If you ate 1/5 of the desert served at
dinner, what percent of the food did you
eat?

The mean outcome for these 10 games with a spread between 3.5 and 6.5 is 4.95.

To find the mean of the outcomes of games with a spread between 3.5 and 6.5, we need to know the outcomes of all the games within that range.

Assuming that we have a set of data containing the outcomes of all games with a spread between 3.5 and 6.5, we can calculate the mean by summing up all the outcomes and dividing by the total number of games.

For example, let's say we have the following outcomes for 10 games with spreads between 3.5 and 6.5:

Game 1:  4.5

Game 2: 5.5

Game 3: 6.5

Game 4: 4.0

Game 5: 3.5

Game 6: 5.0

Game 7: 6.0

Game 8: 3.5

Game 9: 4.5

Game 10: 5.5

To find the mean outcome, we add up all the outcomes and divide by 10:

(4.5 + 5.5 + 6.5 + 4.0 + 3.5 + 5.0 + 6.0 + 3.5 + 4.5 + 5.5) / 10 = 4.95

Therefore, the mean outcome for these 10 games with a spread between 3.5 and 6.5 is 4.95.

It's important to note that this calculation assumes that all the games within the given spread are equally represented in the dataset, and that there are no significant outliers or anomalies that may skew the mean outcome.

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Answer:

Solve for

x

x

by simplifying both sides of the equation, then isolating the variable.

x

≈

0.25181781

Step-by-step explanation:

From the orthogonal basis of the given set, the values of a,b, and c can be obtained as:

a = 47/13, b = -4/13 and c = 162/13.

We use the basic principles of the Gram-Schmidt process to solve this question.

As we know, the vectors of the orthogonal basis are defined as:

v₁ = u₁ = [1, 3, 0]

v₂ = u₂ - proj(v₁, u₂)

v₃ = u₃ - proj(v₁, u₃) - proj(v₂, u₃)

We ultimately need v₃, but for that, we have to evaluate v₂.

v₂ = u₂ - proj(v₁, u₂)

= u₂ - ((u₂ · v₁) / (v₁ · v₁)) * v₁                  (Expression for Projection)

= u₂ - (([-30, 10, 40] · [1, 3, 0]) / ([1, 3, 0] · [1, 3, 0])) * [1, 3, 0]

= u₂ - ((-30 + 30 + 0) / (1 + 9 + 0)) * [1, 3, 0]

= u₂ - (0 / 10) * [1, 3, 0]

= u₂

= [-30, 10, 40].

Now, as we have v₂, we proceed with the expression for v₃, by substituting the values.

v₃ = u₃ - proj(v₁, u₃) - proj(v₂, u₃)

= u₃ - ((u₃ · v₁) / (v₁ · v₁)) * v₁ - ((u₃ · v₂) / (v₂ · v₂)) * v₂

= u₃ - (([4, -3, 2] · [1, 3, 0]) / ([1, 3, 0] · [1, 3, 0])) * [1, 3, 0] - (([4, -3, 2] · [-30, 10, 40]) / ([-30, 10, 40] · [-30, 10, 40])) * [-30, 10, 40]

= u₃ - ((4 + (-9) + 0) / (1 + 9 + 0)) * [1, 3, 0] - ((4*(-30) + (-3)10 + 240) / ((-30)² + 10² + 40²)) * [-30, 10, 40]

= u₃ - ((-5) / 10) * [1, 3, 0] - ((-120 + (-30) + 80) / (900 + 100 + 1600)) * [-30, 10, 40]

= u₃ - (-1/2) * [1, 3, 0] - (-70 / 2600) * [-30, 10, 40]

= u₃ + (1/2) * [1, 3, 0] + (7/26) * [-30, 10, 40]

= [4, -3, 2] + (1/2) * [1, 3, 0] + (7/26) * [-30, 10, 40]

= [4, -3, 2] + [1/2, 3/2, 0] + [-210/26, 70/26, 280/26]

= [4, -3, 2] + [1/2, 3/2, 0] + [-105/13, 35/13, 140/13]

= [4 + 1/2 - 105/13, -3 + 3/2 + 35/13, 2 + 0 + 140/13]

= [47/13, -4/13, 162/13].

(Note: It's better if this calculation is done in parts, and the final solution is assembled at the end)

So, the vectors v₁, v₂, and v₃ form an orthogonal basis when:

v₁ = [1, 3, 0]

v₂ = [-30, 10, 40]

v₃ = [47/13, -4/13, 162/13]

Therefore, the corresponding values of a, b, and c are:

a = 47/13

b = -4/13

c = 162/13

(The clear question has been attached for convenience)

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The computation shows that the placw on the hill where the cannonball land is 3.75m.

To find where on the hill the cannonball lands

So 0.15x = 2 + 0.12x - 0.002x²

Taking the LHS expression to the right and rearranging we have:

-0.002x² + 0.12x -.0.15x + 2 = 0.

So we have -0.002x²- 0.03x + 2 = 0  

I'll multiply through by -1 so we have

0.002x² + 0.03x -2 = 0.

This is a quadratic equation with two solutions x1 = 25 and x2 = -40 since x cannot be negative x = 25.

The second solution y = 0.15 * 25 = 3.75

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Complete question:

The flight of a cannonball toward a hill is described by the parabola y = 2 + 0.12x - 0.002x 2 . the hill slopes upward along a path given by y = 0.15x. where on the hill does the cannonball land?

First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

The system of equations is:

2b + 4.25s = 53.75

b - s = 5  

The number of bagels bought is 12 and the number of sandwiches bought is 7.

2b + 4.25s = 53.75 equation 1

b - s = 5  equation 2

Where:

The elimination method would be used to determine the required values.

Multiply equation 2 by 2

2b - 2s = 10 equation 3

Subtract equation 3 from equation 1 :

6.25s = 43.75

Divide both sides of the equation by 2.25

s = 43.75 / 6.25

s = 7

Substitute for s in equation 1:

2b + 4.25(7) = 53.75

2b + 29.75 = 53.75

2b = 53.75 - 29.75

2b = 24

b = 24 / 2

b = 12

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Answer:

69.8°

Step-by-step explanation:

Since cosФ = -0.3456

Ф = cos⁻¹(-0.3456)

Ф = 110.2°

Since the angles are supplementary, let the acute angle be x

So, x + 110.2° = 180°

x = 180° - 110.2°

x = 69.8°

Answer:

x-8≤17

x ≤ 25

The rate of change (slopes) and initial value (y-intercepts) are as follows:

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

By critically observing the graph which models the given data, we can logically deduce the following rate of change (slopes) and initial value (y-intercepts):

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Answer:

107.72

Step-by-step explanation:

We Know

After buying some marble for 98.00, Frances has 9.72 left.

How much money did Frances have to begin with?

We Take

98 + 9.72 = 107.72

So, Frances has 107.72 at the beginning.

The value of the product expression -3w⁸(-9w) is 27w⁹

From the question, we have the following product expression that can be used in our computation:

-3w^8(-9w)

Rewrite the expression properly

This is represented as

-3w⁸(-9w)

Remove the bracket

So, we have the following representation

-3w⁸(-9w) = -3w⁸ * -9w

Evaluate the product of the constants

-3w⁸(-9w) = 27w⁸ * w

Evaluate the product of the variables

-3w⁸(-9w) = 27w⁹

Hence, the product is 27w⁹

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A) The measure of central tendency that best describes the data for time spent on the internet (min/day) is the median.

The median is the middle value in a set of data when the data is arranged in numerical order. In this case, the data arranged in numerical order is 38, 43, 48, 52, 65, 75, 120. The median value is 52, which is the middle value in the data set.

B) The measure of central tendency that best describes the data for the weight of books (oz) is the mode. The mode is the value that occurs most frequently in a data set. In this case, the data is 12, 10, 9, 15, 16, 10. The mode is 10, as it occurs twice in the data set and is the most frequent value.

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1. The most likely color for the taxi = green

2. The probability that the taxi is blue = 0.25

Let us assume that tg represents the taxi was green and tb represents the taxi was blue;

Also yg represents the taxi appeared green and yb  represents the taxi appeared blue.

9 out of 10 athenian taxis are green

So, P(tg) = 0.90

And, P(tb) = 1 - P(tg)

                = 1 - 0.90

                = 0.10

As under the dim lighting conditions, discrimination between blue and

green is 75% reliable,

P(yb | tb) = 0.75.

So, P(yg | tb) = 1 - P(yb | tb)

                     = 0.25

Similarly P(yg | tg) = 0.75

Thus, P(yb | tg) = 1 - P(yg | tg)

                         = 0.25

P(tb | yb) = P(tb, yb) / P(yb)

               = [P(yb | tb) P(tb)] / [P(yb, tg)P(tg) + P(yb | tb) P(xb)]

               = 0.25

Thus the probability that the taxi is blue = 0.25

P(tg | yb) = 1 - P(tb | yb)

              = 0.75

We can observe that P(tb | yb) > P(tb) but the posterior P(tb | yb) is smaller than 0.5, since the prior P(tb) is very small. Thus, the taxi was most likely green.

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The complete question is:

Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens.All taxi cars in Athens are blue or green. You swear under oath that the taxi was blue.Extensive testing shows that, under the dim lighting conditions, discrimination between blue and green is 75% reliable.

1. is it possible to calculate the most likely color for the taxi? (*hint:* distinguish carefully between the proposition that the taxi *is* blue and the proposition that it *appears* blue.)

2. what is the probability of the taxi being blue, if you know that 9 out of 10 athenian taxis are green?

Step-by-step explanation:

9 4/5. Step-by-step explanation: 7 1/2 + 2 3/10 = 9 8/10 = 9 4/5. klondikegj and 1 more users found this answer helpful. Thanks 1.

Answer:

28980

Step-by-step explanation:

since 1035: nb of apps uploaded \ 28:days

then ; the rule of whole number multiplication is

1035×28=28980( nb of apps×days)

Answer:

y = 2x + 1

Step-by-step explanation:

The gradient of line A is

\(\frac{-6-(-2)}{0-2}=2\)

Parallel lines have the same gradient, so m = 2.

Substituting the coordinates of P into y = mx + c,

\(7=3(2)+c \implies c=1 \implies y=2x+1\)

Answer:

160 square inches

Step-by-step explanation:

step1 : find the area of the square base;

A = 8×8

=64 square inches

step2 : find the are of the triangle:

A=1/2×base×height

=1/2×8×6

=24 square inches

step3 : there are 4 triangles, so you need to find the total area of the 4 triangles:

A=24×4

=96 square inches

step4 : add the area of the square base and total area of the triangles:

A = 64+96

=160 square inches (Ans)

20 m longer  to walk from A to B along the diagonal of the park than to walk along the edges of the park.

What is rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. It can alternatively be described as a parallelogram with a right angle, an equiangular quadrilateral, or a group of triangles with equal angles. A square is a rectangle that has four equal sides.

As given, a park is in the shape of a rectangle and measures length of

40 m and width of 30 m, ∠B = 90°.

So, by Pythagoras theorem,

\(AC^2 = AB^2 + BC^2\\AC^2 = (40)^2 + (30)^2\\AC^2 = 1600 + 900\\AC^2 = 2500\\AC = \sqrt{2500}\\ AC = 50\)

So, the distance from A to B along the diagonal is,

AB = AC + BC = 50 + 40 = 90 m

The distance from A to B along with the edges is,

AB = AD + DC + CB = 40 + 30 + 40 = 110 m.

Therefore, 20 m longer  to walk from A to B along the diagonal of the park than to walk along the edges of the park.

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Answer:

3 2/3

Step-by-step explanation:

divide the 3 by 11 and your product is the whole number, with the remainder being the numerator.

11 / 3 = 9.2

9/3=3

3 2/3

The angles are x is 35° and y is 17° when the angles on protractor ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

Given that,

The angles are given ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

We have to find the angles.

An angle is formed when two straight lines or rays meet at a single terminal. The vertex of an angle is the point at which two points converge. ​The name "angle" comes from the Latin word "angulus," which meaning "corner." ​

The ∠QUS = ∠QUR + ∠RUS

57°=x+22°

x=57°-22°

x=35°

Now, ∠QUT = ∠QUR + ∠RUS + ∠SUT

74°=35°+22°+y
y=74-35-22

y=17°

Therefore, The angles are x is 35° and y is 17° when the angles are given ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

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Answer:

13.6 km/h?

Step-by-step explanation:

98 ÷ 7.2 = 13.61

Answer:

13.6 KM/H

Step-by-step explanation:

So we know the formula for speed is:

S = \(\frac{D}{T}\)

The s is for speed, d for distance and t for time

S=  \(\frac{98KM}{7.2 HRS}\)

S= 13.6111111

S= 13.6

Because 13.6111111 is too long we can round it off so the answer becomes 13.6km/h

HOPE IT HELPED

Answer:

Well the discount with 15% off is $2.25. Now subtract 15.00-2.25 to get 12.75. You are paying $12.75 for the discounted pizza.

Step-by-step explanation:

Answer: Initially it looks like Mindy is making a profit of $0.75 plus the pizza worth $12. So it is a fair deal for Mindy. Now coming to the part of the pizza shop owner, we find that he also gains extra $2.25 from this deal. So it is a fair deal for both the shop keeper and Mindy.

The length of \(CD\) is 2.

Since \(CD\) is tangent to the circle, then \(AD\perp CD\). Then, the triangle \(ABD\) is right angled. Thus, the length of \(CD\) is found by Pythagorean theorem:

\(AC = \sqrt{AD^{2}+CD^{2}}\)     (1)

If we know that \(AB = 1.5\), \(BC = 1\) and \(AD = 1.5\), then the length of \(CD\) is:

\(CD = \sqrt{AC^{2}-AD^{2}}\)

\(CD = \sqrt{2.5^{2}-1.5^{2}}\)

\(CD = 2\)

The length of \(CD\) is 2. \(\blacksquare\)

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0.5x + 6 = 4x - 1

3.5x = 7

x = 2

Only one solution exists for the given equation.

Answer:

one

Step-by-step explanation

For a polynomial function, the number of solutions, or zeros, is generally equivalent to the highest degree. For example, a cubic function (e.g. \(x^3+2x^2\)) has 3 real zeros (x=-2, x=0, and x=0) and a quadratic (e.g. \(x^2-1\)) has 2 real zeros (x=-1 and x=1).

For your problem, \(\frac{1}{2} (x+12)=4x-1\), the highest degree is 1 since this is a linear function. To prove there is only one solution, let's bring all the terms to one side, simplify, and solve for x.

There only one solution to the equation as shown above and as can be seen in step 4, the x is only to the first degree (\(x=x^1\)) which indicates that there is only one solution, 2.

The ratio of pencils to pens can be calculated by dividing the number of pencils by the number of pens. In this case, the ratio of pencils to pens is 10/14.

A ratio is a way to compare two or more values or quantities. It is expressed as a fraction or as a colon-separated pair of numbers. The first number in the ratio represents the number of units of the first quantity, and the second number represents the number of units of the second quantity.

In the case of the ratio of pencils to pens, the first quantity is the number of pencils and the second quantity is the number of pens. To calculate the ratio, you divide the number of pencils by the number of pens. In this case, you would divide 10 by 14, which is equal to 10/14 or 5/7.

The ratio can be expressed as either a fraction or as a colon-separated pair of numbers. In this case, the ratio of pencils to pens is either 5/7 or 5:7.

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AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:

75.36 is the answer.

Step-by-step explanation:

trust me bro.

Answer:

75.39822

Step-by-step explanation:

2πrh+2πr2=2·π·2·4+2·π·22≈75.39822

It said don't round your answer...

Layla visits 6 times to earn a free movie ticket.

According to the question,

Points received for Signing up = 60 points which can be referred  to as a constant.

Let x be the number of times Layla visits movie theatre.

Each visit earns her 11.5 points.

Therefore,  with each visit and number of times Layla earns 11.5x points

She requires 129 points for a free ticket.

So, from the above statements we can represent the following equation,

→ 11.5x + 60 = 129

Solving,

→ 11.5x = 69

→ 115x/10 = 69

→ x = 69 × 10/115

→ x = 6

Therefore, Layla must visit 6 times to earn a free movie ticket.

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