During gym class, there were 7 teams in the four-square match. Each team was made of 5 third-graders.
Which shows how many students were in the four-square match in all?

1. 5 times 5
2. 5 minus 7
3. 7 times 5
4. 7 plus 5

Using cross product, the vector can be proven as [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.

The vector OB can be expressed as OB = b since b is a unit vector and O is the origin.

The vector OA can be expressed as OA = 2b since the magnitude of a is twice that of b.

The angle between a and b is 60°, so we have:

|a| |b| cos 60° = a · b

2|b| · 1/2 = a · b

|b| = a · b

We can now express the vector [OB + (1 - O)A] as:

[OB + (1 - O)A] = b + (1 - O)2b

= (2 - O) b

The cross product of a and [OB + (1 - O)A] is:

a × [OB + (1 - O)A] = a × [(2 - O) b]

= (2 - O) (a × b)

The magnitude of the cross product is:

|a × [OB + (1 - O)A]| = |(2 - O) (a × b)|

= |2 - O| |a| |b| sin 60°

= √3 |2 - O| |b| |a| / 2

= √3 |2 - O| |b|^2 |b| / 2

= √3 |2 - O| |b|^3 / 2

Substituting |b| = a · b, we get:

|a × [OB + (1 - O)A]| = √3 |2 - O| (a · b)^3 / 2

Since |a × [OB + (1 - O)A]| is equal to √k for some constant k, we can set:

√k = √3 |2 - O| (a · b)^3 / 2

Squaring both sides, we get:

k = 3 (2 - O)^2 (a · b)^6 / 4

Therefore, [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.

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Answer:

14, 7, 0, -7.

Step-by-step explanation:

To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.

The expression for the nth term of the sequence is 7(3 - n).

Let's find the value of the first term (n = 1):

T₁ = 7(3 - 1) = 7(2) = 14

The first term of the sequence is 14.

Now, let's find the value of the second term (n = 2):

T₂ = 7(3 - 2) = 7(1) = 7

The second term of the sequence is 7.

Next, let's find the value of the third term (n = 3):

T₃ = 7(3 - 3) = 7(0) = 0

The third term of the sequence is 0.

Finally, let's find the value of the fourth term (n = 4):

T₄ = 7(3 - 4) = 7(-1) = -7

The fourth term of the sequence is -7.

Therefore, the first four terms of the sequence are:

To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.

The expression for the nth term of the sequence is 7(3 - n).

Let's find the value of the first term (n = 1):

T₁ = 7(3 - 1) = 7(2) = 14

The first term of the sequence is 14.

Now, let's find the value of the second term (n = 2):

T₂ = 7(3 - 2) = 7(1) = 7

The second term of the sequence is 7.

Next, let's find the value of the third term (n = 3):

T₃ = 7(3 - 3) = 7(0) = 0

The third term of the sequence is 0.

Finally, let's find the value of the fourth term (n = 4):

T₄ = 7(3 - 4) = 7(-1) = -7

The fourth term of the sequence is -7.

Therefore, the first four terms of the sequence are:

14, 7, 0, -7.

Based on the difference between the temperature when Casey went to bed and when he woke up, the temperature when he went to bed was 7 degrees, which was 12 degrees warmer than -5 degrees.

The temperature difference is determined using subtraction.

Subtraction is one of the four basic mathematical operations, involving the minuend, the subtrahend, and the result of the operation called the difference.

The temperature when Casey woke up to prepare for school = -5

The difference between the temperature when Casey went to bed and when he woke up = 12 degrees warmer.

The temperature when Casey went to bed = 7 degrees (12 - 5)

Thus, we can conclude that Casey had a temperature of 7 degrees when he went to bed but woke up when it was -5 degrees.

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Answer:

Step-by-step explanation:

To solve the equation 9x^2 - 36x = 0 by using the square root method, we first need to rearrange the terms to get x^2 and x on one side:

9x^2 - 36x = 0

Factor out 9x from the left-hand side:

9x(x - 4) = 0

Now we have two factors: 9x = 0 and x - 4 = 0. Solving for x in each factor gives us:

9x = 0: x = 0

x - 4 = 0: x = 4

Therefore, the solutions to the equation are x = 0 and x = 4.

Answer:

x = 0, x = 4

Step-by-step explanation:

Unfortunately, the equation 9x^2 - 36x = 0 cannot be solved using the square root method directly. The square root method is used to solve quadratic equations of the form ax^2 + bx + c = 0 by isolating the x^2 term, taking the square root of both sides, and solving for x. However, in the given equation, there is no constant term (c = 0), and therefore, we need to use a different method to solve it.

As I mentioned earlier, we can factor the equation and use the zero product property to solve for x. This method involves finding two factors of the quadratic equation that multiply to give 0, setting each factor equal to 0, and solving for x. In this case, we can factor out x and obtain the factors x and (9x - 36), which multiply to give 0. By setting each factor equal to 0 and solving for x, we obtain the solutions x = 0 and x = 4.

To solve the equation 9x^2 - 36x = 0 using the factorization method:

Factor out x from the left-hand side of the equation to get:

x(9x - 36) = 0

Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero and solve for x:

x = 0 or 9x - 36 = 0

For the second equation, solve for x:

9x - 36 = 0

9x = 36

x = 4

Therefore, the solutions to the equation are x = 0 and x = 4.

Note that this method involves factoring the quadratic equation and then using the zero product property to obtain the solutions. It works for any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a is not equal to zero.

Answer:

yes you are right

Step-by-step explanation:

move 4 to other side so its -3x=12

divide 12 by -3

x=-4

Answer:

429

Step-by-step explanation:

The areas of each part of the composite figure are;

Triangle A = 20 Square units

Triangle B = 2 Square units

Rectangle C = 4 Square units

Triangle D = 6 Square units

Area is a measurement of the two-dimensional surface of a shape or object. Area is often used when measuring the size of a plot of land or other physical space, such as a room or an outdoor area.

The area of each part of the figure can be found by adding the areas of the individual shapes that make up the figure. The area of a triangle can be found by using the formula A = 1/2bh, where b is the base and h is the height of the triangle. For a rectangle, the area is equal to the length multiplied by the width.

The composite figure's component parts' respective areas are;

20 Square Units = Triangle A

Triangle B = 2 units of the square

Square units = 4 for the rectangle C.

Triangle D = 6 units of the square

The formula for a triangle's area is straightforward;

A = 0.5 × base × height

Triangle A's area is;

Triangle A: (6 + 2 + 2) × 4 × 1/2

= ¹/₂ × 10 × 4

equals 20 square units

Triangle B's perimeter is;

Triangle A equals 1/2 × 2 × 2

equals 2 square units

Length × Width = Area of Rectangle C

= 2 × 2

equals 4 square units

Triangle D's area is;

Triangle D is equal to.5 × 6.

equals 6 square units

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Complete question -

hypotenuse^2 = 16^2 + 25^2

hypotenuse^2 = 256 + 625

hypotenuse^2 = 881

hypotenuse = sqrt(881)

hypotenuse ≈ 29.67 inches

Now that we know the length of the hypotenuse, we can use the 16-inch side and the hypotenuse as the base and height of the triangle, respectively. Plugging these values into the formula, we get:

Area = (16 x 29.67) / 2

Area ≈ 237.36 square inches

Therefore, the area of the triangle is approximately 237.36 square inches.

From the given information provided, the percent of yellow tint in the new mixture is 36.4%.

The total amount of yellow tint in the original mixture is:

0.30 × 50 liters = 15 liters

When 5 liters of yellow tint are added to the mixture, the total amount of yellow tint becomes:

15 + 5 = 20 liters

The total amount of new mixture is:

50 + 5 = 55 liters

To find the percentage of yellow tint in the new mixture, we divide the amount of yellow tint by the total amount of the mixture and multiply by 100:

(20/55) × 100 = 36.4%

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Answer:  1 hour 50 minutes  

Step-by-step explanation: it took her 2 hours to get home

she left home at 11:30 am it took her 45 minutes to jog to the park by the time she got to the park it was 12:15 pm she exercised for  1 hour and 55 minutes by the time she was done her work out it is 1:10 if she finished at 3 pm it took her 1 hour 50 minutes to get home

Answer:

2 ounces per person

Step-by-step explanation:

Using the binomial expansion theorem, the values of integers p and q are -8 and 24, respectively

From the question, we are to use the binomial expansion to expand the given expression and determine the values of p and q.

We can expand (1 - 2x)^4 using the binomial theorem as follows:

(1 - 2x)^4 = 1^4 - 4(1^3)(2x) + 6(1^2)(2x)^2 - 4(1)(2x)^3 + (2x)^4

= 1 - 8x + 24x^2 - 32x^3 + 16x^4

Now, we will compare this expression to the given expression

Comparing the expression to the given expression, 1 + px + qx^2 - 32x^3 + 16x^4

We see that:

p = -8

q = 24

Hence, the values p and q are -8 and 24, respectively.

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Answer:

  m∠2 = 35°

Step-by-step explanation:

You want to know the measure of angle 2 when angle 1 is 35° and both angles 1 and 2 intercept arc PQ.

Inscribed angles 1 and 2 both intercept the same arc: PQ. The problem statement tells you that such angles are equal.

  ∠2 = ∠1 = 35°

The measure of ∠2 is 35°.

__

Additional comment

This is a vocabulary and reading comprehension test.

In order to understand the comment and the question, you need to know the meaning of "inscribed angle", "intercept [an] arc", "equal" (as applied to angles). You also need to know the meaning of the notation m∠1, the measure of angle 1.

You pass the test when you understand the question is telling you that angles 1 and 2 are both 35°.

Z = X/Y is normally distributed because  the ratio of two independent normal variables is itself normally distributed and the same has been proved below:

To prove this, we can use the Central Limit Theorem. This theorem states that if X and Y are independently and identically distributed random variables, then the ratio of the two, Z = X/Y, will be normally distributed regardless of the distribution of X and Y. This is due to the fact that the ratio of two independent normal variables is itself normally distributed.

For example, let X and Y be two independent normal variables. Then their ratio Z = X/Y will follow a normal distribution. This means that the probability density function (pdf) of Z is given by:

f_Z(z) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{z^2}{2\sigma^2}}

where \sigma^2 = \frac{\sigma_x^2}{\sigma_y^2} is the variance of Z.

Therefore, we can conclude that Z = X/Y is normally distributed when X and Y are independent normal distributions.

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Based οn this pattern, we can determine the vοlume οf the next figure in the pattern by using a height οf 4 units: 1 x 1 x 4 = 4 cubic units.

A cube is three-dimensiοnal sοlid οbject that has six square faces οf equal size. It is special type οf rectangular prism in which all six faces are squares οf equal size. A cube has twelve edges οf equal length and eight vertices where three edges meet.

Let's analyze each figure separately and find the vοlume using the fοrmula fοr the vοlume οf a rectangular prism: length x width x height.

First figure: The length, width, and height are all 1 unit, sο the vοlume is 1 x 1 x 1 = 1 cubic unit.

Secοnd figure: The length and width are still 1 unit, but the height is nοw 2 units. Sο, the vοlume is 1 x 1 x 2 = 2 cubic units.

Third figure: The length and width are still 1 unit, but the height is nοw 3 units. Sο, the vοlume is 1 x 1 x 3 = 3 cubic units.

Frοm the analysis, we can see that the pattern is that the length and width οf each figure remain cοnstant at 1 unit, while the height increases by 1 unit fοr each successive figure.

Based οn this pattern, we can determine the vοlume οf the next figure in the pattern by using a height οf 4 units: 1 x 1 x 4 = 4 cubic units.

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Answer:

What's your question

Step-by-step explanation:

How many customers in each tower

For instance, f(x) is equal to 0.5 when x = 1 and equal to 1 when x = 2, function indicating that the amount of water collected rises by 0.5 for each unit increase in time.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

A. It appears that the function f(x) = 2x is exponential.

b. The function may be expressed as f(x) = a * bx, where a denotes the starting value, b the growth factor, and x the input value. As can be seen from the table, the values of f(x) = 2x are exponentially growing by a factor of 2 for each input.

d. A linear function may be used to simulate a tub that collects water from a leaking faucet since the amount of water collected grows steadily over time.

For instance, f(x) is equal to 0.5 when x = 1 and equal to 1 when x = 2, indicating that the amount of water collected rises by 0.5 for each unit increase in time.

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The eccentricity for r=5/2+1sin theta and  the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6

To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:

r = 5/2 + 1sin(θ)

r = 5/2 + 1y/r

r^2 = (5/2)r + y

x^2 + y^2 = (5/2)r + y

x^2 + y^2 = (5/2)√(x^2 + y^2) + y

x^2 - (5/2)√(x^2 + y^2) + y^2 = 0

We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:

x^2/a^2 + y^2/b^2 = 1

Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:

e = √(1 - b^2/a^2)

Plugging in our values, we get:

e = √(1 - 1/(5/2))

e = √(3/5)

e ≈ 0.5

Therefore, the answer is (A) 0.5.

To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:

r = 26.4/4 + 4.4cos(θ)

r = 6.6 + 4.4x/r

r^2 = 6.6r + 4.4x

x = (r^2 - 6.6r)/4.4

We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:

y = (1/4p)x^2

Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:

y = 1.65

However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:

x = 0

Therefore, the answer is (C) x = 6.

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The toe of which the triangle is , is called an isosceles triangle and a right angled triangle.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. There are different types of triangle , some of them are ;

Scalene triangle, isosceles triangle , equilateral triangle e.tc.

To know the type of triangle it is, we need to find the length of each sides.

let A = (2,1)

B = (4,7)

C = ( 6,3)

AB = √ (4-2)²+ (7-1)²

AB = √ 2²+ 6²

AB = √2+36

AB = √40

= 2√10

BC = √ (6-4)²+( 3-7)²

BC = √ 2²+4²

BC = √4+16

BC = √20

= 2√5

AC = √ (6-2)²+(3-1)²

AC = √4²+2²

AC =√ 16+2

AC = √20

= 2√5

therefore since AB² = BC² + AC ² ,the triangle is a right angled triangle

And also since two sides of the triangle are equal it is an isosceles triangle.

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Answer:

The answer is G

If Aaron is 8 years older than Judi, then Aaron's age is 22 years , Judi's age is 14 years and Maree's age is 7 years .

Let Maree's age be = M;

Judi is twice as old as Maree, which means ⇒ Judi's age is 2M;

And Aaron is 8 years older than Judi, which means

⇒ Aaron's age is (2M+8);

We know that the sum of their ages is 43, so we can write an equation:

⇒ M + 2M + (2M + 8) = 43

Simplifying and solving for M:

We get,

⇒ 5M + 8 = 43

⇒ 5M = 35

⇒ M = 7

So, Maree's age is 7 years.

Now, we use this to find Judi's and Aaron's ages:

⇒ Judi = 2M = 2 × 7 = 14

⇒ Aaron = 2M + 8 = 2 × 7 + 8 = 22

Therefore, Judi is 14 years old and Aaron is 22 years old.

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The cost price of the article when a profit of 22% is made after selling it for a certain price 's' can be calculated using the formula c = 0.78 * s.

Let's assume the cost price of the article is 'c'. Then, the profit made on selling the article is:

Profit = Selling price - Cost price

Since a profit of 22% was made on the selling price 's', we can express the selling price as:

Selling price = Cost price + Profit

= Cost price + 0.22 * Selling price

Rearranging this equation, we get:

0.78 * Selling price = Cost price

Substituting the given selling price 's' into this equation, we get:

0.78 * s = c

Therefore, the cost price of the article is 0.78 times the selling price. If we know the selling price 's', we can calculate the cost price 'c' using this formula. For example, if the selling price of the article is $100, then the cost price would be:

c = 0.78 * s

= 0.78 * $100

= $78

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The area of the triangle is 715.7 square units, rounded off to one decimal place.

The given triangle's side lengths and the angles are a = 52, B = 115°, and C = 29°. The area of the triangle can be determined by applying the formula:A = (1/2) a² sin B sin C, where a is the length of the side opposite to angle A.The area of the triangle is  (rounding off to one decimal place)Therefore, the area of the triangle is 715.7 square units, rounded off to one decimal place.

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Answer:

To determine the best value between chocolate bar A and B, we need to calculate the cost per gram of each chocolate bar.

For chocolate bar A, the cost per gram is:

$1.00 ÷ 80 grams = $0.0125 per gram

For chocolate bar B, the cost per gram is:

$1.20 ÷ 85 grams = $0.0141 per gram

Therefore, chocolate bar A is the better value as it costs less per gram compared to chocolate bar B. While chocolate bar B may weigh slightly more, its higher cost per gram means that you are paying more for each gram of chocolate compared to chocolate bar A.

1. The upper bound for the perimeter of the regular hexagon is 21.9 cm.

2. All figures on the calculator display for the calculation of Kelly's average speed is: 99.5 / 10.51 = 9.46717412

3. the lower bound for the area of the rectangle is 2.55 × 10⁵ mm²

4. Upper bound for area = 937.6525 cm²

1. The upper bound for the perimeter of the regular hexagon can be calculated by multiplying the length of one side by 6 (the number of sides in a hexagon):

Upper bound for perimeter = 6 × (3.6 + 0.05) = 21.9 cm (rounded to one decimal place)

2. Kelly's average speed can be calculated by dividing the distance she ran by the time she took:

Average speed = distance / time

The lower bound for the distance is 99.5 m (since 100 m was measured to the nearest meter, the actual distance could be as low as 99.5 m).

The lower bound for the time is 10.51 s (since 10.52 s was measured to the nearest hundredth of a second, the actual time could be as low as 10.51 s).

Therefore, the lower bound for Kelly's average speed is:

Average speed = 99.5 / 10.51 = 9.4617 m/s (rounded to 4 decimal places)

3. The length of the rectangle is 645 mm correct to the nearest 5 mm, which means it could be as small as 642.5 mm or as large as 647.5 mm. We can express this as:

645 mm ± 2.5 mm, similarly

400 mm ± 2.5 mm

Lower bound for length = 645 - 2.5 = 642.5 mm

Lower bound for width = 400 - 2.5 = 397.5 mm

Lower bound for area = 642.5 × 397.5 = 255393.75 mm²

Rounded to 3 significant figures, the lower bound for the area of the rectangle is 2.55 × 10⁵ mm².

4. To calculate the upper bound for the area of the rectangle, we need to multiply the upper bounds for the length and width of the rectangle:

Upper bound for length = 35 + 0.45 = 35.45 cm

Upper bound for width = 26 + 0.45 = 26.45 cm

Upper bound for area = 35.45 × 26.45 = 937.6525 cm²

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Answer:

cubic unit eg m³

Step-by-step explanation:

Raised to power 3

Answer:

Units cubed or unit^3

Explanation:

Volume= (base)(width)(height), therefore, this would be cubed. x^3

Area=(base)(height), therefore, this would be squared. x^2

Therefore , the solution of the given problem of probability comes out to be the medium addition because it has the greatest expected utility (0.72).

The primary goal of the structures within a methodology expression known as criteria is to provide an indication of the probability that the assertion is true or that a specific event will occur. Any number between zero and one, at which 0 is frequently indicated as a possibility and 1 has frequently used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.

Here,

The following formula can be used to determine each option's anticipated financial value:

=> EMV of big addition =  (0.4 * $100,000) plus (0.6 * -$40,000) for a total of $16,000.

=>  EMV of the middle addition is

= (0.4 * $40,000) plus (0.6 * -$10,000) for a total of $14,000.

=>  EMV of a minor addition =  (0.4 * 10,000) plus (0.6 * 5,000), which equals $6,000

The large addition should be chosen by the physicians as it has the greatest expected financial value of $16,000.

dividing each outcome's usefulness value by its likelihood, then adding the results:

=> (0.4 * 1.0) + (0.6 * 0.0) = 0.4 is the EU of the big addition.

=> (0.4 * 0.9) + (0.6 * 0.6) = 0.72 is the EU of medium addition.

Smaller EU =  (0.4 * 0.5) +  (0.6 * 0.6) = 0.58

The doctors should choose the medium addition because it has the greatest expected utility (0.72), according to expected utility theory.

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Answer:  B

Step-by-step explanation:

Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.

Base area of the bag = 4 × 2 = 8 in²

Base area of the candle = 2 × 1 = 2 in²

therefore, we know that base area to be filled with sand:

= 8 - 2 = 6 in²

now, height of sand is known to be between 1/2 and 3/4 inches,

therefore, we can make out that the volume of land is between 6 × 1/2 in³ and 6 × 3/4 in³

3 in³ and 4.5 in ³

therefore, amount of sand is between 3 cubic inches and 4.5 cubic inches, with this we know that Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.

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