You have been asked to construct an aquarium that holds 1000 gallons. It will be a standard rectangular prism with restrictions that the length must be 1 foot longer than the width and the height must be 4.6 feet less than the length. Find the height of the aquarium to the nearest hundredth of an inch.

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

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

Where "m" is the slope and "b" is the y-intercept.

So, having the first equation:

[tex]y=- 6x - 2[/tex]

You can identify that:

[tex]m=-6\\b=-2[/tex]

 By definition, the line intersects the x-axis when [tex]y=0[/tex]. Subsituting this value into the equation and solving for "x", you get that the x-intercept is the following:

[tex]0=- 6x - 2\\\\2=-6x\\\\x=-\frac{1}{3}\\\\x=-0.333[/tex]

Now you can graph the line.

Now you must solve for "y" from the second equation:

[tex]y +2=- 6x\\\\y=-6x-2[/tex]

 You can identify that:

[tex]m=-6\\b=-2[/tex]

Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations  has Infinitely many solutions.

See the graph attached.

Answer:

a

Step-by-step explanation:

Answer:

The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Probability that carbon emissions from the company’s factory exceed the permissible level = 35% = 0.35

Accuracy of the test of emissions level = 85% = 0.85

2. The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is?

These two events, carbon emissions from the company’s factory and the accuracy of the test are independent events, therefore:

Probability that carbon emissions from the factory are within the permissible level = 1 - 0.35 = 0.65

Probability that the test predicts the opposite to be true = 0..35 * 0.85 = 0.2975 (The opposite is that the carbon emissions from the company exceed the permissible level)

Probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is:

0.65 * 0.2975 = 0.193375

The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)

Final answer:

The probability that the emissions are within the permissible level and the test incorrectly predicts the opposite is 0.098 or 9.75% after rounding to the thousandth place.

Explanation:

The probability that carbon emissions from the factory are within the permissible level is the complement of the probability that they exceed the permissible level, which is 100% - 35% = 65% or 0.65. Given that the test has an accuracy of 85%, the probability that the test incorrectly predicts the emissions to be over the permissible level when they are not (a false positive) is 15% or 0.15. Therefore, the probability that emissions are within the permissible level and the test incorrectly predicts the opposite is the product of the two probabilities: 0.65 * 0.15 = 0.0975 or 9.75% when expressed as a percentage. To provide the answer to the thousandth place as required, we express this as 0.098.

Answer: Option 3, and 4

Answer:

The equation of line perpendicular to given line equation and passing through point (4,3) is y = 3 x - 9  .

Step-by-step explanation:

Given as :

The given equation of one line = y = [tex]\dfrac{-1}{3}[/tex]x + 5

∵ Equation of line in slope-intercept form is written as

y = m x + c

where m is the slope of line

And c is the intercept of y

Now, Comparing given line equation with standard slope intercept line equation

∴  m = [tex]\dfrac{-1}{3}[/tex]

Slope of this line = m = [tex]\dfrac{-1}{3}[/tex]

Now, another line is perpendicular to the given line

For perpendicular lines , the products of slope of lines = - 1

Let the slope of another line = M

So, from perpendicular lines condition

m × M = - 1

∴ M = [tex]\dfrac{-1}{m}[/tex]

I.e M = [tex]\frac{-1}{\frac{-1}{3}}[/tex]

So, M = 3

∴ The slope of other line = M = 3 , and the line passing through point (4,3)

Now, Again

The equation of line in slope-intercept form

I.e y = M x + c

Now, satisfying the points on line

So, 3 = 3 × 4 + c

Or, 3 = 12 + c

∴ c = 3 - 12

i.e c = - 9

or, The other line equation = y = 3 x - 9

Hence, The equation of line perpendicular to given line equation and passing through point (4,3) is y = 3 x - 9  . Answer

Answer:

The actual length of car is 48 feet.

Step-by-step explanation:

Given:

Tiffany sketched a picture of a car she used the scale 2 inches : 12 feet.

In her sketch the car is 8 inches long.

Now, to find the length in feet of the actual car.

Let the actual length of car in feet be [tex]x\ feet.[/tex]

And the length of car in her sketch is 8 inches.

So, the ratio of the scale used by Tiffany as given is 2 inches : 12 feet.

Now, to get the actual length of car by using cross multiplication method:

[tex]\frac{2\ inches}{12\ feet} =\frac{8\ inches}{x\ feet}[/tex]

⇒ [tex]\frac{2}{12} =\frac{8}{x}[/tex]

By cross multiplying we get:

⇒ [tex]2x=96[/tex]

Dividing both sides by 2 we get:

⇒ [tex]48=x[/tex]

⇒ [tex]x=48\ feet.[/tex]

Therefore, the actual length of car is 48 feet.

Answer:

x = -0.9

Step-by-step explanation:

You need to isolate x in order to find x so,

-3.4 - x = -2 1/2 or -2.5

-3.4 - x = -2.5

Add 3.4 to -2.5

-3.4 - x = -2.5

+3.4       +3.4

-x = 0.9

x CANNOT be negative so divide -1 to both sides

-x/-1 = 0.9/-1

x = -0.9

Checking answer

-3.4 - (-0.9) = -2.5

-3.4 + 0.9 = -2.5

-2.5 = -2.5

Answer:

[tex]d < 20\ donuts[/tex]

The graph of the solution set in the attached figure

Step-by-step explanation:

 Let

d ----> the possible number of donuts Monica brought

we know that

The number of donuts d multiplied by $0.50 plus the cost of a box of coffee for $5 must be less than $15

so

The inequality that represent this situation is

[tex]0.50d+5 < 15[/tex]

Solve for d

subtract 5 both sides

[tex]0.50d < 15-5[/tex]

[tex]0.50d < 10[/tex]            

Divide by 0.50 both sides

[tex]d < 10/0.50[/tex]      

[tex]d < 20\ donuts[/tex]

The solution is all whole numbers greater than zero and less than 20 ( I say greater than zero because the problem states that Monica brought some donuts)

The solution set is the interval {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}

Answer:

[tex]4\frac{7}{8} * 28 = \frac{39}{8}*28\\= \frac{39*28}{8} \\=\frac{39*7}{2} \\=\frac{273}{2}\\ =136\frac{1}{2} \\[/tex]

Step-by-step explanation:

Answer

given,

352 + 116

we have to break 116 and use it on open number line

breaking of number 116

116 = 100 + 10 + 6

And addition will be shown in the number line attached below

now,

352 + 100 = 452

452 + 10 = 462

462 + 6 = 468

we know

sum of

352 + 116 = 468

Answer:

a = 1 and b = 2

Step-by-step explanation:

Using the Quotient Rule>

d/dx[(sin x)/(2+cos x) ]

=   [(2 + cos x) * cosx -  sin x * - sin x)]  /  (2 + cos x)^2

= 2cos x + cos^2x + sin ^2 x) /  (2 + cos x)^2

But cos^2x + sin^2x = 1 so we have:

(1 +  2 cos x)  /   (2 + cos x)^2

- so a = 1 and b = 2.

The Table represents the graph of a logarithmic function in the form is first table.

A logarithm is defined as the number of powers to which a number must be increased in order to obtain some other numbers. It is the simplest way to express enormous numbers. A logarithm has several key features that demonstrate that logarithm multiplication and division can also be represented in the form of logarithm addition and subtraction.

We have,

y= log (base b) x

Take the value y= -3 and x= 1/8.

So, -3 = log (base b) 1/8

[tex]b^{-3[/tex] = 1/8

[tex]b^{-3[/tex] = 1/2³

[tex]b^{-3[/tex] = [tex]2^{-3[/tex]

On comparing b=2.

Now, if y=1 and x= 2

1= log(base b)2

b= 2

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Answer:

(-6,16), also can be written as x=-6, y=16.

Step-by-step explanation:

By 'sub method' I assume you mean substitution of one solved equation into another. Let's begin by solving x+y=10 for y.

[tex]x+y=10[/tex]

-x on both sides

[tex]y=10-x[/tex]

Now we have an equation that tells us y=10-x. We can now replace 'y' in the other equation with this new definition of y, that being 10-x.

[tex]2x+y=4[/tex]

Substitute 10-x for y

[tex]2x+(10-x)=4[/tex]

When can remove the parentheses as they are unnecessary.

[tex]2x+10-x=4[/tex]

Now we solve for x. We can first simplify, by combining all like terms on each side, those being 2x and -x on the left side. 2x+-x=x.

[tex]x+10=4[/tex]

Now we remove 10 from both sides, to isolate x.

[tex]x=4-10[/tex]

We can again simplify, 4-10=-6

[tex]x=-6[/tex]

Now we have the x coordinate of the point that solves our set of equations. We can plug this number back as an x value of either equation to get the y value for the solution. In this example I will use x+y=10, as it is a simpler equation.

[tex]x+y=10[/tex]

Substitute x for -6.

[tex]-6+y=10[/tex]

Isolate y by adding 6 to both sides, cancelling out the -6 on the left side.

[tex]y=10+6[/tex]

Simplify 10+6=16.

[tex]y=16[/tex]

Now we have an x value, -6, and a y value, 16. These are the x and y values of our solution, therefore the solution is (-6,16).

This is the solution using the sub method. There are other ways to solve this question (although the answer, if done correctly, will always be the same), including plotting both lines on a graph, as shown in the attached image.

Answer:

The correct answer is C. 5⁶

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Number of hens in a bird enclosure = (5³)² * 5⁰

2. What is the total number of hens in the enclosure?

Let's recall a couple of properties of the exponents:

1. When you raise any number to a zero power you'll always get 1, with the exception of zero itself.

x⁰ = 1, x ≠ 0

2. The power of a power property says that to calculate a power of a power you just have to multiply the exponents, this way:

(x⁴)⁵ = x ⁴°⁵ = x²⁰

Now, applying those two properties, we have:

(5³)² * 5⁰ = 5³°² * 1 = 5⁶

The correct answer is C. 5⁶

Answer:

c

Step-by-step explanation:

Answer:

The number of bricks a truck can carry in full load is 308 .

Step-by-step explanation:

Given as :

The weight of each brick = 4 pounds and 14 ounce

The total load a truck can carry = [tex]\dfrac{3}{4}[/tex]  tons

Let The number of bricks truck can carry = n bricks

Now, According to question

∵ 1 ounce = 0.0625 pounds

∴ 14 ounce = 0.0625 × 14 = 0.875 pounds

So, Total weight of each brick = 4 pounds + 0.875 pounds = 4.875 pounds

Again

∵ 1 pound = 0.0005 tons

∴ 4.875 pounds =  0.0005 × 4.875 = 0.0024375 tons

Now, Again

The total load a truck can carry = [tex]\dfrac{3}{4}[/tex] tons = 0.75 tons

And The weight of each brick = 0.0024375 tons

So, The number of bricks = [tex]\dfrac{\textrm total load a truck can carry}{\textrm Total weight of each brick}[/tex]

I.e n = [tex]\dfrac{0.75}{0.0024375}[/tex]

∴ n = 307.69 ≈ 308

So, The number of bricks can truck carry = n = 308

Hence, The number of bricks a truck can carry in full load is 308 . Answer

Answer:

x=-7/9, y=4/3. (-7/9, 4/3).

Step-by-step explanation:

6x+2y=-2

3x-2y=-5

-----------------

9x=-7

x=-7/9

6(-7/9)+2y=-2

-42/9+2y=-2

2y=-2-(-42/9)

2y=-2+42/9

2y=-18/9+42/9

2y=24/9

y=(24/9)/2

y=(24/9)(1/2)

y=24/18

y=4/3

Answer:

y = 2x + 14

Step-by-step explanation:

First, you have to find the slope by using

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

In other words,

[tex] \frac{ - 2 - 6}{ - 8 + 4} [/tex]

The slope is 2.

Then you plug the rest into point-slope form (you can use either of the points, I used the first one)

[tex]y - y1 = m(x - x1)[/tex]

Remember that m is the slope.

[tex]y + 2 = 2(x + 8)[/tex]

Distribute the slope to the parenthesis

[tex]y + 2 = 2x + 16[/tex]

Isolate the y variable

[tex]y = 2x + 14[/tex]

Answer: y=2x+14

Step-by-step explanation:

Yes

Answer: [tex]6y^2i\sqrt{6}[/tex]

Step-by-step explanation:

For this exercise it is important to remember the following property:

[tex]\sqrt[n]{a^n}=a^{({\frac{n}{n})}}=a[/tex]

Then, given the expression:

[tex]\sqrt{-216y^4}[/tex]

You can follow these steps in order to simplify it:

1. Descompose 216 into its prime factors:

[tex]216=2*2*2*3*3*3[/tex]

2. The Product of powers property states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Then:

 [tex]216=2^2*2*3^2*3[/tex]

3. Now you can substitute:

[tex]=\sqrt{-2^2*2*3^2*3*y^4}[/tex]

4. Finally, substituting [tex]\sqrt{-1}=i[/tex] and simplifying, you get:

[tex]=2*3*y^2i\sqrt{2*3}=6y^2i\sqrt{6}[/tex]

Answer:

2d(d³-9d-30)

Step-by-step explanation:

2d⁴ - 6d - 18d² - 54d

= 2d⁴- 18d²-60d

=2d(d³-9d-30)

The gift bag contains 5 ounces of peppermint candies and 11 ounces of chocolate mint.

Step-by-step explanation:

Cost of peppermint candies per ounce = 6 cents

Cost of chocolate mint = 22 cents

Cost of bag = $2.72 = 2.72*100 = 272 cents

Weight of bag = 16 ounce

Let,

x be the ounces of peppermint candies

y be the ounces of chocolate mint

x+y=16     Eqn 1

6x+22y=272    Eqn 2

Multiplying Eqn 1 by 6

[tex]6(x+y=16)\\6x+6y=96\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](6x+22y)-(6x+6y)=272-96\\6x+22y-6x-6y=176\\16y=176[/tex]

Dividing both sides by 16

[tex]\frac{16y}{16}=\frac{176}{16}\\y=11[/tex]

Putting y=11 in Eqn 1

[tex]x+11=16\\x=16-11\\x=5[/tex]

The gift bag contains 5 ounces of peppermint candies and 11 ounces of chocolate mint.

Keywords: linear equation, subtraction

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The measure of m∠J=90°, m∠G=55° and m∠H=35°

Step-by-step explanation:

Inscribed angles subtended by a diameter are right angles. Hence angle GJH =90°

The diameter GH and chord GJ intercepts an arc with a measure of 70°.The measure of an arc of a circle is equal to the measure of the central angle that intercepts the arc. Hence angle GOJ=70°. Radius of circle GO=OJ, which means triangle GOJ is an isosceles triangle thus ∠OJG=∠OGJ =(180° -70°) /2 = 55°. m∠G=55°

m∠H = (180°-(90°+55°) ) = 180° - 145° =35°

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Answer: 5 Kilometers Per Hour

Answer:

1/12 km per minute

Step-by-step explanation:

1 hour=60 minutes

5/60=1/12

Answer:

Therefore, equation of the line that passes through (2,2) and is parellel to the line [tex]y=7x[/tex] is [tex]y=7x-12[/tex]

Step-by-step explanation:

Given:

a line [tex]y=7x[/tex]

To Find:

Equation of line passing through ( 2, 2) and is parellel to the line y=7x

Solution:

[tex]y=7x[/tex]     ...........Given

Comparing with,

[tex]y=mx[/tex]

Where m =slope

We get

[tex]Slope = m = 7[/tex]

We know that parallel lines have Equal slopes.

Therefore the slope of the required line passing through (2 , 2) will also have the slope = m = 7.

Now the equation of line in slope point form given by

[tex](y-y_{1})=m(x-x_{1})[/tex]

Substituting the points and so we will get the required equation of the line,

[tex](y-2)=7(x-2)=7x-14\\\\y=7x-12......Equation\ of\ line[/tex]

Therefore, equation of the line that passes through (2,2) and is parellel to the line [tex]y=7x[/tex] is [tex]y=7x-12[/tex]

Answer:

The equation which has ONLY two solution x = 3 and x = -3 is [tex]P(x)  = x^2 - 9[/tex]

Step-by-step explanation:

Here, the ONLY two rrots of the equation is given as:

x =  3 and x = -3

Now, if x = a is the ZERO of the polynomial, then x  - a  = 0 is the ROOT of the polynomial.

So, here the only roots of the polynomial are : (x-3) and (x+3)

Also, the POLYNOMIAL = PRODUCT OF ALL ROOTS

So, [tex]P(x) = (x-3)(x+3)    = x(x+3) -3(x+3)  = x^2 + 3x - 3x - 9  = x^2 - 9\\\implies P(x)  = x^2 - 9[/tex]

Hence, the equation which has ONLY two solution x = 3 and x = -3 is [tex]P(x)  = x^2 - 9[/tex]

The equation has only two solution x = 3 and x = -3 is [tex]x^2-9[/tex].

We have to determine, the equation which has only two solutions x  = 3 and x = -3.

According to the question,

The two roots of the equation is x = 3 and x = -3,

if x = a is the zero of the polynomial, then x - a  = 0 is the root of the polynomial.

So, here the only roots of the polynomial are : (x-3) and (x+3).

If the [tex]\alpha[/tex] and [tex]\beta[/tex] are the roots of the equation the product of roots can be written as,

[tex]Product \ of \ roots = \alpha \times \beta[/tex]

Substitute the values in the equation,

[tex]= (x-3 ) (x+3)\\\\= x (x+3) - 3(x+3)\\\\= x^2 + 3x -3x -9\\\\= x^2 - 9[/tex]

Hence, The required equation has only two solution x = 3 and x = -3 is [tex]x^2-9[/tex].

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Answer:

circumference of a circle = 2πr

                                            = 2×22/7×7

                                            = 44/7×7

                                            = 308/7

                                            = 44 inches

Answer: 36 cm

Step-by-step explanation:

Given : The square has a perimeter =160 cm.

Perimeter of square = 4 (side)

Therefore , the side of square = (Perimeter)÷ 4

= 160 ÷ 4 = 40 cm

The new length of side after dilation = (Scale factor) x (Length of original figure)

For scale factor = 0.9

The new length of each side of the dilated square = (0.9)x(40)=36 cm

Hence, the new length of each side of the dilated square=  36 cm

Answer:

36cm

Step-by-step explanation:

Given: The square has a perimeter of [tex]160\text{cm}[/tex] ,the square is dilated with a scale factor of [tex]0.9[/tex].

To Find: length of each side of the dilated square.

Solution:

Perimeter of square  [tex]=160\text{cm}[/tex]

length of each side of perimeter  [tex]=\frac{\text{perimeter of square}}{4}[/tex]

                                                       [tex]=40\text{cm}[/tex]

Now,

the square is dilated by scale factor  [tex]0.9[/tex]

new perimeter of square   [tex]=\text{old perimeter}\times\text{scale factor}[/tex]

                                           [tex]=160\times0.9[/tex]

                                           [tex]=144\text{cm}[/tex]

new length of each side of square [tex]=\frac{\text{perimeter}}{4}[/tex]

                                                         [tex]=\frac{144}{4}[/tex]

                                                         [tex]=36\text{cm}[/tex]

Hence the length of each side of dilated square is [tex]36\text{cm}[/tex]

Answer:

Step-by-step explanation:

5p + 2(p + 4) .......because pencil cases (p) sell for 5 bucks a piece....and mechanical pencils (p + 4), sell for 2 bucks a piece. She is basically selling 4 more mechanical pencils then she is pencil cases.

Answer:

[tex]\mathbb{R}-\{0\}[/tex]

[tex](-\infty,0)\ U\ (0,+\infty)[/tex]

Step-by-step explanation:

The domain of a Function

Given a real function f(x), the domain of f is made of all the values x can take, such that f exists. The function given in the question is

[tex]\displaystyle f(x)=-\frac{1}{x^2}-4[/tex]

Finding the domain of a function is not possible by giving x every possible value and check if f exists in all of them. It's better to find the values where f does NOT exist and exclude those values from the real numbers.

Since f is a rational function, we know the denominator cannot be 0 because the division by 0 is not defined, so we use the denominator to find the values of x to exclude from the domain.

We set

[tex]x^2=0[/tex]

Or equivalently

x=0

The domain of f can be written as

[tex]\mathbb{R}-\{0\}[/tex]

Or also

[tex](-\infty,0)\ U\ (0,+\infty)[/tex]

Answer:

I'm guessing none because the discrimant (sqrt of b squared - 4ac is less than zero, signifying it has no real roots

Step-by-step explanation:

have a happy holidays!

Final answer:

Without knowing the individual prices of small and large candles, we cannot solve for the exact numbers of each type sold. A system of equations would normally be used, but in this case, essential price information is missing.

Explanation:

You sell small and large candles at a craft fair and collect $144 selling a total of 28 candles. To solve how many of each type of candle you sold, let's set up a system of equations with two variables. Let x represent the number of small candles and y represent the number of large candles.

The first equation comes from the total number of candles:

x + y = 28

The second equation involves the total amount of money collected:

ax + by = 144

where a and b are the prices of small and large candles respectively.

Unfortunately, the question does not provide the individual prices of the small and large candles, so we cannot continue without that information. To solve this system correctly, you would need to know the price of at least one type of candle.

With the missing price information, we cannot define a and b and therefore cannot provide a numerical solution to this question.

Answer:

D. $23

Step-by-step explanation:

To find the answer, find how much a can costs at that rate and multiply it by 10.

This would be

10 × 6. 90/3=69. 0/3

=23

If you don't understand anything, ask.