NAME
DATE
PERIC
Lesson 3: More about Constant of Proportionality
Cool Down: Fish Tank
Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table
as you answer the questions.
1.
How many gallons of water will be in the fish tank after 3 minutes? Explain your
reasoning.
2.
How long will it take to fill the tank with 40 gallons of water? Explain your reasoning
3. What is the constant of proportionality?

Answer:

A

Step-by-step explanation:

Point A

:] its ok we all dum sometimes lol

(a) On scaling up by a factor of 2 , the equivalent fraction is 18/30.

(b) On scaling up by a factor of 3 , the equivalent fraction is 27/45.

(c) On scaling down by a factor of 3 , the equivalent fraction is 3/5 .

In the question ,

a fraction 9/15 is given ,

Part(a)

to scale up the fraction by a factor of 2 , we multiply the numerator and denominator by 2 .

On multiplying , we get

9/15 = (9*2)/(15*2) = 18/30 .

Part(c)

to scale up the fraction by a factor of 3 , we multiply the numerator and denominator by 3 .

On multiplying , we get

9/15 = (9*3)/(15*3) = 27/45 .

Part(c)

to scale down the fraction by a factor of 3 , we divide the denominator and numerator by 3 .

On dividing , we get

9/15 = (9/3)/(15/3) = 3/5 .

Therefore , (a) On scaling up by a factor of 2 , the equivalent fraction is 18/30.

(b) On scaling up by a factor of 3 , the equivalent fraction is 27/45.

(c) On scaling down by a factor of 3 , the equivalent fraction is 3/5 .

The given question is incomplete , the complete question is

Write three fractions equivalent to 9/15 .

Scale the numerator and denominator up for the first two and down for the third.

(a) Scale up by: __ Equivalent fraction: __

(b) Scale up by: __ Equivalent fraction: __

(c) Scale down by: __ Equivalent fraction: __

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When the given numbers are ordered from least to greatest, the result would be 8/25, 1, 5/4, 1.3

To be able to order the numbers, it would be best to convert them to the same form. In order words, all the numbers should either be decimals or fractions.

Decimals are easier to compare so convert them to decimals:

= 8 / 25                                                    = 5 / 4

= 0.32                                                      = 1.25

The numbers are:
1, 0.32, 1.3, 1.25

The order from least to greatest is:

0.32, 1, 1.25, 1.3

or:

8/25, 1, 5/4, 1.3

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EXPLANATION

Given the equation 8x -4y

When x=2 and y=3 the resulting expression would be as follows:

8*2 -4*3=

=16 - 12

= 4

The answer is 4

[tex]18x \geqslant 566 - 371 \\ 18x \geqslant 195 \\ \frac{18x}{18} \geqslant \frac{195}{18} \\ x \geqslant 10.8333333333[/tex]

YOU CAN EVEN WRITE IT IN THE FRACTION FORM .

BE REMINDED THAT <> CHANGE SIGN WHEN YOU DIVIDE OR MULTIPLY A NEGATIVE NUMBER ONLY.

HOPE THIS HELPS

Answer:

Step-by-step explanation:

18x ≥ 195 if equal to the answer is 10.83(3)

Answer:

7×+12-6×=5(2×+6)=7×-6+12=10×+30=7×-6×-10×=30-12=9×÷9×=18÷9×=×=2

Answer:

see my photo. hope it can help

the total amount is 9000

Answer:

first way: 2 Angles and one side

second way: 2 sides and one angle

Answer:

Step-by-step explanation:

congruent triangles

how to tell if triangles are congruent using SSS, SAS, ASA, and AAS rules

why AAA and SSA do not work as congruence shortcuts

the Hypotenuse Leg Rule for right triangles

how to use CPCTC (corresponding parts of congruent triangles are congruent)

The 99% confidence interval for the population proportion p is 0.833< p < 0.863.

Given that,

x = 3059

n = 3604

Point estimate = sample proportion = x / n =3059/3604=0.848

[tex]1 - \hat p[/tex]  = [tex]1-0.848 =0.152[/tex]

At 99% confidence level the z is ,

[tex]\alpha[/tex] = 1 - 99% = 1 - 0.99 = 0.01

[tex]\alpha[/tex]/ 2 = 0.01 / 2 = 0.005

[tex]Z\alpha[/tex]/2 = [tex]Z*0.005[/tex] = 2.576  (  Using z table   )

Margin of error = E = [tex]Z\alpha / 2 * (\sqrt(((\hat p * (1 - \hat p)) / n)[/tex]

                              = [tex]2.576* (\sqrt((0.848*0.152) /3604 )[/tex]

                               =0.015

A 99% confidence interval for population proportion p is ,

[tex]\hat p - E < p < \hat p + E[/tex]

0.848-0.015< p <0.848+ 0.015

0.833< p < 0.863

Hence, the 99% confidence interval for the population proportion p is 0.833< p < 0.863.

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Answer:

The probability that you draw two balls that are both black is [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

To find probability, take the number of desirable outcomes over the total number of possible outcomes.

In this case, the black balls are desirable. There are four of them.

this means the numerator of the first fraction is 4. The denominator is the total possible outcomes or in this case the total number of black and white balls. This number is 9. The first probability fraction is [tex]\frac{4}{9}[/tex]

Lets say that the first one was black. Now we need to find the probability of drawing another one. Now there are black balls left in the bag. This means that the number of desirable outcomes is 3. There are also 8 balls total. This means the number of total possible outcomes is 8. The second probability is [tex]\frac{3}{8}[/tex]

To get the total probability you multiply both of the individual probabilities together.

[tex]\frac{4}{9} *\frac{3}{8} =\frac{1}{6}[/tex]

A possible solution of the system of inequalities is 5 dimes and, 8 nickels

From the question, the given parameters are:

Number of coins = Not less than 12

Worth = At most $0.95

Represent dime with x and nickels with y

So, we have the following inequalities

x + y >= 12

0.1x +0.05y <= 0.95

Next, we plot the graph of the inequalities (see attachment)

From the graph, we have a possible solution to be (5, 8)

This is so because this point is in the shaded region

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Answer:

y-y1=m(x-x1)

y+1=-2(x-7)

y+1=-2x+14

-1           -1

y=-2x+13

Step-by-step explanation:

Answer:

42

81

91

Step-by-step explanation:

m = mystery

f = fantasy

[tex]\frac{m}{f}[/tex] = [tex]\frac{m}{f}[/tex]

Compare the ratio with the actual numbers.  Solve for the missing number

[tex]\frac{7}{9}[/tex] = [tex]\frac{m}{54}[/tex]  you need to multiply 9 by 6 to get 54 so multiply 7 x 6 to get 42.

[tex]\frac{7}{9}[/tex] = [tex]\frac{63}{f}[/tex]  Multiply 7 x 9 to get 63,so multiply 9 by 9 to get 81.

[tex]\frac{7}{9}[/tex] = [tex]\frac{m}{117}[/tex]  9 x 13 is 117, so multiply 7 by 13 to get 91.

The new expression by using distributive property is: 209.25

What is distributive property?

In mathematics, the distributive property tell the solution method for the expression who are in the form of a(b + c). In this, first add the expression which are in the parenthesis and later multiply it.

According to the question, the given expression is as follows:

70[2.50+(−0.60)]+25[3.75+(−0.70)]

Using distributive property, whose list contains parenthesis, exponents, multiplication/division, addition/subtraction. This is the list in which the given expression need to simplify.

First parenthesis calculation,

2.5 + - 0.6 = 1.9 and 3.75 + - 0.7 = 3.05

Now, substitute the values:

70(1.9) + 25(3.05)

Multiply it: 133 + 76.25;

Add it: 209.25

Hence, the new expression by using distributive property is: 209.25

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The domain of the function is 1 ≤ x < 2.

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates).

We have f : [tex]\frac{1}{\sqrt{x-1} } + \frac{1}{\sqrt{2-x} }[/tex]

[tex]\sqrt{x-1}[/tex] ≥ 0

x- 1 ≥ 0

x ≥ 1

Similarly , [tex]\sqrt{2-x}[/tex] > 0

2 - x > 0

2 > x

So our domain is 1 ≤ x < 2.

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The summer camp registration decreased in 2021 by 5.26 percent.

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Answer:  square root of 104

Step-by-step explanation:

The length of the missing side in the right triangle is approximately √104.

Given is a right triangle with one leg labeled 11 and hypotenuse labeled 15.

We need to find length of the missing side.

To determine the length of the missing side in the right triangle, we can use the Pythagorean theorem.

It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the missing side as "x".

According to the given information:

One leg (one of the shorter sides) is labeled as 11.

The hypotenuse (the longest side) is labeled as 15.

Using the Pythagorean theorem, we can set up the equation:

11² + x² = 15²

Simplifying this equation:

121 + x² = 225

Subtracting 121 from both sides:

x² = 225 - 121

x² = 104

To find the value of "x," we can take the square root of both sides of the equation:

x = √104

Therefore, the length of the missing side in the right triangle is approximately √104.

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its 0=-5

ur mom lolololololoOLOOLOLLLLO

The slope of the line that passes through the points (10,10) and (5,10) is 0

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1 ( 10,10 )

Point 2 ( 5,10 )

To determine the slope, plug these coordinates into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 10 - 10 )/( 5 - 10 )

Slope m = ( 0 )/( 5 - 10 )

Slope m = ( 0 )/( -5 )

Slope m = 0

Therefore, the slope of the line is 0.

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The value of x is 21 °.

1. The vertically opposing angle pairs are equal.

2. The related angle pairs are equivalent.

3. The alternative outside angle pairs are equivalent.

4. There is equality between the alternate interior angle pairs.

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical. We can see parallel lines examples in our daily life like a zebra crossing, the lines of notebooks, and on railway tracks around us.

Given: ∠ 8 = 86° and ∠ 4= (4x + 2)°

Since ∠4 = ∠8 { Because angles on the same side of the parallel sides are equal }

Thus when we equate these two we get ;

86 = 4x +2

4x = 84

x= 21

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The most appropriate choice for tangent to a curve will be given by- 2x + 25y = 10 is the required equation of tangent.

What is tangent to a curve?
In geometry, a tangent line is a straight line that most closely resembles (or "clings to") a curve at a particular point. It could be thought of as the limiting role of straight lines that pass through the specified point and a nearby curve point as the second point gets closer to the first. If two curves share the same tangent at a given point, they are said to be tangent. Similar definitions apply to the tangent plane to an exterior at a point and two surfaces that are tangent at a point.

Equation of  tangent to a curve at a point [tex](x_1, y_1)[/tex]  is given by

[tex]y-y_1 = \frac{dy}{dx}|_{(x_1, y_1)}(x - x_1)[/tex]

Here,
f(x) = [tex]\frac{2}{x}[/tex]
f'(x) = [tex]\frac{d}{dx} (\frac{2}{x})[/tex]

     = [tex]2(-1)x^{-1-1}\\-2x^{-2}[/tex]

[tex]f'(x)|_{(5, 0)} = -\frac{2}{5^2}[/tex]

               [tex]= -\frac{2}{25}[/tex]

Equation of tangent

[tex]y - 0 = -\frac{2}{25}(x - 5)\\\\25y = -2x +10\\2x + 25y = 10[/tex]

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Answer:

No solution

Step-by-step explanation:

The method that will use is substitution

ill use the equation 5x+2y=10 and substitute into the other one

5x+2y=10

2y=10-5x

y=5-2.5x

Now we must insert this equation into another

5x + 2(5-2.5x) = 20

5x+10-5x = 20

10=20

10 does not equal to 20 so it has no solution

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Answer:

$45.70

Step-by-step explanation:

$9.40 four times and $8.10 1 time so 9.40 x 4 = 37.6 + 8.10 = 45.70

Step-by-step explanation:

...............

............

Linear equations

Apply the multiplicative law of distribution.

Rearrange the unknown terms on the left side of the equation.

Combine as terms

Calculate the sum or difference.

Divide both sides of the equation by the coefficient of the variable.

The answer is x = - 9/4. Because if we do the division, the result is not exact; means that the result is decimal.

Answer:

x = -9/4

Step-by-step explanation:

2(5x+3)=6x-3

10x + 6 = 6x - 3

10x - 6x = -3 - 6

4x = -3 - 6

4x = -9

The answer is x = -9/4

A construction company takes 1/8 hours to remove 1/4 metric tons of dirt from a construction site 2 metric tons in an hour.

Ton is the name of a number of different measurement units. It has a lengthy history and a variety of meanings and applications.

It mostly discusses weight units. Due to the ambiguous nature of what ton might mean.

2,240 pounds, or the long ton, the tonne, also known as a metric ton, which is 1,000 kilograms, and the short ton, which is 2,000 pounds.

Its original use as a volume measurement has persisted in terminology like the freight ton and several other units, with capacities ranging from 35 to 100 cubic feet (0.99 to 2.83 [tex]m^{3}[/tex]). The ton has recently been used for specialized purposes such as energy measurement and vehicle classification. It can also be used as a measure of energy or as a power unit in refrigeration; this is commonly referred to as a ton of refrigeration.

Due to the fact that the ton (of any system of measuring weight) is typically the heaviest unit specified in informal speech, its word also has figurative usage, singular and plural, figuratively signifying a big amount or quantity, or to a great degree, as in "We have a ton of homework, there are a ton of bees in this hive, and I really, really adore you."

The best way to do this is to convert all fractions to decimals. Problem starts out looking like this.

Formula

Rate = Tons removed / hours

Tons Removed = 1/4 metric ton

Time taken = 1/8 hour

rate = [tex]\frac{\frac{1}{4} }{\frac{1}{8} }[/tex]

Rather than doing it with the fractions, it is much easier to do it with decimals

1/4 = 0.25

1/8 = 0.125

Now what we get is rate = 0.25 / 0.125 = 2

So, now 2 metric tons can be removed in an hour

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Answer:

[tex]\boxed{\sf{-15y^6}}[/tex]

Step-by-step explanation:

To solve this, you have to use a distributive property to multiply the numbers from left to right.

Distributive property:

A(B+C)=AB+AC

A(B-C)=AB-AC

[tex]\sf{3y^2\left(-5y^4\right)=-3y^2* 5y^4}[/tex]

Multiply.

-3*5=-15

-15y²y⁴

[tex]\sf{y^2y^4=y^2^+^4=y^6}[/tex]

=-15y⁶

Therefore, the final answer is -15y⁶.

I hope this helps, let me know if you have any questions.

The meand and variance are 13.75 cm and 17.52 respectively.

Each possible outcome is equally likely when there is a uniform probability.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

M = ( a + b ) / 2

The variance of the uniform distribution is given by:

V = ( b - a )² / 12

Uniform distribution on the interval ( 6.5, 21 )

Therefore, a = 6.5 and b = 21

Hence, the mean will be:

M = ( 6.5 + 21 )/ 2

M = 27.5 / 2

M = 13.75

The mean of depth is 13.75 cm.

The variance will be:

V = ( b - a )² / 12

V = ( 21 - 6.5 )² / 12

V = 210.25 / 12

V = 17.52

The variance of depth is of 17.52 cm².

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