a snowbank that is 6 inches deep is melting at the rate of 0.5 in per hour . what’s a linear function to model the scenario and identify the domain and range of the function

Answer:

80 ft

Step-by-step explanation:

Answer:

A. 80 ft.

Step-by-step explanation:

Triangle ABC is similar to Triangle DFG so they are proportional. 20/4=5; 25/5=5; so 7*5=35.

20+25+35=80

Answer:

Eli has saved $10

Step-by-step explanation:

Let us use the first letters of their names to represent them.

A for Angela and E for ELi

So, from the first statement, we can write out an equation: E = [tex]\frac{1}{3}[/tex]A + 8, that is, one-third of Angela's savings + $8 will give us Eli's savings

From the second statement, we can write out: E + 10 = (A + 10) + 4 which means that if $10 is added to both their savings, Eli will still have $4 more than Angela.

So, we can solve both equations;

Equation 1: E = [tex]\frac{1}{3}[/tex]A + 8

Equation 2: E + 10 = (A + 10) + 4; which can be rewritten as E + 10 = A + 14

and then E = A + 4

The two equations (in bold), can then be solved simultaneously.

Let us carry out this operation to eliminate the E: Subtract equation 1 from equation 2, so that;

A + 4 - ( [tex]\frac{1}{3}[/tex]A + 8) = E - E

[tex]\frac{2}{3}[/tex]A - 4 = 0

[tex]\frac{2}{3}[/tex]A = 4

A = 4 × [tex]\frac{3}{2}[/tex] = 6

So, if A is 6, and E = A + 4 (from equation 2, that means that E = 6 + 4 = 10

So, Eli has saved $10, while Angela has saved $6.

If we check what was said in the question about their savings, which is what we have represented using the equations, the answers can be confirmed.

Answer:

Eli has saved $10

Step-by-step explanation:

 Let us denote Angela's saving by "x".

  If Eli's saving is $8 more than one-third of Angela's saving, then Eli's saving   is:

 [(1/3 × x) + 8 = x/3 + 8]

 We will make x/3 + 8 to have a common denominator:

 x/3 + 8 = (x+24)/3

 If Eli and Angela each saved $10 more, then their respective savings would have been:

(x+24)/3  +  10 for Eli

x+10 for Angela.

At this savings, Eli would have been $4 richer than Angela.

i.e   [((x + 24)/3) + 10] -  (x+10) = $4

 We will make [(x+24)/3] + 10 to have common denominator.

(x + 24 + 30)/3

= (x + 54)/3

 Then:

  [(x+54)/3]  -  [(x+10)/1] = 4

   [x+54-(3x+30)]/3 = 4/1

    (-2x + 24)/3 = 4

    cross multiply

  -2x + 24 = 12

    -2x = -12

       x = -12/-2

       x = 6

  Since Eli's saving = x/3 + 8

Then his actual saving

  = 6/3 + 8

  = 2 + 8

  = $10

Answer:

[tex]I=7000C[/tex]

Step-by-step explanation:

Let C represent number of dairy cows.  

We have been given that each dairy cow produces 3500 gallons of milk per year. So amount of milk produced by C cows in 1 year would be [tex]3500C[/tex] gallons.

We are also told that the dairy sells milk for 2.00 per gallon. So yearly income I, in dollars for the dairy milk production would be 2.00 times the yearly milk production.

Since yearly milk production from C cows is [tex]3500C[/tex], so Income would be:

[tex]I=2.00(3500C)[/tex]

[tex]I=7000C[/tex]

Therefore, the formula [tex]I=7000C[/tex] represents yearly income (I) as a linear function of C.

Answer:              

2322

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Answer:

x=115 y=65

Step-by-step explanation:

You get 115 for X because angle x is vertical to 115 degrees.

You get 65 because y is supplementary to x, and 180-65=115.

Answer:

x = 115 degree and y = 65 degree

Step-by-step explanation:

Here we can see

x = 115 ( being vertically opposite angles )

So Now

x + y = 180 ( being linear pair )

115 + y = 180

y = 180 - 115

Therefore  y = 65

Hope this helps

Answer:

8.2, 105.00

Step-by-step explanation:

Take the first measures and add the enlargements to get the dimensions of the third quilt. This probably is wrong I just had to answer a question

The probability of drawing at least one face card when drawing two cards with replacement from a standard deck is approximately 0.407.

The student is asking for the probability of drawing at least one face card (Jack, Queen, or King) when drawing two cards with replacement from a standard deck of 52 cards. To find this, we can use the complement rule: subtract the probability of not drawing a face card in both draws from 1. There are 12 face cards in a deck of 52 cards, so the probability of drawing a non-face card (event N) on one draw is 40/52 (since there are 40 non-face cards).

Using the complement rule:

Now perform the calculations:

P(NN) = (40/52) * (40/52) = 0.5929 (approximately).

P(at least one F) = 1 - 0.5929 = 0.4071 (rounded to three decimal places).

Therefore, the probability of drawing at least one face card in two draws with replacement is approximately 0.407.

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: ( 8 , − 3 ) Equation Form: x = 8 , y = − 3

Follow me on instagram at officialholydrip

Answer:

try 45

Step-by-step explanation:

The water level rises at a rate of approximately 2.83 cm per minute. Therefore, the water level would be approximately 34 cm after 12 minutes.

This problem involves the concept of linear relationships and slopes in mathematics. Given that the water level rises by 17 cm every 6 minutes, we can find the rate of increase per minute by dividing 17 cm by 6 minutes. This value, approximately 2.83 cm/minute, is the slope of the linear relationship.

This means each additional minute increases the water level by about 2.83 cm. If we denote the time as x and the water level as y, the linear equation expressing this relationship can be written as y = 2.83x.

To find the value of y when x (time) is 12 minutes, we substitute x = 12 into this equation. So, y = 2.83 * 12 = 33.96 cm. Therefore, the water level would be close to 34 cm after 12 minutes.

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The question is incomplete! Complete question along with answer and explanation is provided below.  

Question:  

Francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. He has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. Explain the error in his solution.

The Probability is (2/12)(4/12) = 8/144

Answer:

P = (2/12)(4/11) = 2/33

Step-by-step explanation:

There are total 3 + 2 + 4 + 3 = 12 marbles

The probability of drawing a yellow marble is given by

P(yellow) = number of yellow marbles/total number of marbles

There are 2 yellow marbles and total 12 marbles

P(yellow) = 2/12

Then Francisco draws a red marble without replacing the first one so that means there are total 11 marbles left.

P(red) = number of red marbles/total number of marbles

There are 4 red marbles and total 11 marbles

P(red) = 4/11

Therefore, the overall probability is

P = (2/12)(4/11) = 2/33

Francisco made the error of calculating the probability with replacement whereas, in reality he did not replaced the marble after drawing the yellow marble, so he should have used total 11 marbles for the calculation of drawing red marble,

Final answer:

The approximate square root of 48 is found by locating it between the perfect squares of 36 (6²) and 49 (7²), leading to a closer estimation of about 6.9 when considering 48 as 16 * 3 and simplifying.

Explanation:

The question asks to find the approximate square root of 48. To do this, we first recognize that the exact square root of 48 is not a whole number, and therefore, we need to find two perfect squares between which 48 lies. The perfect squares closest to 48 are 49 (7²) and 36 (6²). Since 48 is closer to 49, we can estimate that the square root of 48 is slightly less than 7. A more refined method involves thinking of 48 as 16 * 3, which then gives us √16 * √3 = 4√3. Knowing that √3 is approximately 1.732, we can multiply this by 4 to get an approximation of 6.928. Therefore, a good approximation for the square root of 48 is approximately 6.9.

Answer:

  29.7°

Step-by-step explanation:

In a right triangle representing the geometry of the problem, the side opposite the angle is the height of your observation (400 ft). The side adjacent to the angle is the distance from shore (700 ft).

You know the tangent ratio is ...

  Tan = Opposite/Adjacent

so your angle of depression satisfies ...

  tan(angle of depression) = (400 ft)/(700 ft)

Using the inverse function, we find ...

  angle of depression = arctan(4/7) ≈ 29.745°

The angle of depression is about 29.7°.

Answer:

B) [tex]log_3 81=4[/tex]

Step-by-step explanation:

The definition of logarithm is the following:

The logarithm of a certain number x with respect to a certain base b is the exponent by which b should be raised in order to give x. Mathematically, given the equation

[tex]b^y = x[/tex] (1)

The logarithm of x to base b is defined as

[tex]y=log_b x[/tex] (2)

In this problem, we have the following equation:

[tex]3^4=81[/tex]

By comparing it with equation (1), we notice that:

b = 3

y = 4

x = 81

Therefore, by re-arranging the variables using equation (2), we can rewrite it as:

[tex]4=log_3 81[/tex]

Which corresponds to option B.

Answer:

-12

Step-by-step explanation:

2 - -4 = 6 --> y + 6 = x

x = -6, so subtract 6 from x to find y

-6 - 6 = -12

y = -12

Does that help?

To find y when x = -6, given that y varies directly with x and y = -4 when x = 2, we first calculate the proportionality constant k, and then use it to find the new value of y.

If y varies directly with x, this means that y can be expressed as y = kx, where k is the proportionality constant. Given that y = -4 when x = 2, we can first find the value of k by substituting these values into the direct variation equation:

-4 = k(2)

From this, we can solve for k:

k = -2

Now, to find y when x = -6, we substitute -6 for x in the original direct variation equation y = kx, using our found value of k:

y = (-2)(-6)

y = 12

Therefore, when x = -6, y will be 12.

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(a) Equilibrium point: x = 1

(b) Consumer surplus at equilibrium: 0

(c) Producer surplus at equilibrium: 0

We have,

To find the equilibrium point, we need to set the demand (D(x)) equal to the supply (S(x)):

D(x) = S(x)

Given:

D(x) = (x - 7)^2

S(x) = x^2 + 4x + 31

(a) Equilibrium point:

Setting D(x) equal to S(x):

(x - 7)^2 = x^2 + 4x + 31

Expanding and rearranging the equation:

x^2 - 14x + 49 = x^2 + 4x + 31

Simplifying and rearranging further:

-14x - 4x = 31 - 49

-18x = -18

x = 1

Therefore, the equilibrium point is x = 1.

(b) Consumer surplus at the equilibrium point:

Consumer surplus represents the difference between the price consumers are willing to pay and the price they actually pay.

At the equilibrium point, the price consumers are willing to pay (D(x)) is equal to the price they actually pay (S(x)).

Substituting x = 1 into the demand function D(x):

D(1) = (1 - 7)^2

D(1) = (-6)^2

D(1) = 36

Consumer surplus at the equilibrium point is the difference between what consumers are willing to pay and what they actually pay:

Consumer surplus = D(x) - S(x)

Consumer surplus = 36 - S(1)

Consumer surplus = 36 - (1^2 + 4(1) + 31)

Consumer surplus = 36 - (1 + 4 + 31)

Consumer surplus = 36 - 36

Consumer surplus = 0

Therefore, at the equilibrium point, the consumer surplus is 0.

(c) Producer surplus at the equilibrium point:

Producer surplus represents the difference between the price producers are willing to accept and the price they actually receive.

At the equilibrium point, the price producers are willing to accept (S(x)) is equal to the price they actually receive (D(x)).

Substituting x = 1 into the supply function S(x):

S(1) = 1^2 + 4(1) + 31

S(1) = 1 + 4 + 31

S(1) = 36

Producer surplus at the equilibrium point is the difference between what producers are willing to accept and what they actually receive:

Producer surplus = S(x) - D(x)

Producer surplus = 36 - D(1)

Producer surplus = 36 - (1 - 7)^2

Producer surplus = 36 - (-6)^2

Producer surplus = 36 - 36

Producer surplus = 0

Therefore, at the equilibrium point, the producer surplus is also 0.

Thus,

(a) Equilibrium point: x = 1

(b) Consumer surplus at equilibrium: 0

(c) Producer surplus at equilibrium: 0

Learn mroe about supply and demand here:

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The equilibrium point in the market occurs when the demand and supply are equal, which can be found by solving the given function equations. Consumer surplus and producer surplus at the equilibrium point are computed as the area between the demand/supply curves and the equilibrium price.

The equilibrium point is when the demand and supply are equal, this happens i.e., D(x) = S(x). Therefore, we first equate (x-7)^2 = x^2 + 4x + 31. Solving this equation gives us the equilibrium quantity, x.
The consumer surplus is the area between the demand curve and the consumer's actual payment, i.e., the area under D(x) above the equilibrium price. This equals to the integral from 0 to x of D(x) minus the equilibrium price. The producer surplus is the area between the supply curve and the consumer's payment, i.e., the area under S(x) below the equilibrium price. This equals to the integral from 0 to x of the equilibrium price minus S(x).

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Answer:

2/3

Step-by-step explanation:

Answer: 2/3

Step-by-Step:

divide 10 by 5 = 2, then divide 15 by 5 =3, so 2/3

Answer:1/2m>50

Step-by-step explanation:Put a line under the sign.

Answer:

Rational,   0.424242... =  42/99

Step-by-step explanation:

let x = 0.4242424242....

We can convert this to a fraction

100x = 42.424242....

100x - x = 42

99x = 42

x = 42/99  a rational number

Answer: 0.424242424242 is a rational number

Step-by-step explanation:

Answer: 6 in ^2

Step-by-step explanation:

The shapes are congruent, so all the given values have to apply to both shapes. Keeping this in mind, the only answer that works is 6in^2.

The angle that must also measure 130° is angle 4.

Angle 4 must also measure 130°. When two lines intersect, the vertically opposite angles are congruent, meaning angle 1 and angle 4 are equal. Therefore, if angle 1 measures 130°, angle 4 must also measure 130°.

If angle 1 measures 130°, angle 3 must also measure 130°.

When two lines intersect, they form pairs of angles known as vertical angles or vertically opposite angles. These angles are congruent, meaning they have the same measure. The key property of vertical angles is that they are formed by opposite rays.

In the given scenario:

Angle 1 and angle 3 are vertically opposite angles because they are formed by the intersecting lines and share the same vertex.

Since angle 1 measures 130°, according to the properties of vertical angles, angle 3 must have the same measure.

This is a fundamental property of vertical angles: they are always congruent. Therefore, if angle 1 measures 130°, angle 3 must also measure 130°.

For complete question refer to image:

Answer:

The translation rule is (x , y) → (x - 12 , y - 4)

Step-by-step explanation:

Let us revise the translation of a point

An object is translated from A (-6, -4) to A' (-18, -8)

∵ A is (-6 , -4)

∵ A' is (-18 , -8)

∴ x-coordinate = -6

∴ x'-coordinate = -18

- By using the translation rule above

∵ x' = x + h

∴ -18 = -6 + h

- Add 6 to both sides

∴ -12 = h

∴ h = -12

∵ h is a negative value

- That means A translated to the left 12 units

∴ The rule is (x , y) → (x - 12 , y)

∵ y-coordinate = -4

∴ y'-coordinate = -8

∵ y' = y + k

∴ -8 = -4 + k

- Add 4 to both sides

∴ -4 = k

∴ k = -4

∵ k is a negative value

- That means A down 4 units

∴ The rule is (x , y) → (x , y - 4)

The translation rule is (x , y) → (x - 12 , y - 4)

The midpoint of the segment with endpoints (-1, 5) and (-6, -2) is calculated using the midpoint formula and is (-3.5, 1.5).

The question seems to be asking for the midpoint of a segment with given endpoints. However, the numbers provided (-1, 5, -6, -2) do not clearly define a specific segment in a conventional two-dimensional coordinate system. Typically, a line segment in two-dimensional space is represented by the coordinates of its endpoints, such as (x₁, y₁) and (x₂, y₂).

If we assume the numbers are pairs of coordinates, we could interpret them as the endpoints (-1, 5) and (-6, -2). To find the midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂), you use the midpoint formula: Midpoint M = [tex](\frac{x_1 + x_2}{ 2}, \frac{y_1 + y_2}{2})[/tex]

Applying this to the given points: M = [tex](\frac{-1 + (-6)}{ 2}, \frac{5 + (-2)}{ 2} = (\frac{-7}{ 2}, \frac{3 }{ 2})[/tex] = (-3.5, 1.5).

The midpoint of the segment with endpoints (-1, 5) and (-6, -2) is (-3.5, 1.5).

Answer:

18

Step-by-step explanation:

Normally, when you multiply two numbers, their product equal to the product of their greatest common factor and their least common multiple

Let the number be y

The product of 12 and y is 12 y

Also, the product of their greatest common factor and their least common multiple is 6*36=216

Now

12y=216

Divide both sides by 12 to obtain y as

Y=216/12=18

Therefore, the other number is 18.

To prove

Factors of

12=2*2*3

18=2*3*3

Common factors for both are 2*3=6 equal to given GCD

The multiplies are 2*2*3*3=36

Answer:

For a quadratic function in standard form, y=ax2+bx+c

the axis of symmetry is a vertical line x=−b2a .

Step-by-step explanation:

Hope this helps !

Answer:

(6) 1200 square feet

(7) 49 months

Step-by-step explanation:

Let the area of the living room be x square feet. Since the material cost is fixed as $2840 and cost ler square feet provided as $1.9 while and the total cost is given as $5120 then the the problem can be represented as

1.9x+$2840=$5120

Putting like terms together then

1.9x=$5120-$2840=$2280

Making x the subject of the above, by dividing both sides by 1.9 then

X=2280/1.9=1200 square feet.

Therefore, area is 1200 square feet.

(7)

Let the number of months when cost are similar be y.

For satelite option, since fixed cost of $298.9 is charged then monthly rate is $68.7 it means after y months, the expenditure for this plan will be 68.7y+$298.9

For cable option, since it only charges monthly fee of $74.80 then after y months, the expenditure amounts to 74.80y

Since after y months the expenses are same, then we equate both options to be equal. Therefore,

74.80y=68.70y+298.90

Putting like terms together then

74.80y-68.70y=298.90

6.1y=298.90

Dividing both sides by 6.1 to make y the subject then

Y=298.9/6.1=49 months

Answer: the speed of the plane in still air is 101.2 mph

Step-by-step explanation:

Let x represent the speed of the plane in still air.

The pilot flew his​ single-engine airplane 60 miles with the wind from City A to above City B. If the wind was a constant 30 miles per​ hour, it means that the total speed at which he flew the plane while going is (x + 30) mph.

Time = distance/speed

Time spent while going is

60/(x + 30)

He then turned around and flew back to City A against the wind. it means that the total speed at which he flew the plane while returning is (x - 30) mph.

Time spent while returning is

60/(x - 30)

If the total time going and returning was 1.31.3 ​hours, it means that

60/(x + 30) + 60/(x - 30) = 1.3

Cross multiplying, it becomes

60(x - 30) + 60(x + 30) = 1.3(x - 30)(x + 30)

60x - 1800 + 60x + 1800 = 1.3(x² + 30x - 30x - 900)

120x = 1.3x² - 1170

1.3x² - 120x - 1170 = 0

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 1.3

b = - 120

c = - 1170

Therefore,

x = [- - 120 ± √(- 120² - 4 × 1.3 × - 1170)]/2 × 1.3

x = [120 ± √(14400 + 6080)]/2.6

x = [120 ± √20480]/2.6

x = (120 + 143.1)/2.6 or x = (120 - 143.1)/2.6

x = 101.2 or x = - 8.9

Since the speed cannot be negative, then x = 101.2 mph

Answer: The area of the square is increasing at a rate of 90.4 m2/min (square meters/minute)

Step-by-step explanation: Please see the attachments below

Answer:

The area of the square is increasing at 90.51m^2/min

Step by step explanation:

Given;

Change in diagonal length ∆d = 8m/min

Length l = 8m

When l = 8m

d^2 = 2l^2 = 2×8^2 = 128

d = √128

Area of a square = l^2 = (d^2)/2

d = diagonal

Change in area = ∆A = dA/dd

∆A = 2 × d/2 × ∆d = d×∆d

∆A = √128 × 8 = 90.51m^2/min

Answer:

P(A∪B) = 0.92

Step-by-step explanation:

Let's call A the event that the sandwich was made with raspberry Jelly and B the event that the sandwich was made with creamy peanut butter.

So, the probability P(A∪B) that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is calculated as:

P(A∪B) = P(A) + P(B) - P(A∩B)

Where P(A) is the probability that a sandwich was made with raspberry jelly, P(B) is the probability that it was made with creamy peanut butter and P(A∩B) is the probability that it was made with raspberry jelly and creamy peanut butter.

So, replacing P(A) by 0.84, P(B) by 0.27 and P(A∩B) by 0.19, we get that P(A∪B) is equal to:

P(A∪B) = 0.84 + 0.27 - 0.19

P(A∪B) = 0.92

The probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is 0.92, or 92%, computed using the formula for the probability of A or B happening in probability theory.

In probability, when we want to find the probability of event A or event B happening, we use the formula P(A U B) = P(A) + P(B) - P(A ∩ B). Here, event A is the event that a sandwich was made with raspberry jelly, and event B is the event that it was made with creamy peanut butter. Given P(A) = 0.84, P(B) = 0.27, and P(A ∩ B) = 0.19, we can substitute these values into the formula.

So, P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.84 + 0.27 - 0.19 = 0.92.

This means that the probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is 0.92, or 92%.

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