If we are given an acute ∠A, side a, and side b, and the height of the triangle is h = bsin A, state the criteria needed for the following to happen:
No triangles when...
One triangle when... (2 answers)
Two triangles when...

Answer:

The answer to your problem is, A. D.

Step-by-step explanation:

Median: 75

Quartile Value: 85
Range: 40

We can use this info to make some inferences about the test scores in our dataset.

Firstly, the range of the test scores, is 40 points, so the lowest test score must be 75 - 20 = 55 points, and the highest test score must be 75 + 20 = 95 points. Therefore the highest test score is 95

The third quartile value is 85 points, which means that 75% of the test scores are less than or equal to 85 points. Since the median test score is 75 points, we can infer that 50% of the test scores are less than or equal to 75 points. Therefore, the remaining 25% of the test scores must be between 75 and 85 points. Thus, about 25% of test scores are in between 75 and 85. The third option is incorrect, as the lowest possible test score is 55 points, which is greater than 50 points.

Simplified expression of [tex]\rm (8/12)^{(x/y)} \times (x/y)[/tex] is ([tex]\rm 2^{y}[/tex])/([tex]\rm 3^{x/y^2}[/tex]).

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

Assuming you meant to write the expression as:

[tex](8/12)^{(x/y)}[/tex]* (x/y)

We can simplify it as follows:

First, we can simplify the fraction 8/12 to 2/3:

[tex](2/3)^{(x/y)}[/tex] * (x/y)

Next, we can apply the properties of exponents to simplify [tex](2/3)^{(x/y)}[/tex] as follows:

[tex](2/3)^{x/y}[/tex] = [tex](2^{x/y}/3^{x/y})^x[/tex]

= [tex]2^{x/y}[/tex]/[tex]3^{x/y}[/tex]

Substituting this back into the original expression, we get:

([tex]2^{x/y}[/tex]/[tex]3^{x/y}[/tex]) * (x/y)

= ([tex]2^{x/y*x}[/tex])/([tex]3^{x/y*y}[/tex])

= ([tex]\rm 2^{y}[/tex])/([tex]\rm 3^{x/y^2}[/tex]).

So the final simplified expression is ([tex]\rm 2^{y}[/tex])/([tex]\rm 3^{x/y^2}[/tex]).

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Complete question:

Factorize the given term to simplest form:

[tex]\rm (8/12)^{(x/y)} \times (x/y)[/tex]

Chau could rent the boat for 1, 2, 3, 4, 5, 6, or 7 hours and still spend less than $53.

To find out the possible number of hours Chau could rent the boat, follow these steps:
Apply the discount coupon: Chau has a $3 discount, so subtract that from the total amount he wants to spend, which is $53.

$53 - $3 = $50
Determine the maximum number of hours Chau can rent the boat:

The boat costs $7 per hour, so divide the adjusted total amount by the cost per hour.
$50 ÷ $7 ≈ 7.14 hours
Since Chau can't rent the boat for a fraction of an hour, he can rent it for a maximum of 7 hours.

List the possible number of hours: Starting from 1 hour (assuming Chau wants to rent the boat for at least an hour), list all the whole numbers up to the maximum number of hours determined.
Possible number of hours: 1, 2, 3, 4, 5, 6, 7.

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The value of m∠U in the circle is 168 degrees

The tangent of a circle is the line that touches the circle at only one point.

The tangent to a circle is always perpendicular to the radius. Therefore, it forms a right angle.

Therefore, let's use the theorem to find the angle m∠U

Hence,

m∠STU = 90 degrees

m∠UTV = 90 - 84 = 6 degrees

Therefore, the triangle STV is an isosceles triangle. This means the base angle is congruent .

Hence,

m∠SVT = 84 degrees

Therefore,

m∠U = 180 - 6 - 6

m∠U = 180 - 12

m∠U = 168 degrees

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The actual width of the soccer field will be around 70 yards.

We are given that the width of the soccer field in the drawing is 35 inches. To find the actual width of the soccer field, we need to use the scale provided. We can set up a proportion to relate the dimensions in the drawing to the actual dimensions:

1 inch ÷ 2 yards = 35 inches ÷ x

where x is the actual width of the soccer field in yards.

To solve for x, we can cross-multiply:

1 inch × x = 35 inches × 2 yards

Simplifying, we get:

x = (35 inches × 2 yards) ÷ 1 inch

x = 70 yards

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Answer:

Step-by-step explanation:

6

Answer:

$0.03 pretzels cost more than cost of bag of chips.

Step-by-step explanation:

price of 16 snack- size bags of chips = 7.84

Cost of 1 bag of chip = 7.84 /16  = $0.49

Price of 24 snack-size bags of pretzels = 12.48

Cost of 1 snack-size bags of pretzels = 12.48 / 24      = 0.52

$0.03 pretzels cost more than cost of bag of chips.

Answer: 20

Step-by-step explanation:

   First, we put the data values in order from least to greatest.

10 13 14 19 20 23 31 33 39

   Next, we will find the middle value of this list.

10 13 14 19 20 23 31 33 39

--- 13 14 19 20 23 31 33 ---

--- --- 14 19 20 23 31 --- ---

--- --- --- 19 20 23 --- --- ---

--- --- --- --- 20 --- --- --- ---

   The median is 20.

Answer:

The question seems to be incomplete. It mentions that Mr. Smith keeps track of his students' homework completion and how many boys and girls do not complete their homework. It also mentions that he puts students who don't complete their homework into two categories: first-time offenders and repeat offenders, and uses a table to keep track of the results[1][2]. However, it does not provide enough information to answer a specific question.

If you have a specific question related to this topic, please provide more details so that I can assist you better.

the probability that a bulb lasts longer than the advertised figure of 4100 hours is approximately 0.8413 or 84.13%.

The probability that a bulb lasts longer than the advertised figure can be found using the normal distribution formula. In this case, we have a mean of 4400 hours and a standard deviation of 300 hours. The advertised lifetime is 4100 hours. We will calculate the z-score and then use the standard normal distribution table to find the probability. Here's the step-by-step explanation:
Calculate the z-score: The z-score is a measure of how many standard deviations away from the mean a data point is. To calculate the z-score for the advertised lifetime (4100 hours), use the formula:
z = (X - μ) / σ
where X is the advertised lifetime (4100 hours), μ is the mean (4400 hours), and σ is the standard deviation (300 hours).
z = (4100 - 4400) / 300
z = -300 / 300
z = -1
Use the standard normal distribution table: Now that we have the z-score (-1), we can use the standard normal distribution table to find the probability that a bulb lasts longer than the advertised figure. Look for the value corresponding to -1 in the table, which is 0.1587.
Calculate the probability: The value we found in the standard normal distribution table (0.1587) represents the probability that a bulb lasts less than the advertised figure (4100 hours). To find the probability that a bulb lasts longer, we need to subtract this value from 1:
Probability (bulb lasts longer than advertised figure) = 1 - 0.1587
Probability (bulb lasts longer than advertised figure) = 0.8413

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Answer:

The first quartile ([tex]Q_{1}[/tex]) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.

Answer:

The first quartile (Q1) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.

Step-by-step explanation:

The equation of line "g" is y = (-3/4)x + 1. To find the equation of line "g" that goes through the points (-4, 4) and (4, -2), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we can find the slope of the line by using the slope formula, which is:

m = (y2 - y1) / (x2 - x1)

Using the coordinates of the two points given, we have:

m = (-2 - 4) / (4 - (-4)) = -6 / 8 = -3 / 4

Next, we can use the slope-intercept form and one of the two points to find the y-intercept, b. Using the point (-4, 4), we have:

4 = (-3/4)(-4) + b

4 = 3 + b

b = 1

Finally, we can substitute the values of m and b into the slope-intercept form to get the equation of line "g":

y = (-3/4)x + 1

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The measures shown, could the figure be a parallelogram: Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. This indicates that a parallelogram's opposing sides are parallel and congruent (the same length). Moreover, a parallelogram's opposing angles are congruent (have the same measure).

The following are some characteristics of parallelograms:

A parallelogram's opposing sides are parallel and congruent.

A parallelogram's opposing angles are congruent.

The parallelogram's subsequent angles are additional (their sum is 180 degrees).

A parallelogram's diagonals split each other in half (cut each other in half).

For the given quadrilateral to be a parallelogram the opposite sides need to be congruent.

Thus,

10 = x + 2

x = 8

Also,

2x - 3 = x + 5

2x - x = 5 + 3

x = 8

Hence, the measures shown, could the figure be a parallelogram: Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.

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If the math SAT scores followed a normal-distribution, then the probability that

(a) sample mean is less than 475 is 00.1151,

(b) sample mean is greater than 500 is 0.2119,

(c) sample mean is between 475 and 500 is 0.6730.

The mean score (μ) = 490, the standard-deviation (σ) = 50,

Part (a) :

The random sample of 16 people is selected,

So, σₓ = σ/√n = 50/√16 = 12.5,

⇒ P(x < 475) = P[ (x-μ)/σ < (475-490)/12.5],

⇒ P(z < -1.2) = 0.1151.

So, Probability that sample mean is less than 475 is 0.1151.

Part (b) :

The probability that the mean score is greater than 500 is written as :

⇒ P(x > 500) = 1 - P(x < 500) = 1 - P[z < (500 - 490)/12.5],

⇒ 1 - P(z < 0.8)

⇒ 1 - 0.7881 = 0.2119.

So, probability that mean score is greater than 500 is 0.2119.

Part (c) :

The probability that the mean score is between 475 and 500 is written as :

⇒ P[ (475 - 490)/12.5 < z < (500 - 490)/12.5 ],

⇒ P( -1.2 < z < 0.8)

⇒ P(z < 0.8) - P(z < -1.2)

From the normal table,

⇒ 0.7881 - 0.1151 = 0.6730,

So, probability that mean score is between 475 and 500 is 0.6730.

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Answer:

What kind of shape is it? a triangle???

Step-by-step explanation:

please provide the shape so i can help you

The rotation that we need to apply to CD is of 270° clockwise.

We want a clockwise rotation that maps CD in E'F'.

Remember that a rotation of 90° will move the figure from one quadrant to the previous one. We can see that E'F' is on the third quadrant. while CD is on the second qudrant, then we need to go from.

Second to first quadrant ---> 90°

First to fourth quadrant ---> 90°

Fourth to third quadrant ---> 90°

Adding these 3 we get.

90° + 90° + 90° = 270°

So we need to applly a rotation of 270° clockwise to CD.

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Answer:

23,381/160 or 146 21/160

Step-by-step explanation:

56 3/4 = 227/4

1 3/8 = 11/8

1 1/5 = 6/5

227/4( 11/8 + 6/5)

227/4(55/40 + 48/40)

227/4( 103/40) = 23,381/160 or 146 21/160

The number of student council members who like neither bowling nor ice skating is 27.

Let's denote the following:

We are given the following information:

c = 3 * b (number of students who like bowling but not ice skating is triple the number who like ice skating but not bowling)

50% of students like one but not both activities, so (b+c)/72 = 0.5

9 students like both activities, so d = 9

The total number of students is 72.

Let's solve for a, b, and c:

From (2), we have b + c = 36.

From (1), we can rewrite c as c = 3b.

Substituting this into the equation from (2), we get:

b + 3b = 36

4b = 36

b = 9

Now, we can find the value of c:

c = 3b = 3 * 9 = 27

Finally, we can find the value of a.

We know that a + b + c + d = 72:

a + 9 + 27 + 9 = 72

a + 45 = 72

a = 27

Therefore, the number of student council members who like neither bowling nor ice skating is 27.

The correct answer is not among the options provided.

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When a vertical line intersects the graph of a function more than once, it indicates that for that output there is more than one input, which means the function is not a relation.  (option b).

In mathematics, functions are an essential concept used to describe relationships between sets of numbers. A function is a set of ordered pairs, where each input corresponds to exactly one output.

Conversely, if every vertical line intersects the graph at most once, then the graph represents a function. This is because there is only one output for each input, satisfying the definition of a function.

It's important to note that not all relations are functions. A relation is a set of ordered pairs, while a function is a relation where each input corresponds to exactly one output.

Therefore, if a vertical line intersects a graph more than once, it indicates that there is more than one output for that particular input, and the relationship is not a function.

Hence the option (b) is correct.

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Answer:

( -1, -1)

Step-by-step explanation:

We see on the graph, point x is located at (-1,-1)

We can write the quadratic expression 10x^2 + tx + 8 as:

10x^2 + tx + 8 = 10x^2 + (a+b)x + ab

where a and b are constants that we want to determine, and (a+b)x is the middle term in the quadratic expression.

We can factor 10 as 25 and 8 as 22*2, so we have:

10x^2 + tx + 8 = (2x + c)(5x + d)

where c and d are the constants that we need to determine.

Expanding the right-hand side of this equation, we get:

(2x + c)(5x + d) = 10x^2 + (2d+5c)x + cd

Comparing this to the original expression, we see that:

2d + 5c = t

cd = 8

We can use these equations to solve for c and d in terms of t:

c = (t - 2d)/5

d = 8/c

Substituting d in terms of c in the first equation, we get:

2(8/c) + 5c = t

Multiplying through by c, we get a quadratic equation in c:

16 + 5c^2 = tc

We want this equation to have real solutions for c, so the discriminant must be non-negative:

25t^2 - 80 >= 0

Solving this inequality for t, we get:

t <= -8/5 or t >= 8/5

Therefore, the quadratic expression 10x^2 + tx + 8 can be written as the product of two binomials for all values of t less than or equal to -8/5 or greater than or equal to 8/5.

To determine which team typically has the tallest players, we need to compare the measures of center for each team. Since the data sets have outliers, it's better to use the median as a measure of center.

Calculating the median for each team:

Allstars: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.

Champs: arrange the heights in order from smallest to largest: 58, 60, 60, 65, 67, 67, 68, 69, 70, 70, 75. The median is the middle value, which is also 68 inches.

Since both teams have the same median height of 68 inches, we can't say that one team typically has taller players than the other based on this measure alone. Therefore, neither option (C) nor (D) is correct. Instead, we need to choose between options (A) and (B) based on the mean height for each team.

Calculating the mean for each team:

Allstars: add up all the heights and divide by the total number of players: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 1006/15 ≈ 67.1 inches.

Champs: add up all the heights and divide by the total number of players: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 996/15 ≈ 66.4 inches.

Thus, the team with the higher mean height is the Allstars, so the correct answer is option (A): "The Allstars, with a mean of about 67.1 inches."

Answer:

A.) w=P/2-l

Step-by-step explanation:

Part A.)

P=2(l+w)

P/2= l+w

P/2-l= w

w=P/2-l

Part B.) In order to get (l+w) by itself, so I could subtract l, I had to divide both sides by two. Then I was able to subtract l from both sides to get just w on the right.

Answer:

Always need to do research to improve your studies

The effective annual yield is approximately 3.164%.

Answer:

45618.7

Step-by-step explanation:

[tex]f = p \times (1 + r \n) ^{nt} = f \: 43000[/tex]

If Julian wrote the last term as -3x⁴ instead of -3x², then the first term of the polynomial in standard form would be:

3x⁴ + 6y⁴ + 5x²y² - 10xy³ + 9x³y - 214. The correct option is B.

It should be noted that to simplify the polynomial and write it in standard form, we need to combine like terms and arrange them in descending order of their exponents.

First, we can combine the like terms of x²y²

4x²y² + x^2y² = 5x²y²

Next, we can combine the like terms of xy³:

-8xy³ - 2xy³ = -10xy³

Then, we have the following terms left:

9x³y, 6y⁴, -3x² -214

To write this polynomial in standard form, we need to arrange the terms in descending order of their exponents:

6y⁴ + 5x²y² - 10xy³ + 9x³y - 3x² - 214

If Julian wrote the last term as -3x^4 instead of -3x^2, then the first term of the polynomial in standard form would be:

3x⁴ + 6y⁴ + 5x²y² - 10xy³ + 9x³y - 214

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Answer: Sure, I'd be happy to help you with these questions! Here are the solutions:

To find the area of R, we need to find the points of intersection between the two curves.

Setting y = 3sin(2x) and y = e^x equal to each other, we get:

3sin(2x) = e^x

Taking the natural logarithm of both sides, we get:

ln(3sin(2x)) = x

Now, we can find the x-coordinates of the intersection points by graphing the two curves or using a numerical method, such as a graphing calculator or Newton's method. The intersection points are approximately x = 0.306 and x = 2.313.

To find the area of R, we can integrate the difference between the two curves with respect to x:

A = ∫(e^x - 3sin(2x)) dx from x = 0.306 to x = 2.313

This integral can be evaluated using integration by substitution or a numerical method, such as a calculator or computer software. The area of R is approximately 2.828 square units.

To find the volume of S, we can use the formula for the volume of a solid of revolution:

V = ∫πy^2 dx from x = 0.306 to x = 2.313

Here, y = e^x - 3sin(2x) is the radius of the cross sections of the solid generated by rotating R around the x-axis.

This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of S is approximately 41.201 cubic units.

To find the volume of Q, we can use the formula for the volume of a solid of revolution around a horizontal line:

V = ∫π(y - 5)^2 dx from x = 0.306 to x = 2.313

Here, y = e^x - 3sin(2x) is the distance from the horizontal line y = 5 to the cross sections of the solid generated by rotating R around the line y = 5.

This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of Q is approximately 14.503 cubic units.

To find the volume of P, we can use the formula for the volume of a solid with known cross-sectional area:

V = ∫A(x) dx from x = 0.306 to x = 2.313

Here, the cross sections of P are semicircles perpendicular to the x-axis. The radius of each semicircle is given by:

r = (1/2)(e^x - 3sin(2x))

So the area of each semicircle is:

A = (1/2)πr^2 = (1/8)π(e^x - 3sin(2x))^2

Therefore, the volume of P is:

V = ∫(1/8)π(e^x - 3sin(2x))^2 dx from x = 0.306 to x = 2.313

This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of P is approximately 5.654 cubic units.

I hope this helps! Let me know if you have any further questions.

Step-by-step explanation:

Cos u - cos u sin²u simplifies to cos³(u). We can solve it in the following manner.

Starting with the expression Cos u - cos u sin²u, we can factor out cos(u) to get:

Cos u - cos u sin²u = cos(u) (1 - sin²(u))

Using the identity sin²(u) + cos²(u) = 1, we can substitute cos²(u) for 1 - sin²(u):

cos(u) (1 - sin²(u)) = cos(u) cos²(u) = cos³(u)

Therefore, Cos u - cos u sin²u simplifies to cos³(u).

In mathematics, a factor refers to a number, algebraic expression, or function that divides or multiplies with another number, algebraic expression, or function without leaving a remainder. For example, in the expression 12x, 12 is a factor of the expression because it can be divided evenly by 12.

In algebra, factoring is the process of finding the factors of an algebraic expression, which means breaking it down into simpler parts that can be multiplied together to get the original expression. Factoring is an important skill in algebra, as it allows us to simplify and solve equations, identify common factors, and manipulate expressions more easily.

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