. Mallory took two trips to the pizzeria to purchase food for her party. On her first trip, she bought 5 pizza pies and 3 bottles of soda, which cost her $50.50 without tax. On her second trip, she bought 2 pizza pies and 6 bottles of soda, which cost her $31.00 without tax. How much did each pizza pie cost?

W1, W2, W3 and W4 are all true in this model.

(a)

In any model U for which W3 is true, the predicates G and H, regarded as subsets of U, must be disjoint because the formula W3 = (Vx) (G(x)~ H(x)) is true when, and only when, every element of U which is a member of the subset G is not a member of the subset H. The predicate G is defined as a subset of U such that G(x) holds if and only if x satisfies a certain condition. Similarly, H(x) holds if and only if x satisfies another certain condition. But W3 is true only when G(x) is true and H(x) is false for all x in U. Therefore, the sets G and H are disjoint.(b) ProofAny model in which W1, W2, W3 and W4 are all true must have at least 3 elements. The formula W1 = (3x)(3y) (G(x) ^ G(y) ^ ~ E(x, y)) is true only when there are at least two elements in U such that G holds for each of them and they are not related by E. Hence, there are at least two elements x and y in U such that G(x) and G(y) are true and E(x, y) is false. By W2 = (x)E(x, x), every element of U is related to itself by E. Therefore, there must be a third element z in U such that E(x, z) is false and E(y, z) is false. Therefore, U must have at least 3 elements.One such model with 3 elements is U = {a, b, c} where G(a) and G(b) are true and E(a, b) is false. Then E(a, a), E(b, b) and E(c, c) are true and E(a, c), E(b, c) and E(c, a) are false.

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In any model U for which W3 is true, the predicates G and H, regarded as subsets of U, must be disjoint. This can be explained by the following:Let's assume that there exists a model U where W3 is true, but G and H are not disjoint, i.e.,

they have an element in common, say a. Let's consider the truth value of the following statement G(a) V H(a) in U:if G(a) is true in U, then ~ H(a) is true in U, by the definition of W3. Similarly, if H(a) is true in U, then ~ G(a) is true in U, by the definition of W3. Thus, the statement G(a) V H(a) is false in U in either case, which contradicts the fact that U is a model for W3 (which asserts the existence of an element x for which\(G(x) ^ ~ H(x)\) is true in U). This contradiction shows that G and H must be disjoint in any such model.(b) Let's consider the following model U:{0, 1, 2},

where G = {0, 1}, H = {1, 2}, E = {(0,0), (1,1), (2,2)},

and W = U. We can see that this model satisfies all of the well-formed formulae W1, W2, W3, and W4, and it has 3 elements. Thus, any model in which W1, W2, W3, and W4 are all true must have at least 3 elements.

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About 49 tiles will be needed to cover the floor

A square is a shape having equal sides. The area of a square is expressed as:

A = L²

L is the side length of a square.

If a square tile has a side length of x²y units, the area of the square tile will be:

A = (x²y)²

As = x⁴y² units²

Similarly, if a quart floor has a side length of 7x⁵y⁶ units. The area of the quart floor will be expressed as:

Aq = (7x⁵y⁶)²

Aq = 49x¹⁰y¹²

Divide both areas to get the number of tiles that will cover the floor

Number of tiles = 49x¹⁰y¹²/x⁴y²

Number of tiles = 49x⁶y¹⁰

This shows that about 49 tiles will be needed to cover the floor.

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Answer:

Let the length of the rectangle be x and the width of the rectangle be y.

Then, we can use the Pythagorean Theorem to find the value of x and y:

x2 + y2 = 62

x2 + y2 = 36

We can use trigonometry to find the value of x and y:

x = 6 sin 30°

y = 6 cos 30°

Therefore, the length of the rectangle is 6 sin 30° cm and the width of the rectangle is 6 cos 30° cm.

Step-by-step explanation:

First of all

You should draw a straight line which is AC=6cm

Then you should take the centre of the line and draw

30 degree in centre. Then you should draw straight line from

30 degree to bisect center point. Then take 3 cm in compass

and join their point.

Answer:

For the first figure :

Cylinder :

Radius =7cm

height = 15cm

Total Surface Area:

2 \times \pi \times r(h + r)2×π×r(h+r)

= 2×22/7×7 (15+7)

= 22×44

= 968 cm sq.or 9.68m sq.

For the second figure :

Diameter = 24cm (radius= 24/2= 12cm)

•Height = 18 cm

Total Surface area:

2 \times \pi \times r(h + r)2×π×r(h+r)

= 2×22/7×12 (18+12)

= 2×22/7×12 (30)

= 2×22×12×5

= 2640 cm. sq or 26.4 m.sq

The total surface area of this cylinder is 967.1cm²

The formula for calculating the total surface area of a cylinder is expressed as:

TSA = 2πr(r+h)

Given the following

radius r = 7cm

Height h =15cm

Substitute

TSA = 2π(7)(7+15)

TSA = 14π(22)

TSA=967.1 cm²

The total surface area of this cylinder is 967.1cm²

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Answer:

x = 0

Step-by-step explanation:

-10x + 10x + 5x + 5 = 5

5x + 5= 5

5x = 0

x = 0

Step-by-step explanation:

multiply and the both number and divide by bytwo

In the case above, the correct vectors are:

The solution for the Ship's vector are:

Note that the Horizontal aspect = 30 cos 30  

                                                   = 25.98.

For the  Vertical aspect = 30 sin(-30)

                                        = -15.

Hence it will be  <25.98, -15>.

In regards to the current's vector:

The Horizontal aspect=  5 sin 20

                                       = 1.71.

The Vertical aspect = 5 cos 20

                                     = 4.7.

Hence it will be <1.71, 4.7>.

Therefore, In the case above, the correct vectors are:

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Answer:

1

Step-by-step explanation:

2 divided by 2

Answer:

1 table

Step-by-step explanation:

2 x 0.5 = 1

Hope this helps!

Answer:

The answer is C

Step-by-step explanation:

I used process of elimination. 9000 - 20% = 7200

The answer is C) $9000

The expression that is equivalent to \(Cos(\frac{\pi }{2}+r )\) is \(-Sinr\).

Given trigonometric expression is:

\(Cos(\frac{\pi }{2}+r )\)

The value of \(Cos(\frac{\pi }{2}+\theta )\) is \(-Sin\theta\) because \(\frac{\pi }{2} +\theta\) lies in the second quadrant and the cosine function is negative in the second quadrant.

So, \(Cos(\frac{\pi }{2}+r )= -Sin r\)

The range of sine and cosine functions is the same i.e. [-1,1].

Both the functions are periodic functions with periods 2π.

Hence, the expression that is equivalent to \(Cos(\frac{\pi }{2}+r )\) is \(-Sinr\).

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The expression \((3xy^{-3})^{-2}\) without negative exponents is  \(\frac{y^6}{9x^2}\).

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An expression in exponents \((3xy^{-3})^{-2}\).

Now, Changing the place of exponents from the numerator to the denominator or vice versa changes its sign.

Therefore, \((3xy^{-3})^{-2} = 3^{-2}x^{-2}y^{6}\).

\(3^{-2}x^{-2}y^{6} = \frac{y^6}{3^2x^2}\).

\(\frac{y^6}{3^2x^2} = \frac{y^6}{9x^2}\).

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Answer:

2. sec x + c

1.1 view attached pic

1.2 view attached pic

Step-by-step explanation:

To make up each label for the 5,341 precincts, we would need four digits.

To choose a simple random sample (SRS) of 20 voting precincts from Indiana's 5,341 precincts, we need to assign labels to each precinct. The number of digits required for each label depends on the maximum number of precincts we have.

In this case, since we have 5,341 precincts, the maximum label we would need to assign is 5,341. To determine the number of digits needed, we count the number of digits in this maximum label.

The maximum label has four digits (5,341). Therefore, to make up each label for the 5,341 precincts, we would need four digits.

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Answer:

4 weeks

Step-by-step explanation:

The number of weeks for a total of 16 quizzes will be 4 weeks.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that Jacob took a total of 12 quizzes over the course of 3 weeks. The number of weeks for 16 quizzes will be calculated as below:-

12 quizzes = 3 weeks.

1 quizzes = 3 / 12 weeks

16 quizzes = ( 3 / 12 ) x 16 = 4 weeks

Therefore, the number of weeks for a total of 16 quizzes will be 4 weeks.

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The equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is y = (-5/3)x + 5.

To find the equation of a line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b. Given the point (3, 0) on the x-axis, we know that when x = 3, y = 0. This gives us one point on the line, and we can use it to calculate the slope (m).

Using the slope formula: m = (y2 - y1) / (x2 - x1)

Substituting the values (0 - 5) / (3 - 0) = -5 / 3

So, the slope (m) is -5/3. Now, we can substitute the slope and one of the given points (0, 5) into the slope-intercept form (y = mx + b) to find the y-intercept (b).

Using the point (0, 5):

5 = (-5/3) * 0 + b

5 = b

The y-intercept (b) is 5. Therefore, the equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is:

y = (-5/3)x + 5

To sketch the diagram, plot the points (3, 0) and (0, 5) on the x-y plane and draw a straight line passing through these two points. This line represents the graph of the equation y = (-5/3)x + 5.

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Events a and b are not mutually exclusive.

Based on the information provided, it is not possible to determine the relationship between events a (the ticket has a value of 8) and b (the ticket is white) without further information. The relationship between two events can be classified as mutually exclusive, dependent, or independent based on their probabilities and how they are related.

Mutually exclusive events: Events that cannot occur at the same time. If events a and b are mutually exclusive, it means that a ticket cannot have a value of 8 and be white at the same time. In this case, a and b are not mutually exclusive because it is possible for a ticket to have a value of 8 and be white.

Dependent events: Events that are influenced by each other. To determine if events a and b are dependent, we need to know if the occurrence of one event affects the probability of the other event. Without further information, we cannot determine whether a and b are dependent or not.

Independent events: Events that are not influenced by each other. If events a and b are independent, it means that the probability of one event occurring does not affect the probability of the other event occurring. Without further information, we cannot determine whether a and b are independent or not.

In conclusion, based on the given information, we can only say that events a and b are not mutually exclusive. We cannot determine whether they are dependent or independent without additional information.

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Answer: B. $29.25

Step-by-step explanation:

Given, Beginning price =  $24.75

Over the next 5 days,

On Monday, gain of  $2.50 represented by + $2.50.

On Tuesday, loss of $3.25 represented by - $3.25 .

On Wednesday,  loss of $0.75 represented by - $0.75.

On Thursday, gain of $1.25 represented by + $1.25.

On Friday, gain of $4.75 represented by + $4.75.

Price of the share of stock at the end of Friday = (Beginning price)+ ( + $2.50 - $3.25- $0.75+ $1.25+ $4.75)

= $( 24.75 + 2.50 -3.25 -0.75 +1.25 +4.75)

= $29.25

Hence, the correct option is B. $29.25.

True. Small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

Small p-values indicate that the observed sample data provides strong evidence against the null hypothesis. The p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test. It represents the probability of observing the obtained sample data, or more extreme data, if the null hypothesis is true.

When the p-value is small (typically less than a predetermined significance level, such as 0.05), it suggests that the observed sample data is unlikely to have occurred by chance under the assumption of the null hypothesis. In other words, a small p-value indicates that the observed data is inconsistent with the null hypothesis.

Conversely, when the p-value is large (greater than the significance level), it suggests that the observed sample data is likely to occur by chance even if the null hypothesis is true. In such cases, there is not enough evidence to reject the null hypothesis. Therefore, small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

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Answer:

The percentage of the students who have grade point averages that are no more than 1.82 is 2.5%

Step-by-step explanation:

The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviations from the mean and 99.7% are within three standard deviations from the mean.

Given that:

Mean (μ) = 2.62, Standard deviation (σ) = 0.4

68% are within one standard deviation = μ ± σ = 2.62 ± 0.4 = (2.22, 3.02)

95% are within two standard deviations = μ ± 2σ = 2.62 ± 2(0.4) = (1.82, 3.42)

The percentage of the students have grade point averages that are no more than 1.82 is 100% - [95% + (100% - 95%)/2] = 100% - 97.5% = 2.5%

The weighted average of a data set is 36.

Here,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

We have to find the weighted average of a data set.

What is Weighted Average?

Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set.

Now,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

The weighted average is given by the formula;

\(x = \frac{f_{1} x_{1} + f_{2} x_{2}+ f_{3} x_{3}+ ...... f_{n} x_{n}}{f_{1} +f_{2} + f_{2}}\)

Hence,

The weighted average of a data set;

x = 20 x 3 + 40 x 5 + 50 x 2 / 3+5+2

x = 360/10 = 36

Hence, The weighted average of a data set is 36.

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Answer:

ux² + 3x²

Step-by-step explanation:

( u + 3 )x²

= ( u*x² ) + ( 3*x² )

= ux² + 3x²

Answer the question 1st:

1-corresponding angles=180

then,90+90=180

2-not parallel

3-not parallel

4-corresponding angles=180

          x+x=180

          2x=180

          x=180/2

          x=90degree

5-suppose x for two angles

then, same as 4 no. x + x=180

6= alternate angles are always equal.

Answer:

12 i think

Step-by-step explanation:

Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer

Answer:

When writing your own two-column proof, keep these things in mind:

Number each step.

Start with the given information.

Statements with the same reason can be combined into one step. ...

Draw a picture and mark it with the given information.

You must have a reason for EVERY statement.

Step-by-step explanation:

The cross-tabulation analysis is the analytical technique that assesses the statistical significance of categorical variable relationships.

If you are doing research analysis and want to compare the results of one or more variables with the results of another variable, there is only one solution i.e. cross-tabulation or crosstab.

For reference, a crosstab is a two (or more) dimensional table that records the number (frequency) of respondents with certain characteristics described in the table cells. Crosstabs provide a wealth of information about relationships between variables.

Cross-tabulation analysis has its own terminology, using terms such as 'banner', 'stub', 'chi-square statistic', and 'expected value'.

Cross-tabulation analysis (also cross-tabulation or crosstabs) is one of the most useful analytical tools and a workhorse in the market research industry.

Cross-tabulation analysis, also called contingency analysis, is most commonly used to analyze categorical (nominal measurement scale) data.

A cross-tabulation analysis is basically just a table of data that shows the results for an entire group of respondents and the results for a subgroup of respondents. This allows you to explore relationships in your data that aren't immediately apparent by just looking at the overall survey responses.

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Answer:

\(2b - 3ac \\ a = 5 \: \: \: \: b = - 2 \: \: \: c = - 2 \\( 2 \times - 2 )- (3 \times 5 \times - 2) \\ (- 4) - ( - 30) \\ - 4 + 30 = 26\)

Answer:

x=-6, y=1

Step-by-step explanation:

Let's solve your system by substitution.

y=x+7;−2x−11=y

Step: Solve y=x+7 for y:

y=x+7

Step: Substitute x+7 for y in −2x−11=y:

−2x−11=y

−2x−11=x+7

−2x−11+−x=x+7+−x(Add -x to both sides)

−3x−11=7

−3x−11+11=7+11(Add 11 to both sides)

−3x=18

−3x/ −3 = 18/ −3  (Divide both sides by -3)

x=−6

Step: Substitute−6 for x in y=x+7:

y=x+7

y=−6+7

y=1  (Simplify both sides of the equation)

Answer:

x=−6 and y=1

the orthonormal basis for the subspace is {(0, 24/25, 7/25), (0, 0.997, 0.077)}.

The given basis is B = {(0, 24, 7), (0, 0,5)}

Let the given vectors in the order be v1 and v2. Then, v1 = (0, 24, 7) and v2 = (0, 0, 5)

The Gram-Schmidt orthonormalization process to transform the given basis for a subspace of Rn into an orthonormal basis for the subspace is given below;

Orthogonalization

Step 1:Normalize the first vector v1 by dividing it by its magnitude ║v1║v1= (0, 24, 7)U1= v1 / ║v1║= v1 / √(0+576+49)= v1 / √625= (0, 24/25, 7/25)

Step 2:Project the second vector v2 onto U1b2= v2 - (v2 • U1)U1b2= (0, 0, 5) - [(0, 0, 5) • (0, 24/25, 7/25)](0, 24/25, 7/25)

U1b2= (0, 0, 5) - (7/5)(0, 24/25, 7/25)U1b2= (0, 0, 5) - (168/125)(0, 24, 7)U1b2= (0, 0, 5) - (0, 32256/15625, 9408/15625)

U1b2= (0, -32256/15625, 221/625)

Normalizing U1b2 by dividing it by its magnitude;U2= U1b2 / ║U1b2║= (-0, 0.997, 0.077)Therefore, U1= (0, 24/25, 7/25) and U2= (0, 0.997, 0.077).

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