The ships kitchen stocks 1 3/5 quarts of ice cream for every 1/4 cake. There are 10 cakes in the kitchen. How many quarts of ice cream are there?


Please explain if you really really know the answer

Answer:

  -15

Step-by-step explanation:

You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].

The average rate of change is defined as ...

  AROC(g) = (g(b) -g(a))/(b -a)

We can evaluate this directly, or we can simplify it a bit first.

 AROC = ((3b² +3) -(3a² +3))/(b -a)

  = (3b² -3a²)/(b -a)

  = 3(b -a)(b +a)/(b -a)

  = 3(b +a)

The AROC on the interval [a, b] = [-9, 4] is then ...

  AROC = 3(4 +(-9)) = 3(-5)

  AROC = -15

__

Additional comment

In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.

Answer:

There is 5% of the juice left.

Step-by-step explanation:

We know that originally, the container had 80 oz of orange juice, this is 100% in our case.

Then we can write a relation:

80 oz = 100%

Now there are 4 ounces left, in the same way as before, we can write this as:

4 oz = X%

We want to find X%

First, let's write our equations:

4 oz = X%

80 oz = 100%

We can take the quotient between these two equations to get:

(4oz/80oz) = (X%/100%)

We need to solve this for X%, then we get:

(4oz/80oz)*100% = X% = 5%

This means that 4 oz is 5% of the initial volume of the juice container.

Then we can conclude that there is 5% of the juice left.

b equal for the top of the bookcase to have the correct area= 5 cm2

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

L × b = 300

b = 300 / L

b = 300 / 60 = 5

Hence, b equal for the top of the bookcase to have the correct area= 5 cm2.

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Answer:

B.  There is no maximum value.

C.  There is no maximum value of z.

Step-by-step explanation:

To solve this linear programming problem using graphical methods, start by graphing the feasible region determined by the given constraints:

We can graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.

Rearrange the first three inequalities to isolate y:

[tex]\boxed{\begin{aligned}2x - 3y & \leq 12\\2x - 12 & \leq 3y \\3y &\geq 2x - 12\\y& \geq \dfrac{2}{3}x-4\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}x + y & \geq 3\\y & \geq -x+3\\ \phantom{w}\\\phantom{\dfrac12}\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}3x + 4y & \geq 24\\4y & \geq -3x + 24\\y & \geq -\dfrac{3}{4}x + 6\\\phantom{w}\end{aligned}}[/tex]

Graph the inequalities.

The feasible region is the region that is shaded by all of the inequalities.

Please see the attached graph.

A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function.

If a feasible region is unbounded, and the coefficients on the objective function are all positive, then an unbounded feasible region will have a minimum but no maximum, since there is no limit on how big it can get.

Therefore, as the feasible region for the given constraints is unbounded, and the coefficients of the objective function z = 3x + 4y are all positive, there is no maximum value.

The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description  are;

Alternate Interior Angles; 2. ∠4 and ∠8

Consecutive Exterior  Angles; 5. ∠1 and ∠6

Alternate Exterior Angles; 3. ∠1 and ∠5

Transversal; line l

Consecutive Interior Angles; 4. ∠3 and ∠4

Corresponding Angles; 1. ∠1 and ∠7

A transversal is a line that intersects two or more other lines.

The description of the relationship between the angles in the question are;

Alternate Interior Angles

Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal

Alternate Exterior Angles

Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.

Consecutive Interior Angles

Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.

Corresponding Angles

Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.

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Answer:

1039.23 square inches

Step-by-step explanation:

                      a = 20 inches

    [tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]

                                                   [tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]

The values of x that could make the triangle into different types of triangles are:

For a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the third side.

Right Triangle:

A triangle is a right triangle if it satisfies the Pythagorean theorem: a² + b² = c², where c is the longest side (hypotenuse).

6² + 8² = x²

36 + 64 = x²

100 = x²

x = 10

Acute Triangle:

A triangle is acute if the sum of the squares of the two shorter sides is greater than the square of the longest side. Since we already know that the right triangle has x = 10, we can choose a value for x that is less than 10 to form an acute triangle.

Let's take x = 9:

6² + 8² > 9²

36 + 64 > 81

100 > 81

Obtuse Triangle:

A triangle is obtuse if the sum of the squares of the two shorter sides is less than the square of the longest side. We can choose a value for x that is greater than 10 to form an obtuse triangle.

Let's take x = 11:

6² + 8² < 11²

36 + 64 < 121

100 < 121

The possible values of x for each triangle type are:

Right Triangle: x = 10

Acute Triangle: x = 9

Obtuse Triangle: x = 11

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Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

The demand equation for commodity A is Xa = (4/10)Xb.

A demand equation is a mathematical representation of the relationship between the quantity of a good or service that consumers are willing to buy and the various factors that influence that demand, such as price, income, and preferences.

In the given question,

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

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The demand equation for commodity A is Xa = (4/10)Xb.

What is demand equation?

A demand equation is a mathematical formula that expresses the relationship between the quantity of a good or service that consumers are willing and able to purchase and various factors that affect that quantity, such as price, income, and the prices of other goods.

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

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Answer: what shape?

Step-by-step explanation:

More info please

Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

The constant of proportionality of this table  is: k = 1/7.

The ratio between two quantities that are directly proportional is the constant of proportionality.

When y and x are two values that are direct proportion to one another, the proportionality constant k is defined as k=y/x.

Thus, using the x and its respective y values.

As the values are in direct proportion.

The constant of proportionality is:

k = 1/7

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Answer:

5683200

Step-by-step explanation:

Move the decimal 4 places to the right because [tex]10^4[/tex] has 4 zeros.

Step-by-step explanation:

y = x^2 / z      now triple x and z

y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z  <==== this is 3 times the original

    y is tripled

Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

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Answer:The leading term in a polynomial is the term with the highest degree.

Step-by-step explanation:

Step-by-step explanation:

y = 3 x^2 - 4 x - 1

leading coefficient is 3  and its sign is ' + '   or positive

Answer:

Matt's typing speed increased by 18.75%.

Step-by-step explanation:

To find the percent increase, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

Using this formula, we can calculate the percent increase in Matt's typing speed as follows:

percent increase = (38 - 32) / 32 x 100%

percent increase = 6 / 32 x 100%

percent increase = 0.1875 x 100%

percent increase = 18.75%

All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]

We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.

Let's start with the original quadrilateral ABCD. The length of AB is:

[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]

Similarly, the lengths of BC, CD, and DA are:

[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]

[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]

[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]

Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:

[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]

Similarly, the lengths of B'C', C'D', and D'A' are:

[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]

[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]

[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]

Now we can find the ratio of corresponding side lengths:

[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]

[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]

Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.

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The probability based on the information will be;

a. Likely, probability is 25%

b. Likely, probability is 25%

c. Impossible, probability is 0%

d. Unlikely, probability is 33.3%

The probability of rolling a 5 on a 6 sided die is 1/6 or approximately 16.67%.

The probability of not rolling a 5 on a 6 sided die is 5/6 or approximately 83.33%. This can also be:

= 100 - 16.67

= 83.33%

The probability of spinning an even number on a spinner with numbers 1-8 is 4/8 or 1/2 or 50%.

The probability that a white horse is George is 1/5 or 20%.

An event that has probability of 0% is something that is impossible, such as rolling a 7 on a 6-sided die. An event that has a probability of 100% is something that is certain, such as flipping a coin and getting either heads or tails.

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Answer:

2 real zeros at x = - 2 , x = 1

Step-by-step explanation:

f(x) = x² + x - 2

to find the zeros let f(x) = 0 , that is

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x + 1 = 0 ⇒ x = - 1

there are 2 real zeros , x = - 2 and x = 1

Answer:x=23

Step-by-step explanation:

x+1+7x-5=180

8x-4=180

8x=184

x=184/8

x=23

Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).

Answer:

168 cm^2

Step-by-step explanation:

This rhombus is made up of two triangles. To find triangle area, base x height/2 (but bc there are two triangles we don’t need to divide by 2). To do this, 14 x 12 to get 168cm^2

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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The blanks of the number pyramid puzzle can be filled with numbers calculated below.

A number pyramid puzzle is a type of mathematical puzzle where a pyramid-shaped grid of numbers is given, with some of the numbers missing.

Check the attached image for labeling. Since each number is the product of the two numbers directly beneath it. We can say:

m = -4 * 0.5 = -2

k = 0.5 * 1/8 = 1/16

x * (-1/8) = 8

x = 8/(-1/8)

x = -64  

y = x * 1/8

y = -64 * 1/8

y = -8

j = m * k

j =  -2 * 1/16 = -1/8

p = -48 * m

p = -48 * (-2) = 96

n = y * 8

n = -8 * 8 = -64

t = p * j

t = 96 * (-1/8) = -12

w = -1/2 * n

w = -1/2 * (-64) = 32

c = t * 1/16

c = -12 * 1/16 = -3/4

u = 1/16 * w

u = 1/16 * 32 = 2

d = c * u

d = -3/4 * 2 = -3/2

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(a) The relative rate of growth of the bacterium population is 15% per unit time; (b) the initial population of the culture is 90 bacteria; (c) the culture will contain approximately 239 bacteria at time t=5.

(a) The relative rate of growth of the bacterium population can be calculated by taking the derivative of the function n(t) with respect to t and then dividing it by the value of n(t) at that point, which gives:

relative rate of growth = (dn/dt) / n(t)

= (0.15 * 90[tex]e^0.15t[/tex]) / (90[tex]e^0.15t[/tex])

= 0.15

Therefore, the relative rate of growth is 15%.

(b) The initial population of the culture at t=0 is given by plugging in t=0 in the function n(t):

n(0) = 90[tex]e^0.15[/tex]*0

= 90

Therefore, the initial population of the culture is 90.

(c) The number of bacteria in the culture at time t=5 can be found by plugging in t=5 in the function n(t):

n(5) = 90[tex]e^0.15[/tex]*5

= 385.97 (rounded to two decimal places)

Therefore, the culture will contain approximately 385.97 bacteria at time t=5.

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Answer:

B.......................

Answer:2.04

Step-by-step explanation: