

[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]

[tex]R_{out}= \dfrac{2A}{50+t}[/tex]

The differential equation can be expressed as:

[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]

Integrating the linear differential equation; we have::

[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]

[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]

multiplying above integrating factor fields; we have:

[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]

[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]

[tex](50 + t)^2 A = (50 + t)^3+c[/tex]

A = (50 + t) + c(50 + t)²

Using the given conditions:

A(0) = 20

⇒ 20 = 50 + c (50)⁻²

-30 = c(50) ⁻²

c = -30 × 2500

c =  -75000

A = (50+t) - 75000(50 + t)⁻²

The no. of pounds of salt in the tank after 35 minutes is:

A(35) = (50 + 35) - 75000(50 + 35)⁻²

A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]

A(35) =69.6193 pounds

A(35) [tex]\simeq[/tex] 70 pounds

Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.

Answer:

4.

Step-by-step explanation:

(x^2 + 7x - 9) + (3x^2 - 2x) + (x^2 + 7x - 9) + (3x^2 - 2x)

x^2 + 7x - 9 + 3x^2 - 2x + x^2 + 7x - 9 + 3x^2 - 2x

Rearranging order:

3x^2 + 3x^2 + x^2 + x^2 + 7x + 7x - 2x - 2x - 9 - 9

Combine like terms

8x^2 + 10x - 18

Answer:

it's 2

Step-by-step explanation:

a= -3/4

b=0

c=2

your answer should be 1/3 if I did my math right

Answer:

y = -2x - 3

Step-by-step explanation:

Given:

Equation of -x +2y =4

Point of (-2,1)

-x + 2y = 4

y = x/2 + 2 or y = 1/2x + 2

Which means the equation's slope is m = 1/2.

The slope of the perpendicular line is negative inverse which is m = -2.

Now we have an equation of y = -2x + a.

Use (-2, 1) to find a:

1 = (-2)(-2) + a

a = -3

y = - 2x - 3

Answer:

$69.21

Step-by-step explanation:

Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]

Let h be the height of the box

V = Volume of the box = [tex]620\ \text{cm}^3[/tex]

[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]

Now surface area of the box with an open top is given

[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]

Differentiating with respect to x we get

[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]

Equating with zero

[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]

Double derivative of the function

[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]

So, x at 10.74 is the minimum value of the function.

[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]

So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.

The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]

The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]

Cost of the base is $0.40 per square cm

Cost of the side is  $0.10 per square cm

Minimum cost would be

[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]

The minimum cost of the box is 69.21 dollars.

Answer:

[tex]r = 1.34[/tex]

Step-by-step explanation:

Given

Solid = Cylinder + 2 hemisphere

[tex]Volume = 10cm^3[/tex]

Required

Determine the radius (r) that minimizes the surface area

First, we need to determine the volume of the shape.

Volume of Cylinder (V1) is:

[tex]V_1 = \pi r^2h[/tex]

Volume of 2 hemispheres (V2) is:

[tex]V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3[/tex]

[tex]V_2 = \frac{4}{3}\pi r^3[/tex]

Volume of the solid is:

[tex]V = V_1 + V_2[/tex]

[tex]V = \pi r^2h + \frac{4}{3}\pi r^3[/tex]

Substitute 10 for V

[tex]10 = \pi r^2h + \frac{4}{3}\pi r^3[/tex]

Next, we make h the subject

[tex]\pi r^2h = 10 - \frac{4}{3}\pi r^3[/tex]

Solve for h

[tex]h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}[/tex]

[tex]h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}[/tex]

[tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]

Next, we determine the surface area

Surface area (A1) of the cylinder:

Note that the cylinder is covered by the 2 hemisphere.

So, we only calculate the surface area of the curved surface.

i.e.

[tex]A_1 = 2\pi rh[/tex]

Surface Area (A2) of 2 hemispheres is:

[tex]A_2 = 2\pi r^2+2\pi r^2[/tex]

[tex]A_2 = 4\pi r^2[/tex]

Surface Area (A) of solid is

[tex]A = A_1 + A_2[/tex]

[tex]A = 2\pi rh + 4\pi r^2[/tex]

Substitute [tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]

[tex]A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2[/tex]

Open bracket

[tex]A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]

[tex]A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]

[tex]A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2[/tex]

[tex]A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2[/tex]

Take LCM

[tex]A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}[/tex]

[tex]A = \frac{20}{r} + \frac{4\pi r^2}{3}[/tex]

Differentiate w.r.t r

[tex]A' = -\frac{20}{r^2} + \frac{8\pi r}{3}[/tex]

Equate A' to 0

[tex]-\frac{20}{r^2} + \frac{8\pi r}{3} = 0[/tex]

Solve for r

[tex]\frac{8\pi r}{3} = \frac{20}{r^2}[/tex]

Cross Multiply

[tex]8\pi r * r^2 = 20 * 3[/tex]

[tex]8\pi r^3 = 60[/tex]

Divide both sides by [tex]8\pi[/tex]

[tex]r^3 = \frac{60}{8\pi}[/tex]

[tex]r^3 = \frac{15}{2\pi}[/tex]

Take [tex]\pi = 22/7[/tex]

[tex]r^3 = \frac{15}{2 * 22/7}[/tex]

[tex]r^3 = \frac{15}{44/7}[/tex]

[tex]r^3 = \frac{15*7}{44}[/tex]

[tex]r^3 = \frac{105}{44}[/tex]

Take cube roots of both sides

[tex]r = \sqrt[3]{\frac{105}{44}}[/tex]

[tex]r = \sqrt[3]{2.38636363636}[/tex]

[tex]r = 1.33632535155[/tex]

[tex]r = 1.34[/tex] (approximated)

Hence, the radius is 1.34cm

The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.

Given :

The volume of a cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

The total volume of the two hemispheres is given by:

[tex]\rm V' = 2\times \dfrac{2}{3}\pi r^3[/tex]

[tex]\rm V' = \dfrac{4}{3}\pi r^3[/tex]

Now, the total volume of the solid is given by:

[tex]\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]

Now, substitute the value of the total volume in the above expression and then solve for h.

[tex]\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]

[tex]\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}[/tex]

Now, the surface area of the curved surface is given by:

[tex]\rm A = 2\pi r h[/tex]

Now, the surface area of the two hemispheres is given by:

[tex]\rm A'=2\times (2\pi r^2)[/tex]

[tex]\rm A'=4\pi r^2[/tex]

Now, the total area is given by:

[tex]\rm A_T = 2\pi rh+4\pi r^2[/tex]

Now, substitute the value of 'h' in the above expression.

[tex]\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2[/tex]

Simplify the above expression.

[tex]\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}[/tex]

Now, differentiate the total area with respect to 'r'.

[tex]\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]

Now, equate the above expression to zero.

[tex]\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]

Simplify the above expression in order to determine the value of 'r'.

[tex]8\pi r^3=60[/tex]

r = 1.34 cm

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Answer:

its y=-5x

Step-by-step explanation:

Why?

linear functions have only the slope, they dont include the y-intercept

Answer:

A negative number, a negative integer, a negative multiple of 3, etc.

Step-by-step explanation:

Answer:

integer

???????

Step-by-step explanation:

I'm not sure

Answer:

10

Step-by-step explanation:

A decagon is a polygon that has 10 sides !

Answer:

3

Step-by-step explanation:

Given a line with points; (2, 5) (3, 8).

1. Find the slope of the given line

The formula for finding the slope is:

[tex]\frac{y_{2}-y_{1} }{x_{2} - x_{1}}[/tex]

Substitute in the values;

[tex]x_{1} = 2\\y_{1} = 5\\x_{2} = 3\\y_{2} = 8[/tex]

[tex]\frac{8-5}{3-2}[/tex]

simplify;

[tex]\frac{3}{1}[/tex]

= 3

2. Find the slope of the parallel line;

Remember, when two lines are parallel, they run alongside each other, of infinitely long, but they never touch. Hence two parallel lines have the same slope. Therefore, the slope of a line that is parallel to the given one will also have the same slope as the given one, which is 3.

Answer:

The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)

Step-by-step explanation:

Let us use these facts above to solve the question

∵ The quadratic function f(x) = y has a vertex point (-4, -5)

∵ g(x) = f(x + 2) + 3

→ By using the two facts above

∴ f(x) is translated 2 units to the left

∴ f(x) is translated 3 units up

→ That means the vertex point must move 2 units left and 3 units up

∵ The rule of translation is T (x, y) → (x - 2, y + 3)

∵ The coordinates of the vertex point of f(x) are (-4, -5)

∴ Its image is (-4 - 2, -5 + 3)

∴ Its image is (-6, -2)

∴ The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)

Answer: h is 5 and k is 2

Step-by-step explanation:

The equation of the transformed of the parent cube root function is

y = ∛(x-4) - 1.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

The given graph represents a transformation of the parent cube root function.

The Parent cube root function is

y = ∛(x -h) - k

where the value of h  and k is equal to 0

h=0, k=0 in parent function

The graph changes direction at (0,0) in parent function.

From the given graph we can see that the graph changes direction at (4,-1) which means the graph is shifted 4 units to the right and 1 unit down

So, the value of h=4  and value of k=1

The equation of the transformed function,

y = ∛(x-4) - 1

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Answer:

There are 64 trucks!

Step-by-step explanation:

The fraction of the shape which is shaded in simplest form is 1/3.

The square in the diagram provided has a total of 12 boxes .

The number of shaded part is 4

To calculate the shaded fraction of the shape we have to use the formula:

Number of shaded part/ Total number of boxes present.

= 4/12

We can divide the numerator and denominator by 4 to get the simplest form.

= 1/3

The fraction of the shape which is shaded in simplest form is therefore

= 1/3.

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Answer:

53.3 degrees

Step-by-step explanation:

∆DEF and ∆RSQ are similar. We know this, because the ratio of their corresponding sides are equal. That is:

DE corresponds to RS

EF corresponds to SQ

DF corresponds to RQ.

Also <D corresponds to <R, <E corresponds to <S, and <F corresponds to <Q.

The ratio of their corresponding sides = DE/RS = 6/3 = 2

EG/SQ = 8/4 = 2

DF/RQ = 4/2 = 2.

Since the ratio of their corresponding sides are equal, it means ∆DEF and ∆RSQ are similar.

Therefore, their corresponding angles would be equal.

Thus, m<Q = m<F

Let's find angle F

m<F = 180 - (98 + 28.7)

m<F = 53.3°

Since <F corresponds to <Q, therefore,

m<Q = 53.3°

Answer:

a) 0.0977

b) 0.3507

c) No it is not unusual for a broiler to weigh more than 1610 grams

Step-by-step explanation:

Mean = 1395 grams

Standard deviation = 200 grams. Use the TI-84 Plus calculator to answer the following.

We solve using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

(a) What proportion of broilers weigh between 1160 and 1250 grams?

For x = 1160

z = 1160 - 1395/300

= -0.78333

Probability value from Z-Table:

P(x = 1160) = 0.21672

For x = 1250 grams

z = 1250 - 1395/300

z = -0.48333

Probability value from Z-Table:

P(x = 1250) = 0.31443

The proportion of broilers weigh between 1160 and 1250 grams is

0.31443 - 0.21672

= 0.09771

≈ 0.0977

(b) What is the probability that a randomly selected broiler weighs more than 1510 grams?

For x = 1510

= z = 1510 - 1395/300

z = 0.38333

Probability value from Z-Table:

P(x<1510) = 0.64926

P(x>1510) = 1 - P(x<1510) = 0.35074

Approximately = 0.3507

(c) Is it unusual for a broiler to weigh more than 1610 grams?

For x = 1610

= z = 1610 - 1395/300

z = 0.71667

Probability value from Z-Table:

P(x<1610) = 0.76321

P(x>1610) = 1 - P(x<1610) = 0.23679

No it is not unusual for a broiler to weigh more than 1610 grams

Answer:

10 apples

Step-by-step explanation:

if Person a bought twice as many apples as person b then it would be ten considering 10 x 2 = 20

eqaution: 10 divided by 2

Answer:

$2,639.19

Step-by-step explanation:

Her balance at the end of the month is

$2358.19 - $80.00 + $99.50 = $2537.69

So the finance charge is 2537.69 * 0.04% = $101.50

and her new balance is $101.50 + $2537.69 = $2639.19

Answer:

Z = -6.3

Step-by-step explanation:

Given that:

[tex]\mathbf{H_o :p= 0.28}[/tex]

[tex]\mathbf{H_o :p < 0.28}[/tex]

Since the alternative hypothesis is less than 0.28, then this is a left-tailed hypothesis.

Sample sixe n = 800

[tex]\hat p[/tex] = 0.217

The standard error [tex]S.E(p) = \sqrt{\dfrac{p(1-p)}{n}}[/tex]

[tex]S.E(p) = \sqrt{\dfrac{0.28(1-0.28)}{800}}[/tex]

[tex]S.E(p) \simeq0.015[/tex]

Since this is a single proportional test, the test statistics can be computed as:

[tex]Z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

[tex]Z = \dfrac{0.217- 0.28}{0.01}[/tex]

Z = -6.3

Answer:

3 to the 4th power is 81.

Step-by-step explanation:

You would do 3 × 3, which would get you to 9. Then, you multiply 9 × 9, which gives you 81.

Answer: x=6/5

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

Answer:

The first one

Answer:

1. Express the width of the rectangle in terms of the length X.

width = 500 - X

2. Express the surface area of the rectangle in terms of X.

area = -X² + 500X

3. What value of X gives the maximum surface area?

maximum surface area results from the rectangle being a square, so 1,000 ÷ 4 = 250

X = 250 ft

4. What is the maximum surface area?

maximum surface area = X² = 250² = 62,500 ft²

Step-by-step explanation:

since the perimeter = 1,000

1,000 = 2X + 2W

500 = X + W

W = 500 - X

area = X · W = X · (500 - X) = 500X - X² or -X² + 500X

The area of a shape is the amount of space it occupies.

The length is represented as x.

Let the width be y.

So, we have:

[tex]\mathbf{Perimeter =2(x + y)}[/tex]

This gives

[tex]\mathbf{2(x + y) = 1000}[/tex]

Divide both sides by 2

[tex]\mathbf{x + y = 500}[/tex]

Make y the subject

[tex]\mathbf{y = 500 -x}[/tex]

So, the width in terms of x is 500 - x

The surface area is calculated as:

[tex]\mathbf{A = xy}[/tex]

Substitute [tex]\mathbf{y = 500 -x}[/tex]

[tex]\mathbf{A = x(500 - x)}[/tex]

So, the surface area in terms of x is x(500 - x)

Expand [tex]\mathbf{A = x(500 - x)}[/tex]

[tex]\mathbf{A = 500x - x^2}[/tex]

Differentiate

[tex]\mathbf{A' = 500- 2x}[/tex]

Equate to 0

[tex]\mathbf{500- 2x = 0}[/tex]

Rewrite as:

[tex]\mathbf{2x = 500}[/tex]

Divide both sides by 2

[tex]\mathbf{x = 250}[/tex]

So, the value of x that gives maximum surface area is 250

Substitute 250 for x in [tex]\mathbf{A = x(500 - x)}[/tex]

[tex]\mathbf{A = 250 \times (500 - 250)}[/tex]

[tex]\mathbf{A = 250 \times 250}[/tex]

[tex]\mathbf{A = 62500}[/tex]

Hence, the maximum area is 62500

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Answer:

multiply it by .12 then it says for 12 months, multiply it by 12 then

Step-by-step explanation:

Answer:

Test statistic Z= 1.713

The calculated Z- value =  1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the  mean annual salary of all lawyers in a city is  different from $110,000

Step-by-step explanation:

Step(i):-

A researcher wants to test if the mean annual salary of all lawyers in a city is

different from $110,000

Mean of the Population  μ = $110,000

Sample size 'n' = 53

Mean of the sample x⁻ = $114,000.

standard deviation of the Population = $17,000,

Level of significance = 0.01

Null hypothesis :

There is no difference between the  mean annual salary of all lawyers in a city is  different from $110,000

H₀:  x⁻ =  μ

Alternative Hypothesis :  x⁻ ≠  μ

Step(ii):-

Test statistic

                 [tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

                 [tex]Z = \frac{114000-110000}{\frac{17000}{\sqrt{53} } }[/tex]

                Z =  1.7130

Tabulated value Z = 2.576 at 0.01 level of significance

The calculated Z- value =  1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the  mean annual salary of all lawyers in a city is  different from $110,000

The area of a rectangle is the product of length and width thus the area will be 1358 square meters.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

The perimeter of the rectangle = 2( length + width).

It is known that,

Area of rectangle = length × width.

Area = 97 x 14 = 1358 sqare meters

Hence "The area of a rectangle is the product of length and width thus the area will be 1358 square meters".

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Answer:

7) y = -2

8) x = 4

Step-by-step explanation:

Any straight horizontal/vertical line you find will be x= or y=. The vertical lines are always x= because they only touch the x axis. It's the opposite for horizontal lines. For example, on number 7, the line touches -2 on the y axis. That's why it's "y=-2". Same goes for 8. the line only touches 4.

I hope this helped and wasn't confusing!

Answer:

$1,815

Step-by-step explanation:

Use the simple interest formula, I = prt

Plug in the values we know:

I = prt

I = (1,500)(0.07)(3)

I = 315

Add this to the original amount:

1500 + 315

= 1,815

So, John will have $1,815 in his account after 3 years.