4. Javier bought a microwave for $105. The cost
was 30% off the original price. What was the
price of the microwave before the sale?

The logical statement [tex]$(a \wedge b) \rightarrow(b \vee c)$[/tex] is a tautology. Hence, Option B  and Option C is the most appropriate answer to the given question.

A tautology is a logical statement where the conclusion is always equivalent to the premise. No matter what the individual parts are, the result is always a true statement; i.e. a tautology is always true. The opposite of tautology is either a contradiction or a fallacy.

say, "x=y or x≠y".

Similarly, "either the ball is red, or the ball is not red" is always true, irrespective of the color of the ball.

Here, checking the truth tables of each of the options

we can conclude that the truth values of (P v Q)→Q and P v (P→Q) are always true.

So, (P V Q) →Q and P v (P→Q) are tautology statements.

Hence, option B and option C are the correct choices for this question.

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The number of pint jar needed to hold 5 gallon of sauce is 40 jars.

Pint and gallons are both units of volume. The number of pint jars needed to hold 5 gallon of sauces can be determined by changing the unit of volume. Conversion of units refers to the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. According to the conversion of units, 1 gallon is equal to 8 pint. Hence, applying the conversion rate to the total volume of tomato sauce made:

5 gallons = 5*8 = 40 pint

If a jar holds 1 pint of sauce, the number of jars to hold the total volume of sauce is 40 pint jar.

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the time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. 0.1875 is the the probability it takes between 54.7 and 56 min. round to 4 decimal places.

The probability of any event occurring is given by the formula P(x) = (x-a)/(b-a). In this case, the probability of the task taking between 54.7 and 56 minutes is (56-54.7)/(57-43) = 0.1875. This probability is equal to the area under the uniform distribution graph between 54.7 and 56 minutes. As the graph is a rectangle, the area is simply the width multiplied by the height, so 0.1875. Rounding to 4 decimal places, the probability is 0.1875.

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Answer:

This is answer of 530.4 Q

A significant relationship between x and y is  b. large p-value for the estimated slope.

Simple linear regression is used to estimate the connection among  quantitative variables. You can use easy linear regression whilst you need to know: How robust the connection is among variables (e.g., the connection among rainfall and soil erosion). The fee of the established variable at a positive fee of the impartial variable (e.g., the quantity of soil erosion at a positive stage of rainfall). Simple linear regression is used to version the connection among  non-stop variables. Often, the goal is to are expecting the fee of an output variable (or response) primarily based totally at the fee of an input (or predictor) variable.

Thus, option b is the correct choice.

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Answer:

nth term = a+(n-1)d

Step-by-step explanation:

where a=first term

n=nth term

d=common difference=2nd term - 1st term=5

Answer:8

Step-by-step explanation:

Answer:

  A, C, E

Step-by-step explanation:

You want the values from the list that are included in the solution set of -6(1 + 2x) ≥ 6(2x - 1) + 2x.

Simplifying the inequality, we get ...

  -6 -12x ≥ 12x -6 +2x

  0 ≥ 26x . . . . . . . . . . . . . add 12x+6

  x ≤ 0 . . . . . . . . . . . . divide by 26

The solution set includes 0 (choice C) and all negative values (choices A and E).

The Probability of getting less than 555 orders = x<555/ccc

Suppose we discuss about two events which can be occurred at any time but the occurrence of one event is not dependent on other event. In such case the probability of occurring each event is called independent probability.

The probability of two independent events is calculated by the formula

probability of one event × probability of another event

If A and B are two events occurred independently

    probability of happening two events = P(A)×P(B)

In our problem, order for cake over telephone is one event

         order for cake manually is another event

10 percent order get over telephone

So, percent of probability to get order from phone = 10/100 = 1/10

She got total ccc cake order in a month before getting order over phone

let. X is a number of orders she got before getting her first telephone order.

Therefore, the probability that it takes fewer than 555 orders for Lilyana to get her first telephone order = X<555/ccc

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Answer:

Step-by-step explanation:

Formula for Circumference of a circle is 2* pi * radius

If r=16

C= 2*π*16

C=32π

Answer:

a) n less than or equal to 21

b) n greater than or equal to 5

c) n > 3/5

Step-by-step explanation:

i hope this helps!!

Answer:

A.) n ≤ 21

B.) n  ≥ 5

C.) n > 3/5

Step-by-step explanation:

For the first question it says that the number is no more than 21, so it could be equal to or less than 21

For the second question, it says that the number is at least 5, so it could be equal to or greater than 5

Finally, for the last question it says that the number is more than 3/5, so greater than would be the correct inequality symbol to use

Answer:

It will cost $86.00 for the care to be towed 7 miles.

Step-by-step explanation:

C(x) = 3x + 65  Substitute in 7 for x

C(7) = 3(7) + 65

C(x) = 21 + 65

C(x) = 86

Answer

86 Dollars

Step-by-step explanation:

It is given that

[tex]c(x) = 3x + 65 \\ [/tex]

Since,x is the number of miles the car is towed which in this case is 7

So, If we input 7 in the function C(x)

[tex]c(7) = 3 \times 7 + 65[/tex]

We know through BODMAS that multiplication is done before addition.

Thus,

[tex]c(7) = 21 + 65 \\ because \: 3 \times 7 = 21 \\ [/tex]

and so,

[tex]c(7) = 86 \\ because \:21 + 65 = 86[/tex]

and so,

c(7) = 86

We also know that C(x) is the cost of having the car towed which is equal to 86 for the case of towing the car 7 miles

Thus,The cost of having the car towed 7 miles is 86 Dollars

Solid chance this is way above your knowledge level



A parabola is a curve in the shape of a U that is defined as the set of all points that are equidistant to a fixed point (called the focus) and a fixed line (called the directrix).

To write the equation of a parabola with a focus at (-2, 5) and a directrix at x = 3, we can use the standard form of the equation of a parabola, which is:

y = (1/(4f))x^2 + k

Where f is the distance between the focus and the vertex (the point where the parabola changes direction), and k is a constant that determines the position of the parabola along the y-axis.

To find the value of f, we can use the distance formula:

f = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) is the coordinate of the focus and (x2, y2) is the coordinate of the vertex.

Since the focus is at (-2, 5) and the directrix is at x = 3, we can use the y-coordinate of the focus as the y-coordinate of the vertex, and the x-coordinate of the directrix as the x-coordinate of the vertex. Therefore, the coordinate of the vertex is (3, 5).

Substituting these values into the distance formula, we get:

f = sqrt((3 - (-2))^2 + (5 - 5)^2)

= sqrt((5)^2 + (0)^2)

= sqrt(25)

= 5

Now that we have the value of f, we can substitute it into the standard form of the equation of a parabola to get:

y = (1/(4*5))x^2 + k

= (1/20)x^2 + k

This is the equation for a parabola with a focus at (-2, 5) and a directrix at x = 3. The constant k determines the position of the parabola along the y-axis.

Using proportions and constant of proportionality, the train always move the same distance and the cost is always the same

Proportion can defined as the comparison between two numbers or ratios. Using proportions, when two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The proportional relationship between two numbers can be represented as

y = kx

i)

In this question, let's determine if they have the same constant of proportionality.

y = kx

6 = k(2)

k = 3

12 = k(4)

k = 3

Since they have the same constant of proportionality, the train always go the same distance each minute.

ii)

The time travelled in 10 minutes

y = 3x

y = 3(10)

y = 30

The distance in 10 minutes is 30km

b)

Using constant of proportionality to determine if they have a proportional relationship;

y = kx

21 = k(3)

k = 7

42 = k(6)

k = 7

The equation is y = 7x and the constant of proportionality is 7.

The cost for each person is always the same

ii) From y = 7x

63 = 7x

x = 63 / 7

x = 9

The predicted number for a cost of $63 is 9

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The area enclosed by the curve x = t2 − 3t, y = t and the y-axis is 9/2

In this question we have been given parametric equations x = t^2 − 3t, y = t

In this question we need to find the area enclosed by the curve x = t2 − 3t, y = t and the y-axis.

The curve has intersects with y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Now we have to draw the graph,

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

Now, find the area under the curve using the above formula

A = ∫[a to b] g(t)f'(t) dt

so, A = ∫[0 to 3] t (2t - 3) dt

A = ∫[0 to 3] (2t^2 - 3t) dt

A = [2/3 t^3 - 3/2 t^2]_[t = 0, t = 3]

A = 2/3 3^3 - 3/2 3^2

A = 18 - (3^3)/2

A = 18 - 27/2

A = 9/2

Therefore,  the area of the curve is 9/2.

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Answer:

b

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

y = - [tex]\frac{1}{2}[/tex] x - 7 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

the slopes are not equal thus not parallel

• the product of the slopes of perpendicular lines is equal to - 1

2 × - [tex]\frac{1}{2}[/tex] = - 1

Thus the 2 lines are perpendicular to each other.

Rabbit leaps two feet. Kangaroo leaps sixteen feet. sEight time as far as the rabbit, the kangaroo jumps.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

A bunny leaps two feet. The kangaroo leaps 16 feet. The kangaroo leaps eight times farther than the rabbit.

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X is an algebraic variable which has no defined value. X is kind of universe variable taken in most of the equations.

The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.

Solution:

Given: - 5x - 15 > 10 + 20x

Let us solve the inequality by isolating the variable x.

Add 5x on both sides

- 5x - 15 + 5x > 10 + 20x + 5x

- 15 > 10 + 25x

Subtract 10 from both sides

- 15 - 10 > 10 - 10 + 25x

- 25 > 25x

Divide both sides by - 25

-1 > x

x < - 1

The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.

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Answer:

-2

Step-by-step explanation:

i did it

The percentage represented is 72%, and the decimal is 0.72

First lets find the decimal, it will be equal to the quotient between the total number of shaded squares and the total number of squares.

There are 200 squares in total, and of these 200, there are 144 shaded ones, then the decimal is:

d = 144/200  = 0.72

To find the percentage, you only need to multiply the decimal by 100%, we will get:

p = 100%*0.72 = 72%

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The equation of line that would graph his salary over time will be;

⇒ y = 1/685x - 38.89

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

After 4 years, he makes $56,785; after 9 years, he makes $60,210.

Now,

Since, After 4 years, he makes $56,785; after 9 years, he makes $60,210.

Hence, The equation of line passes through the points (56,785, 4) and

(60,210, 9).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (9 - 4) / (60210 - 56785)

m = 5 / 3425

m = 1/685

Thus, The equation of line with slope 1/685 is,

⇒ y - 4 = 1/685 (x - 56,785)

⇒ y - 4 = 1/685x - 42.89

⇒ y = 1/685x - 42.89 + 4

⇒ y = 1/685x - 38.89

Therefore, The equation of line that would graph his salary over time will be;

⇒ y = 1/685x - 38.89

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Answer:  the area of the rectangle is 456 square millimeters.

Step-by-step explanation:

the perimeter is 88 mm, so if we let L be the length of the rectangle and W be the width, we can write the following equation to find the perimeter:

2L + 2W = 88 mm

Since the base of the rectangle is 38 mm, we know that the width of the rectangle is 38 mm, so we can substitute that value into the equation above to get:

2L + 2(38 mm) = 88 mm

Solving for L, we get:

2L = 88 mm - 2(38 mm)

2L = 88 mm - 76 mm

2L = 12 mm

Therefore, the length of the rectangle is 12 mm. Now that we know both the length and the width, we can find the area by multiplying the length and the width:

Area = L * W

Area = 12 mm * 38 mm

Area = 456 mm^2

Thus, the area of the rectangle is 456 square millimeters.

Answer:

A=228mm

Step-by-step explanation:

What formulas do we know?

Parameter= 2(length)+2(width)

Area= length x width

We can just substitute in values for parameters so,

88=2(length) + 2(38)

88=2L + 78 ------> 12=2L -------> L=6

Now we know width (which is just B) and Length (what we calculated)

Now we use area ----> Area= length x width

Area= (38)(6)-----> 228mm

Answer:

The correct answer would be 5000 x ^108

Step-by-step

For ∬∂WF⋅dS differentiable each of the following regions is 0, [tex]\frac{18 \sqrt{2}}{15}, -\frac{16 \sqrt{2}}{15}[/tex]

Let the f=[tex]\left(y^2+z^3, x^3+z^2, x z\right) \\[/tex],

Differentiability of Function: For a function to be differentiable at any point x=a in its domain, it must be continuous at that particular point but vice-versa is not always true. In complex analysis, complex-differentiability is defined using the same definition as single-variable real functions. This is allowed by the possibility of dividing complex numbers

Solution: For checking the continuity, we need to check the left hand and right-hand limits and the value of the function at a point x=a.

This means that f'(a) must exist, or equivalently:

[tex]$$\lim _{x \rightarrow a^{+}} f^{\prime}(x)=\lim _{x \rightarrow a^{-}} f^{\prime}(x)=\lim _{x \rightarrow a} f^{\prime}(x)=f^{\prime}(a)$$[/tex]

(A).

[tex]& x^{2 / t} y^2 \leq z \leq 2 \\\\& \int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}} \int_{z=\gamma^2}^2 \gamma \cos \theta d z d \gamma d \theta \\\\&=\int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}}[\gamma \cos \theta][z]_{\gamma^2}^2 d \gamma d \theta \\[/tex]

[tex]&=\int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}}\left(2-\gamma^2\right) \gamma \cos \theta d \gamma d \theta \\\\&=\int_{\theta=0}^{2 \pi}\left[\gamma^2-\frac{\gamma^4}{4}\right]_0^{\sqrt{2}} \cos \theta d \theta \\\\&=\int_{\theta=0}^{2 \pi} \cos \theta d \theta \\\\&=[\sin \theta]_0^{2 \pi} \\&=0[/tex]

(B).

[tex]& \ x^2+y^2 \leq 2 \leq 2 . \quad, x \geqslant 0 \\[/tex]

[tex]& \int_{0=-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_{\gamma=0}^{\sqrt{2}} \int_{z=\gamma^2}^2 \gamma^2 \cos \theta d z d \gamma d \theta . \\\\& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^{\sqrt{2}} \gamma^2 \cos \theta[z]^2 \gamma^2 \cdot d \gamma d \theta \text {. } \\[/tex]

[tex]& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^{\sqrt{2}} \cos \theta\left(2-\gamma^2\right) \gamma^2 d \gamma d \theta . \\\\& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos \theta\left[\frac{2}{3} \gamma^3-\frac{\gamma^5}{5}\right]_0^{\sqrt{2}} d \theta \text {. } \\[/tex]

[tex]& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos \theta\left[\frac{4}{3} \sqrt{2}-\frac{4 \sqrt{2}}{5}\right] d \theta . \\\\& =[\sin \theta]_{-\frac{\pi}{2}}^{\frac{\pi}{2}} d \theta\left[\frac{4}{4} \sqrt{2}-\frac{4 \sqrt{2}}{5}\right] \\\\& =\left[\frac{4 \sqrt{2}}{3}-\frac{4 \sqrt{2}}{5}\right] \\[/tex]

[tex]& =\left[\frac{4 \sqrt{2}}{3}-\frac{4 \sqrt{2}}{5}\right] \\\\& =\left[\frac{20 \sqrt{2}-12 \sqrt{2}}{15}\right]=2\left[\frac{8 \sqrt{2}}{15}\right] \\\\& =\frac{18 \sqrt{2}}{15}[/tex]

(C).

[tex]x^2+y^2 & \leqslant z \leqslant 2, x \leq 0 \\[/tex]

A+B+C

0=B+C

B=-C or C=-B

C=[tex]-\frac{16 \sqrt{2}}{15}[/tex]

Therefore, the differentiable of each function is 0, [tex]\frac{18 \sqrt{2}}{15}, -\frac{16 \sqrt{2}}{15}[/tex].

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Let F=[tex]\left(y^2+z^3, x^3+z^2, x z\right) \\[/tex]) . Evaluate ∬∂WF⋅dS for each of the following regions W:

A.[tex]& x^{2 / t} y^2 \leq z \leq 2 \\\\ \\[/tex]

B. [tex]& \ x^2+y^2 \leq 2 \leq 2 . \quad, x \geqslant 0 \\[/tex]

C. [tex]x^2+y^2 & \leqslant z \leqslant 2, x \leq 0 \\[/tex]

Answer: 0.03 pounds

Step-by-step explanation:

To determine how much trail mix went in each bag, you need to divide the total amount of trail mix by the number of bags.

In this case, you would divide 3 pounds of trail mix by 10 bags to find that each bag contained 0.3 pounds of trail mix.

You can also express this amount in ounces. Since there are 16 ounces in a pound, each bag contained 4.8 ounces of trail mix (0.3 pounds * 16 ounces/pound = 4.8 ounces).

The present ages of the father and his son are 50 and 30 years respectively.

An algebraic expression can be defined as an expression made up of constants, variables, terms, coefficients, and factors.

These expressions are also made up of mathematical or arithmetic operations, which includes;

From the information given;

Let the son's age be x

Let the father's age be x + y

x + x + y = 80

2x + y = 80

Then, 2x - y = 40

From equation (1), make 'y' the subject

y = 80 - 2x

Substitute the value

2x - (80 - 2x) = 40

2x - 80 + 2x = 40

collect like terms

4x = 120

x = 30

y = 80- 2(30)

y = 20

Hence, their ages are 30 years and 50 years

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The sale price of the shirt is equal to $12

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We are given that Original price of the shirt = $16

The Sale price = 34% of the original price

If original price = $16, then Sales price will be 34% of original price - original price

= 0.34 × 16 - 16

Apply BODMAS multiply before subtracting;

=16 - 0.34 × 16

=$16 - $4

Sales price = $12

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The complete question is

Shirts are on sale for 34 of the original price. If the original price was $16, what is the sale price?

The two linear equations can be written as:

y = 2*x + 1

y = x + 2

Remember that a general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

First, we know that one of the lines has an y-intercept at y = 1, then:

y = a*x + 1

And the line passes through (1, 3), replacing these values we get:

3 = a*1 + 1

3 - 1 = a

2 = a

That line is y = 2*x + 1

The other line has a y-intercept at y = 2, then:

y = a*x + 2

This line also passes through (1, 3), then:

3 = a*1 + 2

3 = a + 2

3 - 2 = a

1 = a

The line is:

y = a*x + 2

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