The Hampton family has a fish tank holding 10450 ml of water. The water is leaking at a rate of 270ml per minute. Write a function to model this situation

Answers

Answer 1

Ok, lets visualize this scenario. We have a tank that is holding10450 ml of water. Then it tells use it is leaking at a rate of 270 ml per minute. Well, leaking would suggest something is being subtracted. Also, per minute means it is being subtracted each minutes so we use an x to represent the minutes. Ok, lets build the model

10450 - 270x = 0
The model above will tell us how many minutes it will take for the tank to be empty.

If we insert a number for x, the model below will tell us how many ml has leaked for the number of minutes we inserted into x.
10450 - 270x

Related Questions

Don't understand how to do the graph

Answers

this question is asking you to show how adding two more students with the score of 80 will affect the graph and its growth.

you are lying 120 ft away from a tree that is 50 feet tall you look up at the top of the tree approxmaelty how far is your head from the top of the tree in a straight line

Answers

check the picture below.

lim x→25 x−25 /√x−5

Answers

Final answer:

The solution involves multiplying by the conjugate of the denominator to simplify the expression, leading to the finding that the limit as x approaches 25 of (x-25)/(√x-5) equals 10.

Explanation:

The question asks to evaluate the limit lim x→25 (x−25)/(√x−5). At first glance, directly substituting x = 25 into the equation would lead to a 0/0 form, indicating a need for algebraic manipulation to resolve the indeterminate form.

To simplify, we can multiply the numerator and the denominator by the conjugate of the denominator, which is (√x + 5). This approach is helpful in dealing with limits that involve square roots.

Following this step:

Multiply both the numerator and denominator by (√x + 5).

The numerator becomes (x - 25)(√x + 5).

The denominator turns into x - 25 after applying the difference of squares.

Simplify to get (√x + 5), since (x - 25) in numerator and denominator cancel out.

Finally, substitute x = 25 into the simplified form to get 10 as the answer. Therefore, lim x→25 (x−25)/(√x−5) = 10

Find the value of x. Round the length to the nearest 10th the diagram is not shown to scale

Answers

In the given diagram:
measure angle DAB + measure angle BAC = 90 degrees
we are given that measure angle DAB = 10 degrees
Therefore:
measure angle BAC = 90 - 10 = 80 degrees

Now, triangle ABC is a right-angled triangle which means that we can use the trigonometric functions.
The function that we will use is:
cos theta = (adjacent) / (hypotenuse) where
theta = 80 degrees
adjacent = 500
hypotenuse is "x" that we want to calculate.

Substitute to get x as follows:
cos 80 = 500 / x
x = 500 / cos 80 = 500 / 0.1736 = 2879.4 m

Arlan needs to create a box from a piece of cardboard. The dimensions of his cardboard are 10 inches by 8 inches. He must cut a square from each corner of the cardboard, in order to form a box. What size square should he cut from each corner, in order to create a box with the largest possible volume?

A. 0.5 inches
B. 1 inch
C. 1.5 inches
D. 2 inches

Answers

1) Dimensiones of the cardboard:

length: 10 inches
width: 8 inches

2) dimensions of the squares cut

length: x
width: x

3) dimensions of the box:

length of the base = 10 - 2x
width of the base = 8 - 2x
height = x

4) Volume of the box

V = (10 - 2x) (8 - 2x) x = x [80 - 20x - 16x + 4x^2] = x [ 80 - 36x + 4x^2 ] =

V = 80x - 36x^2 + 4x^3

5) Maximum volume => derivative of V, V' = 0

V' = 80 - 72x + 12x^2 = 0

6) Solve the equation

Divide by 4 => 3x^2 - 18x + 20 = 0

Use the quadratic formula: x = 1.47 and x = 4.53 (this is not valid)

So, the answer is the option C. 1.5 inches.

Graph parallelogram ABCD on a coordinate plane with vertices A(3,4) B(6,1) C(0,-2) and D(-3,1).
Find the slope of each side.
What do you notice about the slopes?

Answers

SLOPES

AB = (1 - 4) / (6 - 3) = -3 / 3 = -1
BC = (-2 - 1) / (0 - 6) = -3 / -6 = 1/2
CD = (1 - (-2)) / (-3 - 0) = 3 / -3 = -1
DA = (4 - 1) / (3 - (-3)) = 3 / 6 = 1/2

EXPLANATION

Every line has one side parallel to it and I know this because the slope is equal.

A parallelogram, the opposite sides have equal slopes.

To graph the parallelogram ABCD on a coordinate plane, we can plot the given points A(3,4), B(6,1), C(0,-2), and D(-3,1), and then connect them in order to form the parallelogram.

Here are the steps to find the slope of each side:

Plot the Points:

Plot the points A(3,4), B(6,1), C(0,-2), and D(-3,1) on the coordinate plane.

Connect the Points:

Connect the points in order (A to B to C to D to A) to form the parallelogram.

Find the Slope:

The slope of a line passing through two points

(x_1 ,y_1 ) and (x_2 ,y_2 ) is given by the formula m= y_2 -y_1/ x_2- x_1

Calculate the slope for each pair of consecutive points:

Slope of AB: mAB = 1−4/6−3

Slope of BC: mBC = −2−1/0−6

Slope of CD: mCD = 1−(−2)/−3−0

Slope of DA: mDA = 4−1/ 3−(−3)

Now, observe the slopes:

mAB and mCD

are the slopes of opposite sides. They should be equal for a parallelogram.

mBC and mDA are the slopes of the other pair of opposite sides. They should also be equal for a parallelogram.

So, for a parallelogram, the opposite sides have equal slopes.

For commission as a realtor, Michelle earns $349 plus 3% of the purchase price for each home she helps buy or sell. If she earned $8,965 in commission on a certain home, find its purchase price.

ANSWER:
$8965- $349= $8616
3/100x= 8616
8616 x 100/ 3= $287,200.

I'm posting this because somebody inboxed me asking for help and before I even got to help them, they deleted the inbox and i couldn't remember their name. I hope you see this and benefit from it, sorry!

Answers

Well, let us solve this step by step.

We know that Michelle earns 349 plus 3% of the Purchase price. Let us call the Purchase price as P, so that:

Earnings, E = 349 + 0.03 P

So if she earns 8,965 (E = 8,965) so we can find P:

8,965 = 349 + 0.03 P

0.03 P = 8,616

P = $287,200

Final answer:

Michelle's total commission from a house sale was $8,965, from which $349 is a fixed commission. The rest, $8616, represents the 3% of the selling price of the house. By solving the simple equation $8616 = 0.03 * X, we find that the home price is $287,200.

Explanation:

This problem is a simple, but common, practice in the world of linear equations. The first step is to understand that the base commission of $349 is a constant that Michelle earns every time, whilst the remaining part of her commission comes from the 3% percentage of the sale price. After subtracting the base commission from the total commission, we get a value of: $8965 - $349 = $8616. This value is equal to 3% of the house price.

We can express this as: 8616 = 0.03 * X, where X is the value of the house. By isolating X (the house price), we divide both sides by 0.03 to get the house price. Therefore, the home price would be $8616 / 0.03 = $287,200.

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Which of the following give an equation of a line that passes through the point (6/5,-19,5) and is parallel to the line that passes through the organ and point (-2,-12)

A. y= 6x-11
B. y= 6x-19/5
C. y= 6x-6/5
D. y= 6x+1

Answers

parallel lines, have the same slope, so the slope of the line through 0,0 and -2,-12, is the same as for the line running through (6/5,-19.5) as well, so what is it anyway?

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 0}})\quad % (c,d) &({{ -2}}\quad ,&{{ -12}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-12-0}{-2-0}\implies \cfrac{-12}{-2}\implies 6[/tex]

so, we're looking for the equation of a line whose slope is 6, and goes through (6/5,-19/5)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ \frac{6}{5}}}\quad ,&{{ -\frac{19}{5}}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 6 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-\left( -\frac{19}{5} \right)=6\left(x-\frac{6}{5} \right) \\\\\\ y+\cfrac{19}{5}=6x-\cfrac{36}{5}\implies y=6x-\cfrac{36}{5}-\cfrac{19}{5}\implies y=6x-\cfrac{55}{5} \\\\\\ y=6x-11[/tex]

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 9. the hypotheses h0: μ = 73 and ha: μ < 73 are to be tested using a random sample of n = 25 observations.

Answers

Part A:

The z score of the hypothesis testing of n samples of a normally distributed data set is given by:

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

Given that the population mean is 73 and the population standard deviation is 9, then the number of standard deviation below the null value of x = 72.3 is given by the z score:

[tex]z= \frac{72.3-73}{9/\sqrt{25}} \\ \\ = \frac{-0.7}{9/5} = \frac{-0.7}{1.8} \\ \\ =-0.39[/tex]

Therefore, 72.3 is 0.39 standard deviations below the null value.

Part B:

The test statistics of the hypothesis testing of n samples of a normally distributed data set is given by:

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

Thus given that x = 72.3, μ = 73, σ = 9 and n = 25,

[tex]z= \frac{72.3-73}{9/\sqrt{25}} \\ \\ = \frac{-0.7}{9/5} = \frac{-0.7}{1.8} \\ \\ =-0.39[/tex]

The p-value is given by:

P(-0.39) = 0.3483

Since α = 0.005 and p-value = 0.3483, this means that the p-value is greater than the α, ant thus, we will faill to reject the null hypothesis.

Therefore, the conclussion is do not reject the null hypothesis. there is not sufficient evidence to conclude that the mean drying time is less than 73.

Part C:

In general for the alternative hypothesis, [tex]H_a :\mu\ \textless \ \mu_0[/tex]

[tex]\beta(\mu') = P\left(X \ \textgreater \ \mu_0-z_{1-\alpha}\frac{\sigma}{\sqrt{n}}|\mu'\right) \\ \\ = 1-P\left(-z_{1-\alpha}+\frac{\mu_0-\mu'}{\sigma/\sqrt{n}}\right) [/tex]

So for the test procedure with α = 0.005

[tex]\beta(70) = 1 - P\left(-z_{0.995}+\frac{73-70}{9/5}\right) \\ \\ =1 - P(-2.5755+1.6667)=1-P(-0.9088) \\ \\ =1-0.1817\approx\bold{0.8183 }[/tex]

Part D:

For α = 0.005, and a general sample size n we have that

[tex]\beta(70) = 1 - P\left(-z_{0.995}+\frac{73-70}{9/\sqrt{n}}\right) \\ \\ =1 - P\left(-2.5755+ \frac{3}{9/\sqrt{n}} \right)[/tex]

Since, we want n so that β(70) = 0.01, thus

[tex]1 - P\left(-2.5755+ \frac{3}{9/\sqrt{n}} \right)=0.01 \\ \\ \Rightarrow P\left(-2.5755+ \frac{3}{9/\sqrt{n}} \right)=1-0.01=0.99 \\ \\ \Rightarrow P\left(-2.5755+ \frac{3}{9/\sqrt{n}} \right)=P(2.3262) \\ \\ \Rightarrow -2.5755+ \frac{3}{9/\sqrt{n}}=2.3262 \\ \\ \Rightarrow \frac{3}{9/\sqrt{n}}=4.9017 \\ \\ \Rightarrow \frac{9}{\sqrt{n}} = \frac{3}{4.9017} =0.6120 \\ \\ \Rightarrow \sqrt{n}= \frac{9}{0.6120} =14.7051 \\ \\ \Rightarrow n=(14.7051)^2=216.2[/tex]

so we need n = 217.

Part E

[tex]P-value=P(\bar{X}\leq\bar{x}) \\ \\ =P(\bar{X}\leq72.3)=P\left(z\leq \frac{72.3-76}{9/10} \right) \\ \\ =P\left(z\leq \frac{-3.7}{0.9} \right)=P(z\leq-4.111) \\ \\ =\bold{0.00002}[/tex]

If two non collinear segments in the coordinate plane have slope 3 what can you conclude

Answers

Two non co-linear segments with a slope of 3 in a coordinate plane would mean that the two segments are parallel to each other and not attached to each other. Having the same slope is the definition of being parallel in the same plane.

jody has 2 red marbles 6 blue marbles and yellow marbles what is the ratio to red to blue

Answers

1 to 2
is the answer because 2/6 simplifies to 1/2 which would be the ratio of 1:2.

For the data in the table does y vary directly with x? X=16,32,48-Y=4,16,36

Answers

Data:

x          y

16        4

32      16

48      36

Direct relation means that the ratio y / x is constant.

So, let's examine this ratio:

Ratio y / x

4/16 = 1/4

16/32 = 1/2

36/48 = 3/ 4

Given that the ratio y/x is not constant, the conclusion is that y does not vary directly with x.

I'm doing the same test.. what are the answers ?

90,175,087,309 in expanded form

Answers

90,000,000,000
+ 0
+ 100,000,000
+ 70,000,000
+ 5,000,000
+ 0
+ 80,000
+ 7,000
+ 300
+ 0
+ 9

Expanded Factors Form:
9 × 10,000,000,000
+ 0 × 1,000,000,000
+ 1 × 100,000,000
+ 7 × 10,000,000
+ 5 × 1,000,000
+ 0 × 100,000
+ 8 × 10,000
+ 7 × 1,000
+ 3 × 100
+ 0 × 10
+ 9 × 1

Expanded Exponential Form:
9 × 1010
+ 0 × 109
+ 1 × 108
+ 7 × 107
+ 5 × 106
+ 0 × 105
+ 8 × 104
+ 7 × 103
+ 3 × 102
+ 0 × 101
+ 9 × 100

Word Form:

ninety billion, one hundred seventy-five million, eighty-seven thousand, three hundred nine

90,000,000,000 + 0 + 100,000,000 + 70,000,000 + 5,000,000 + 0 + 80,000 + 7,000 + 300 + 0 + 9

on monday 2/3 of the team practiced tuesday 7/8 wednesday 1/2 and thurday 3/4 on which day were the most team memebers present at practice

Answers

Monday: 2/3

Tuesday: 7/8

Wednesday: 1/2

Thursday: 3/4

You have to compare the fractions:

There are several methods to compare fractions. I will use the conversion to a common denominator.

This is how you convert all the fractions to an equivalent form with common denominator.

The least common denominator is: 3 * 2^3 = 24

Original fraction       equivalent fraction

2/3 2*8 / 3*8 = 16 / 24

7/8                           7*3 / 8*3 = 21 / 24

1/2                           1*12 / 2* 12 = 12 / 24

3/4                            3*6 / 4*6 = 18 / 24

Now you can compare the fractions: 12/24 < 16/24 < 18/24 < 21/24.

So, you see that the greatest fraction is 21 /24, i.e. 7/8, and the answer is the day when 7/8 of the team practiced.

Answer: Tuesday.

7x300=7x blank hundreds

Answers

Hello There!

7 x 300 = 7 x three hundreds

Hope This Helps You!
Good Luck :)

- Hannah ❤

Hey there!

7 x 300 = 7x three hundreds

Hope this helps! :)

26×107 What is the value of the second partial product

Answers

2782 is the answer my friend

3.5 x 10^4 write the following number in standard form (decimal).

Answers

Answer:

35,000

Step-by-step explanation:

christie decided to make bracelets for her class. two-fifths of the bracelets were done on Monday and three-sevenths were done on Tuesday what part of the bracelets are finished?

Answers

[tex]\bf \stackrel{Monday}{\cfrac{2}{5}}+\stackrel{Tuesday}{\cfrac{3}{7}}\impliedby \stackrel{LCD}{35}\implies \cfrac{14+15}{35}\implies \stackrel{done}{\cfrac{29}{35}}[/tex]

What is the like term for 4m+(-3n)+n? What is the like term for c+2c+c-5c+1

Answers

a) The three terms have variables m, n, n. The two like terms are the last two terms, which both have variable n: -3n, n.

b) The 5 terms have variables c, c, c, c, -. The like terms are the first four, which all have variable c: c, 2c, c, -5c.

What is the slope and y intercept of y=-27.4x

Answers

[tex]y = mx + b[/tex]

This is slope intercept form, where m is the slope and b is the y - intercept. If we compare the to our equation:

[tex]y = -27.4x + 0[/tex] (we can add a 0, because 0 dosen't change the value)

In this case:

[tex]m(slope) = -27.4 ; b(y-inter) = 0[/tex]

Hope this helps!

Find the surface area of the surface given by the portion of the paraboloid z=3x2+3y2 that lies inside the cylinder x2+y2=4. (hint: convert to polar coordinates after setting up the integral)

Answers

Parameterize the part of the paraboloid within the cylinder - I'll call it [tex]S[/tex] - by

[tex]\mathbf r(u,v)=\langle x(u,v),y(u,v),z(u,v)\rangle=\left\langle u\cos v,u\sin v,3u^2\right\rangle[/tex]

with [tex]0\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex]. The region's area is given by the surface integral

[tex]\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=2}\int_{v=0}^{v=2\pi}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\int_{v=0}^{v=2\pi}\int_{u=0}^{u=2}u\sqrt{1+36u^2}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=2}u\sqrt{1+36u^2}\,\mathrm du[/tex]

Take [tex]w=1+36u^2[/tex] so that [tex]\mathrm dw=72u\,\mathrm du[/tex], and the integral becomes

[tex]=\displaystyle\frac{2\pi}{72}\int_{w=1}^{w=145}\sqrt w\,\mathrm dw[/tex]
[tex]=\displaystyle\frac\pi{36}\frac23w^{3/2}\bigg|_{w=1}^{w=145}[/tex]
[tex]=\dfrac\pi{54}(145^{3/2}-1)\approx101.522[/tex]

Final answer:

To find the surface area of the specified area in the paraboloid, convert the original cartesian coordinates to polar coordinates. Then set up and solve the appropriate double integral over the region defined by the circle in polar coordinates.

Explanation:

To find the surface area of a paraboloid z=3x²+3y² inside the cylinder x²+y²=4, you first set up the integral and then convert to polar coordinates. As per the given paraboloid equation, we know that dz/dx = 6x and dz/dy = 6y. Therefore, the differential of surface area in polar coordinates can be given as √(1+(6r*cosø)²+(6r*sinø)²) rdrdø.

Next, integrate this over the area of a circle in polar coordinates, from r=0 to r=2 and ø=0 to ø=2π. The limits of 2 and 2π come from the given cylinder equation x²+y²=4, which represents a circle of radius 2 in polar coordinates.

The final integral in terms of r and ø should yield the desired surface area of the paraboloid which lies inside the cylinder.

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Evaluate 5 c - 3 d+11 when c= 7 and d= 8

Answers

5x7-3x8+11
35-24+11
11+11
The answer is 22

the answer is 11 because you just plug in the numbers for the letter variables and solve

Are all rectangles similar

Answers

Yes all rectangles are similar but not all are equal, (geometry)

yes. All rectangles are similar no matter how big or small they are (of course, they have to stay as a rectangle)

hope this helps

Solve the equation V=1/3 Bh for B

Answers

v=1/3Bh
multiply both sides by 3over 1
3/1V=bh
because 3/1 and 1/3 cancel out
then divide by h
so your h cancels out and your answer is
(3/1V)/h = B

To solve the equation V = 1/3 Bh for B, multiply both sides by 3 to eliminate the fraction and then divide by h, resulting in B = 3V/h.

The equation given is V = 1/3 Bh, where V represents volume, B is the area of the base of the three-dimensional figure, and h is the height. To solve for B, the area of the base, you need to isolate B on one side of the equation. Follow these steps:

Multiply both sides of the equation by 3 to get rid of the fraction on the right-hand side, resulting in 3V = Bh.Next, to solve for B, divide both sides of the equation by h, which gives you B = 3V/h.

Therefore, the formula B = 3V/h is used to calculate the base area B given the volume V and height h of the figure.

Choose the equation below that represents the line passing through the point (−3, −1) with a slope of 4. (1 point) y = 4x − 11 y = 4x + 11 y = 4x + 7 y = 4x – 7 y − 3 = 4(x + 1) y + 3 = 4(x − 1)

Answers

To find the answer, we can use the equation y-y1=a(x-x1), since we already have a point that the line passes through and we know the slope of the line. So, we can plug in our known values into the equation, making it y+1=4(x+3) since the double negatives end up making our values positive. Then, we can continue solving it by distributing the 4, which makes our equation y+1=4x+12. Then, we can subtract 1 from both sides, making the answer y=4x+11.

Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?

7.98 × 45.67 = 3,644.466
12.3 × 3.8 = 467.4
0.45 × 2.3 = 1.035
14.22 × 2.8 = 398.16

Answers

B??????????????????????????????????????

Answer:

Option 3 - [tex]0.45\times2.3= 1.035[/tex]

Step-by-step explanation:

To find : Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?

Solution :

The correct placement of decimal in product is based on the number of digits after decimals as the number of digits after decimal of one number added to number of digits after decimal of second number is the required place in the result a decimal place.

1) [tex]7.98\times 45.67 = 3,644.466[/tex]

Not correct, decimals are 4 so place after 4 numbers.

2) [tex]12.3\times3.8= 467.4[/tex]

Not correct, decimals are 2 so place after 2 numbers.

3) [tex]0.45\times2.3= 1.035[/tex]

Correct, decimals are 3 so place after 3 numbers.

4) [tex]14.22\times2.8= 398.16[/tex]

Not correct, decimals are 3 so place after 3 numbers.

Therefore, option 3 is correct.

What is 120.571 in expanded form?

Answers

Hi there,

100 +20 +0 + 0.5+ 0.07+ 0.001

Hope this helps :)

Use the equation v=10/p to determine the pressure when the volume is 12 liters

Answers

v = 10/p
12 = 10/p
10/12 = 5/6 or 0.83 (3 repeating)
so p = 5/6 or 0.83 (3 repeating)

Sent a pic of the solution (s).

Where does the graph of the linear equation, y = 1/2 x - 3, cross the y-axis?

Answers

negative 2 is where it crosses

You solve the equation by choosing x=0, as x will always be zero, when a line crosses the y-axis
y = 0,5x-3 = 0,5*0-3= -3

Megan Mei is charged 2 points on a $120,000 loan at the time of closing. The original price of the home before the down payment was $140,000. How much do the points in dollars cost Megan? A. $4,200 B. $2,800 C. $8,200 D. $2,400

Answers

1 point = 1% of the loan.
The loan is $120,000.
Therefore 2 points cost 0.02*$120,000 = $2,400

Answer: D. $2,400

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Amount of original price of the home before the down payment = $140000

Amount of loan at the time of closing = $120000

Megan Mei is charged 2 points on that amount means

[tex]2\%\ on\ \$120000\\\\=\frac{2}{100}\times 120000\\\\=0.02\times 120000\\\\=\$2400[/tex]

Hence, Option 'A' is correct.

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