Simplify. 12c + 3 (c + 10) + 12

The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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The rate of change of temp w.r.t time is -1.875°F

What is rate of change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" (ROC) is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line. The Greek letter delta () is frequently used to represent the ROC.

The term "rate of change" (ROC) describes the rate at which something changes over time.

Thus, it is not the amount of individual changes themselves but rather the acceleration or slowdown of changes (i.e., the pace).

Time             Temperature              Difference

4                          89.5                               -

10                        78.25              78.25 - 89.5 = -11.25

16                        67.00              67 - 78.25 = -11.25      

There is a common difference of -11.25 in each successive term.

Therefore, cooling of a chemical represents a linear function.

Rate of change of temp from 4 min to 10 min

=78.25 - 89.5 = -11.25

= -11.25/6

=-1.875

So, the rate of change of temp w.r.t time is -1.875°F

which means temperature is decreasing continuously when the time is increasing

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Answer:

for the first one its the 3 answer

Step-by-step explanation:

i know because i had a similar quiz like yours and it was hard do i got a friend to help and i got 100% trust meeeeeeee

Given that x is equal to 1 and S is the centroid of the triangle NLQ, NS will have a length of 4 units.

The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition. The centroid of a triangle is the location where the triangle's three medians connect. It may alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Here,

We may infer from the centroid's features that it divides each median in a ratio of 2:1.

NS=2SR

7x-3=2(5x-3)

7x-3=10x-6

3x=3

x=1

NS=7x-3

=7*1-3

=4 units

The length of NS will be 4 units as the value of x is 1 and S is the centroid of triangle NLQ.

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Answer: Both of the tables are proportional because they each go up at an even constant rate. The first table goes up at a constant rate of 8. The second table, goes up at a constant rate of 0.70.

Step-by-step explanation:

Answer: 100−2(12+13)

12+13=25

100−2×25

2×25=50

100-50=50

the answer is 50 :)

Answer:

50

Step-by-step explanation:

To solve this equation, use PEMDAS:

P - Parentheses

E - Exponents

M/D - Multiplication/Division

A/S - Addition/Subtraction

PEMDAS is the method that is used for the order of operations. Multiplication and division are interchangeable, so when there are only those signs left, you solve from left to right. This also applies to addition and subtraction.

Equations must always be solved in the order of PEMDAS -- P, then E, then M/D, then A/S.

Now, to solve the equation:

100 - 2(12 + 13)    First, solve what is in the parentheses (P).

100 - 2(25)           Next, multiply 2 × 25 (M).

100 - 50               Finally, subtract 50 from 100 (S)

50

100 - 2(12 + 13) = 50

Quantity demanded decreases by 8.5 when the price of a burger increases by $1.

Demand curve is a graph which describes the variation of the demand of a goods or a commodity with the variation in the price.

Given demand curve equation is,

Qd = -8.5P + 217

Suppose that the price of a burger increases by $1.

Then the demand equation becomes,

Qd' = -8.5 (P + 1) + 217

      = -8.5P - 8.5 + 217

      = (-8.5P + 217) - 8.5

      = Qd - 1

That is, the quantity demanded decreases by 8.5 when price increases by $1.

Hence the decrease in the quantity demanded is 8.5.

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Answer:

9.2

Step-by-step explanation:

102/11

i would take him 9.2 months to pay back

Ideally, he will repay the whole amount of $102 in 10 months where he will pay $11 for first 9 months and $3 in the 10th month.

Given information:

Keith borrowed $102 from his dad, and he is paying him back $11 each month.

So, Keith will pay back his dad an amount of $11 every month till the debt is cleared.

Now, the number of months required by Keith to repay will be calculated as,

\(\dfrac{102}{11}=9+\dfrac{3}{11}\)

Now, Keith will need \(9+\dfrac{3}{11}\) months to completely repay his debt.

Fraction of month is not an option for repayment. So, he will pay $11 regularly for 9 months which will be $99 in the repayment, and the remaining $3 will be paid by him in the 10th month.

Therefore, ideally, he will repay the whole amount of $102 in 10 months where he will pay $11 for first 9 months and $3 in the 10th month.

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Answer:

00.35 prett simple this fraction

Answer:

82

Step-by-step explanation:

\(4^3 + \frac{96}{8} \cdot 5 - 42 = 64 + 12\cdot 5 - 42 = 64 + 60 - 42 = 82\)

Answer:

82

Step-by-step explanation:

PEMDAS

\(4^{3}\) + [(96 ÷ 8) x 5] - 42

\(4^{3}\) + [(12) x 5] - 42

4^3 + (60) - 42

64 + 60 - 42

124 - 42

82

hope this helps :)

Answer:

data bar

Step-by-step explanation:

Answer:

chart

Step-by-step explanation:

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

The volume of the cardboard box is approximately 13197.402 cubic inches.

The volume of a cardboard box is 216 dm³, we can convert it to the English system of measurements.

1 dm (cubic decimeter) is equivalent to 1 liter.

To convert dm³ to cubic inches, we can use the following conversion factors:

1 dm³ = 61.0237 cubic inches

Using this conversion factor, we can calculate the volume of the box in cubic inches:

The cube carton volume is 216 dm3 and the cube edge value is 6 dm.

The volume of the cube is calculated by dividing the edge values. In other words, volume = edge 3.

To find the edge (side) value, you can solve for the volume formula as follows:

edge 3 = volume.

edge = ∛ volume,

Where ∛ is the cube root.

Applying this formula to the given problem gives edge = ∛(216 dm³).

Edge = 6dm. Therefore, the side (edge) value of the cube is 6dm.

Volume (cubic inches) = 216 dm³ * 61.0237 cubic inches/dm³

= 13197.402 cubic inches

Question :- If the volume of a cubic cardboard box is 216 dm³

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Answer:

12.56 cents

14.08 cent

Step-by-step explanation:

The unit price for each of the following items could be obtained thus :

The unit price = price of one item

Therefore, given that x numbers of a certain item cost y ;

The unit price will be : y / x

frozen orange juice

16.0 oz at $2.01

12 oz at $1.69

If 16 oz cost $2.01

1 oz = $2.01 / 16 = $0.125625 * 100 = 12.56 cents

If 12 oz = $1.69

1 oz = $1.69 / 12 = $0.1408333 * 100 = 14.08 cent

The soccer ball is above 15 feet between 0.25 seconds and 1 second.

To determine when the soccer ball is above 15 feet, we need to find the values of t that satisfy the inequality h(t) > 15.

Given the quadratic function h(t) = -16t² + 20t + 11, we can rewrite the inequality as follows:

-16t² + 20t + 11 > 15

Subtracting 15 from both sides:

-16t² + 20t - 4 > 0

Simplifying further:

-16t² + 20t - 4 = -4(4t² - 5t + 1) = -4(t - 1)(4t - 1) > 0

Now, we can solve for t by finding the values that make the inequality true. We have two factors: (t - 1) and (4t - 1).

Setting each factor greater than zero and solving for t:

t - 1 > 0 => t > 1

4t - 1 > 0 => 4t > 1 => t > 1/4

So, we have t > 1 and t > 1/4. To satisfy both conditions, t must be greater than the maximum of 1 and 1/4, which is 1.

Therefore, the soccer ball is above 15 feet for t > 1 second.

The correct answer is:

C. The soccer ball is above 15 feet between 0.25 seconds and 1 second.

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The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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Answer: No

Step-by-step explanation:

Answer:

I believe it is false

Step-by-step explanation:

The solution to the inequalities will be,

( 5 ) y ≥ 2

( 6 ) x < 3

( 7 ) No solution.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

The given inequalities will be calculated as:-

-4 ≤ 4( 6y - 12 ) - 2y

-4 ≤ 24y - 48 - 2y

-4 ≤ 22 y - 48

22y ≥ 44

y ≥ 2

4x + 3 < 3x + 6

4x - 3x < 6 - 3

x < 3

-5r + 6 ≤ -5( r + 2 )

-5r + 6 ≤ -5r - 10

No solution

Therefore, the inequalities are solved above.

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Answer:

(A)System A has no solution

(B)System B has a unique solution (x,y) = (0,2).

Explanation:

System A

Given the system of equations:

Rewrite both equations in the slope-intercept form:

On observation, the slopes of the two equations = -1/3.

This means that the two lines are parallel and thus, the system has no solution.

System B

Given the system of equations:

Add both equations:

Divide both sides by -8.

Substitute y=2 into the first equation to solve for x.

The system has a unique solution (x,y) = (0,2).

Answer:

the answer is [c]

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

The limits are : Limits y = \(-\sqrt{9-z^2} \leq y\leq 0\)  and   Limits z = \(-3 \leq z\leq 3\).

The volume of a cylinder is the capacity of the cylinder, which calculates how much matter it can hold. In geometry, there is a specific formula for calculating the volume of a cylinder, which measures the amount of liquid or solid that can be uniformly immersed in it. A cylinder is a three-dimensional shape with two congruent and parallel identical bases. There are different types of cylinders. They are:

(1) Right cylinder: a cylinder with a circular base and of which each line segment constituting the lateral surface is perpendicular to the base.

(2) Inclined Cylinder: A cylinder whose sides are inclined at an angle not equal to a right angle to the base.

(3) Elliptical cylinder: a cylinder with an elliptical base.

(4) Straight hollow cylinder: Cylinder made up of two straight cylinders, one inside the other.

According to the question:

The cylinder has the equation y² + z² = 1 (with x in [0, 2]).

So, we can write the volume 1 dV as (x = 0 to 2) (z = -1 to 1)(y = -a(1 - z²) to a(1 - z²)) 1 dy dz dx.

y-axis in left: y²+ z² =9

y-axis in the plane: y =0

The left part of the circle is :

\(-\sqrt{9-z^2} =y\)

Limits y : \(-\sqrt{9-z^2} \leq y\leq 0\)

Limits z : \(-3 \leq z\leq 3\)

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Answer:

\(\frac{s}{s-4}\)

Step-by-step explanation:

Given

\(\frac{s^2+6s}{s^2+10s+24}\) ÷ \(\frac{s-4}{s+4}\) ( factor and simplify fraction on left )

= \(\frac{s(s+6)}{(s+4)(s+6)}\) ÷ \(\frac{s-4}{s+4}\) ← cancel (s + 6) on numerator/ denominator

Leave first fraction, change division to multiplication, turn second fraction upside down

= \(\frac{s}{s+4}\) × \(\frac{s+4}{s-4}\) ← cancel (x + 4) on numerator/ denominator

= \(\frac{s}{s-4}\)

Answer:

There is 1 solution

Step-by-step explanation:

y = -3 (x+1) ^2

Using the zero product property

0 =  -3 (x+1) ^2

Divide by -3

0 =   (x+1) ^2

Take the square root of each side

sqrt(0) =  sqrt( (x+1) ^2)

0 = x+1

Subtract 1 from each side

-1 =x

There is 1 solution

The sheet decreased by 1.5 meters and is now at 2.5 meters.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, s=−0.25t + 4 represents the thickness of the ice over t weeks. To find the thickness at 6 weeks, substitute t=6.

s = -0.25(6)+4

s = 2.5 meters

It started at t= 0 at 4 meters. So it decreased by (4 - 2.5) = 1.5 meters.

The start of spring has 4 meters because when t= 0, s= -0.25(0)+4 = 4

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During the cold winter months, a sheet of ice covers a lake near the Arctic Circle. At the beginning of spring, the ice starts to melt.

The variable s models the ice sheet's thickness (in meters) t

weeks after the beginning of spring.

s=−0.25t+4s=-0.25t+4

s=−0.25t+4

By how much does the ice sheet's thickness decrease every 6 weeks?

The measurement of the drill as a decimal is 0.3125

Measurement can be described as the length or size of an object

A drill has a size of 5/16 inch

Convert the fraction which is the size of the drill in inches to decimal

5/16 = 0.3125

Hence the measurement of the drill in decimal is 0.3125

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