If
α
and
β
are the other angles of a right angled triangle, show that
sin2α=sin2β
. 13 Write
3sinx−5cosx
in the form
kcos(x+a)
where
k>0
and
0

The maximum number of sports drinks that can be purchased for $80 is 90 when they are priced at $0.70 per drink. (option B)

Let's start by finding the number of sports drinks that can be purchased for $80 when they are priced at $0.80 per drink.

The price of each drink is $0.80, and the shipping and handling cost is $10.

Let x be the number of sports drinks that can be purchased for $80:

0.80x + 10 = 80

Subtracting 10 from both sides:

0.80x = 70

Dividing both sides by 0.80:

x = 87.5

Since we cannot purchase a fraction of a sports drink, we must round down to the nearest whole number, which is 87.

Now let's check if we can purchase more sports drinks for $80 when they are priced at $0.70 per drink.

The price of each drink is $0.70, and the shipping and handling cost is $17.

Let y be the number of sports drinks that can be purchased for $80:

0.70y + 17 = 80

Subtracting 17 from both sides:

0.70y = 63

Dividing both sides by 0.70:

y = 90

Since we cannot purchase a fraction of a sports drink, we must round down to the nearest whole number, which is 90.

Therefore, the maximum number of sports drinks that can be purchased for $80 is 90 when they are priced at $0.70 per drink.

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To find (f ∘ g)(x), we need to substitute g(x) into f(x) wherever we see x in the expression for f(x).

So we have:

f(g(x)) = f(3x + 1) = (3x + 1)^2 - 8 = 9x^2 + 6x - 7

Therefore, the correct answer is: 9x^2 + 6x - 7.

Answer:

Circumference = 37.7 feet

Step-by-step explanation:

Use these formulas, then solve for the answer

C=2πr

d=2r

C = π times d

C = π times 12

C = 37.699

The inequality of the scenario is 8.50n + 9 ≤ 43

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

Amount = $43

The cost of n books and 4 pens can be expressed as:

8.50n + 2.25(4)

We can simplify this expression:

8.50n + 9

We know the student has a total of $43 to spend, so we can set up an inequality:

8.50n + 9 ≤ 43

Subtracting 9 from both sides, we get:

8.50n ≤ 34

Dividing both sides by 8.50, we get:

n ≤ 4

Hence, the inequality that best represents the scenario is: n ≤ 4 or 8.50n + 9 ≤ 43

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Complete question

For this item, select the answers from the drop-down menus A student has $43 in total to buy books that cost \$8.50 each and pens that cost $2.25 each. The student buys n number of books and 4 pens

Complete the inequality to best represent the scenario.

Answer:

24+2x

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = 24+2x

55.5% is equivalent to 5/9.

percentage, a relative value indicating hundredth parts of any quantity.

A baseball team won of its games of  5/9 this season.

We need to find the equivalent percentage of 5/9.

To convert 5/9 to a percentage, we can multiply it by 100.

(5/9) x 100 = 55.5%

So, the percentage equivalent to 5/9 is 55.5%.

Therefore, 55.5% is equivalent to 5/9.

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A1. We can use Gaussian Elimination to determine if the system has a unique solution, infinite many solutions, or no solution. Gaussian Elimination is a method of solving linear equations by reducing a system of equations to a simpler form.

First, we need to write the system of equations in matrix form:

| 2 4 3 | | x1 | = | f |
| 1 d -3 | | x2 | = | g |
| 1 2 c | | x3 | = | h |

Next, we will use Gaussian Elimination to reduce the matrix to row echelon form:

| 1 2 c | | x1 | = | h |
| 0 (d-2) (-3-c) | | x2 | = | (g-h) |
| 0 (4-2d) (3-2c) | | x3 | = | (f-2h) |

Now, we can check for the conditions that determine the number of solutions:

1. If the rank of the coefficient matrix is less than the rank of the augmented matrix, then the system has no solution.

2. If the rank of the coefficient matrix is equal to the rank of the augmented matrix, and the rank is equal to the number of variables, then the system has a unique solution.

3. If the rank of the coefficient matrix is equal to the rank of the augmented matrix, and the rank is less than the number of variables, then the system has infinite many solutions.

In this case, if (d-2) ≠ 0 and (4-2d) ≠ 0, then the system has a unique solution. If (d-2) = 0 and (4-2d) = 0, then the system has infinite many solutions. If (d-2) = 0 and (4-2d) ≠ 0, or (d-2) ≠ 0 and (4-2d) = 0, then the system has no solution.

Therefore, we can find a relation which gives a unique solution or infinite many solutions by using Gaussian Elimination and checking the conditions for the number of solutions.

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Answer:

10

Step-by-step explanation:

To find out how many students participate in both sports and music, we can use the formula:

Total = Group A + Group B - Both

where "Total" is the total number of students participating in sports or music, "Group A" is the number of students participating in sports, "Group B" is the number of students participating in music, and "Both" is the number of students participating in both.

Plugging in the given values, we get:

Total = 100

Group A = 60

Group B = 50

Both = ?

100 = 60 + 50 - Both

Simplifying the equation, we get:

Both = 60 + 50 - 100

Both = 10

Therefore, 10 students participate in both sports and music.

The value of the painting at t = 4 is $400 (V(4) = $400) and the value of the painting at t = 6 is $800 (V(6) = $800).

To find the value of the painting at t = 4 and t = 6, we can simply plug in these values into the function V(t) = 100 • 2^t/2, for t >= 0 where t is the number of years since the painting was purchased, and V(t) is its value (in dollars) at time t, and simplify.

For t = 4, we have:
V(4) = 100 • 2^4/2
V(4) = 100 • 2^2
V(4) = 100 • 4
V(4) = 400

For t = 6, we have:
V(6) = 100 • 2^6/2
V(6) = 100 • 2^3
V(6) = 100 • 8
V(6) = 800

Therefore, V(4) = $400 and V(6) = $800.

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The main of the given function f(x) is all real numbers except x=-4.

To find the main, we need to find the roots of the function. That is, we need to find out the values of x for which the value of f(x) is equal to 0.


Solving for the roots, we get the following equation:
8x2-9x+1=0


Solving this equation using the quadratic formula yields:
x = (-9 ± √73)/16


Therefore, the roots of the equation are:
x = 0.41 and -4.41


Since the only root which belongs to all real numbers is x = -4, it is the main of the given function.

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Part A: The height of the container is 5cm.

Part B: The cost of the coffee is $2.83.

Part C: The height of the container is 9cm.

Part D: The cost of the hot chocolate powder is $49.35.

What is volume of cylinder ?

The volume of a cylinder is the amount of space occupied by a cylindrical shape. It is given by the formula:

V = πr²h

where V is the volume, r is the radius of the circular base of the cylinder, and h is the height of the cylinder. The formula is derived by multiplying the area of the circular base (πr²) by the height (h) of the cylinder.

According to the question:
Part A:

Given that the container is a cylinder with a radius of 3cm, we can use the formula for the volume of a cylinder to find the height of the container. The formula for the volume of a cylinder is:

V = πr²h

where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the given values, we get:

45π = π(3)²h

Simplifying and solving for h, we get:

h = 5

Therefore, the height of the container is 5cm.

Part B:

The volume of the container is 45π cm³ and the cost of coffee is $0.02 per cubic centimeter. Therefore, the total cost of the coffee is:

Total cost = Volume x Cost per unit volume

Total cost = 45π x $0.02

Total cost = $0.90π

Rounding to two decimal places, we get:

Total cost = $2.83

Therefore, the cost of the coffee is $2.83.

Part C:

Given that the container is a cylinder with a radius of 5cm, we can use the same formula for the volume of a cylinder to find the height of the container. Substituting the given values, we get:

225π = π(5)²h

Simplifying and solving for h, we get:

h = 9

Therefore, the height of the container is 9cm.

Part D:

The volume of the container is 225π cm³ and the cost of hot chocolate powder is $0.07 per cubic centimeter. Therefore, the total cost of the hot chocolate powder is:

Total cost = Volume x Cost per unit volume

Total cost = 225π x $0.07

Total cost = $15.75π

Rounding to two decimal places, we get:

Total cost = $49.35

Therefore, the cost of the hot chocolate powder is $49.35.

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The correct answer is D. 3x + 2 < -7 or 3x + 2 > 7.

The correct compound inequality that can be used to solve the inequality |3x+2|>7 is D. 3x + 2 < -7 or 3x + 2 > 7.


When solving an absolute value inequality, we need to remember that the absolute value of a number is always positive. This means that if |3x+2|>7, then 3x+2 must be either greater than 7 or less than -7.

To write this as a compound inequality, we can use the word "or" to indicate that either one of these conditions must be true. This gives us the compound inequality 3x + 2 > -7 or 3x + 2 > 7.

However, we need to be careful with the first part of the compound inequality. Since we know that 3x+2 must be less than -7, we need to use the less than symbol (<) instead of the greater than symbol (>). This gives us the correct compound inequality, 3x + 2 < -7 or 3x + 2 > 7.

Therefore, the correct answer is D. 3x + 2 < -7 or 3x + 2 > 7.

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The dependent variable and independent variable in the 15th question is

t = dependent and m = independent variable.

A variable is a quantity that may change within the context of a mathematical problem or experiment.

Given is a statement, The temperature, t, of water and the number of minutes, m, the water is in the freezer, we need to identity the dependent variable and independent variable for this statement,

Independent variable :-

It is a variable that doesn't change by the other variables.

Dependent variable :-

The dependent variable is the variable that is used for tested in an experiment.

Here, the temperature of the water is dependent on the number of minutes it has been kept in the freezer,

So, the temperature of the water is the dependent variable and the number of minutes it has been kept in the freezer is the independent variable.

Hence, the dependent variable and independent variable in the 15th question is t = dependent and m = independent variable.

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The question 17 is not completely mentioned

The root(s) and multiplicity for each term are:
- Root: x = -3/2, Multiplicity: 4
- Root: x = 10, Multiplicity: 2
- Root: x = -1/2, Multiplicity: 6

The root(s) and multiplicity for each term are as follows:

- The term (2x+3) has a root of x = -3/2 and a multiplicity of 4. This means that the value of x = -3/2 makes the term (2x+3) equal to zero and that this root appears 4 times in the equation.
- The term (x-10) has a root of x = 10 and a multiplicity of 2. This means that the value of x = 10 makes the term (x-10) equal to zero and that this root appears 2 times in the equation.
- The term (2x+1) has a root of x = -1/2 and a multiplicity of 6. This means that the value of x = -1/2 makes the term (2x+1) equal to zero and that this root appears 6 times in the equation.

In summary, the root(s) and multiplicity for each term are:
- Root: x = -3/2, Multiplicity: 4
- Root: x = 10, Multiplicity: 2
- Root: x = -1/2, Multiplicity: 6

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Answer:

slope: -4

y intercept: (0,-12)

The first four terms of the sequence generated by g_(1)=(1)/(2) g_(n)=6g_(n-1), for all integers n>=2 are (1/2), 3, 18, and 108.

The first four terms of the sequence generated by g_(1)=(1)/(2) g_(n)=6g_(n-1), for all integers n>=2 are (1/2), 3, 18, and 108.

To find the first four terms of the sequence, we can use the given formula and plug in the values for n.

For the first term, n=1, so we use the formula g_(1)=(1)/(2) to get the first term, which is (1/2).

For the second term, n=2, so we use the formula g_(n)=6g_(n-1) and plug in the value for n and the value of the first term for g_(n-1):

g_(2)=6g_(2-1)=6g_(1)=6(1/2)=3

For the third term, n=3, so we use the same formula and plug in the value for n and the value of the second term for g_(n-1):

g_(3)=6g_(3-1)=6g_(2)=6(3)=18

For the fourth term, n=4, so we use the same formula and plug in the value for n and the value of the third term for g_(n-1):

g_(4)=6g_(4-1)=6g_(3)=6(18)=108

Therefore, the first four terms of the sequence are (1/2), 3, 18, and 108.

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The closest answer choice to 26.25 cm² is G. 16.5 cm².

What is area ?

Area is a measurement of the amount of space inside a two-dimensional figure, such as a square, rectangle, triangle, parallelogram, or circle. It is expressed in square units, such as square centimeters (cm²), square meters (m²), square inches (in²), or square feet (ft²).

Based on the given image, we can use the ruler to measure the dimensions of the parallelogram.

From the ruler, we can see that the base of the parallelogram is approximately 7.5 cm, and the height is approximately 3.5 cm. Therefore, the area of the parallelogram is:

Area = base x height

Area = 7.5 cm x 3.5 cm

Area = 26.25 cm² (rounded to the nearest 0.5 cm)

Among the answer choices provided, the closest one to the calculated area of the parallelogram is 26.5 cm², which is not provided in the answer choices.

Therefore, The closest answer choice to 26.25 cm² is G. 16.5 cm².

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Therefore, the volume of the larger cylinder is 44.8. [tex]m^{3}[/tex], which is closest to option (c) 437.5. [tex]m^{3}[/tex].

Volume is a measure of the amount of space occupied by an object or substance. It is a three-dimensional quantity that is usually measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or gallons (gal).

Given by the question.

The ratio of the volumes of two similar solids is the cube of the ratio of their corresponding side lengths. In this case, the ratio of the scale factor of the cylinders is 5:2, so the ratio of their volumes is (5/2) ^3 = 125/8.

If the volume of the smaller cylinder is 28 m^3, then we can set up the following equation to solve for the volume of the larger cylinder:

(125/8) * V = 28

where V is the volume of the larger cylinder.

Simplifying this equation, we get:

V = 28 * (8/125) * 125

V = 224/5

V = 44.8 [tex]m^{3}[/tex]

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The total fluid intake for the meal is 493.055 mL

Converting:

1/3 glass of orange juice

= (1/3) x 8 oz = 2.67 oz

= 79.027 mL (rounded to 3 decimal places)

1/2 cup of tea

= (1/2) x 6 oz

= 3 oz = 88.720 mL (rounded to 3 decimal places)

1/2 pint of milk

= (1/2) x 16 oz

= 8 oz = 236.588 mL (rounded to 3 decimal places)

1 tuna fish sandwich = no fluid intake

1 popsicle (3oz)

= 3 oz

= 88.720 mL (rounded to 3 decimal places)

Total fluid intake

= 79.027 mL + 88.720 mL + 236.588 mL + 0 mL + 88.720 mL

= 493.055 mL (rounded to 3 decimal places)

Therefore, the total fluid intake for the meal is 493.055 mL.

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The number which is a cube number, an odd number, middle digit is prime and is of less than 6 digit is 1331.

The only number that satisfies all the given conditions is 1331.

The number 1331 is a cube number because it is 11 to the power of 3,

which is written as ⇒ (11 × 11 × 11 = 1331).

The number 1331 is also a square number because it is 11 to the power of 2, which means

⇒ (11 × 11 = 121), and 121 is a square number.

The number 1331 is not divisible by 2, so it is an odd number.

The middle digit of the number 1331 is 3, which is a prime number.

And also, the number 1331 has less than 6 digits.

Therefore, the required number is 1331.

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The given question is incomplete, the complete question is

I am a cube number, a square number, an odd number ,my middle digit is prime and i have less than 6 digits, Find that number.

The unit conversion the value is 6.75 ft.

The same feature is expressed in a different unit of measurement through a unit conversion. Time can be stated in minutes rather than hours, and distance can be expressed in kilometres rather than miles, or in feet rather than any other unit of length.

Here the given unit measurement is ,

=> 6ft 9 inches.

We know that, to convert inches into feet we need to divide by 100. Then,

=> 9 inches = 9/12 = 0.75 ft.

Now total measurement = 6+0.75 = 6.75 ft.

Hence the after unit conversion the answer is 6.75 ft.

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A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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Answer: 6 oz

Step by step:

5 < 6

Did i miss something?

Answer: 6 oz. is greater than 5 oz.

Step-by-step explanation:

Imagine you had 6 dogs. Now let's say that one passed away due to a car accident. Now you have 5 dogs. We can say by the fundamental theorem of common sense that you indeed did have more dogs before that accident. Using that logic in the grand scheme of metrics, we can say that 6oz is larger as a value than 5oz.

a. The probability that brand A will be preferred as the best is 0.65 or 65%.

b. The probability that brand A will be preferred as the best and brand B as the second best is 0.22 or 22%.

c. The probability that brand B will be preferred as the second best given brand A is preferred as the best is 0.615.

What is probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

a) The probability that brand A will be preferred as the best can be calculated by adding up the frequencies of outcomes where brand A is listed first, which are (A, B, C), (A, C, B), and (C, A, B), and dividing by the total number of outcomes:

P(A is preferred as the best) = (220 + 180 + 250) / 1000 = 0.65

Therefore, the probability that brand A will be preferred as the best is 0.65 or 65%.

b) The probability that brand A will be preferred as the best and brand B as the second best can be calculated by adding up the frequency of the outcome (A, B, C), where brand A is listed first and brand B is listed second, and dividing by the total number of outcomes:

P(A is preferred as the best and B is preferred as the second best) = 220 / 1000 = 0.22

Therefore, the probability that brand A will be preferred as the best and brand B as the second best is 0.22 or 22%.

c) To find the probability that brand B will be preferred as the second best given brand A is preferred as the best, we need to consider only the outcomes where A is listed first:

P(B second | A first) = (A, B, C) + (A, C, B) / P(A first)

P(B second | A first) = (220 + 180) / 650

So the probability that brand B will be preferred as the second best given brand A is preferred as the best is 400/650 = 0.615.

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The answer is yes, more than one triangle can be formed using the three angle measures of triangle QPC. This is because the sum of the three angle measures of a triangle is always equal to 180 degrees.

A triangle is a three-sided geometric figure, consisting of three straight lines connecting three vertices. It is one of the most fundamental shapes in geometry and is used as the basis for a variety of mathematical concepts.

If two angle measures are given, any third angle measure between 0 and 180 degrees can be chosen to form a triangle. Thus, if two angle measures of triangle QPC are given, any third angle measure between 0 and 180 degrees can be used to form a triangle.

For example, if two angle measures of triangle QPC are 45 degrees and 65 degrees, then any third angle measure between 0 and 180 degrees can be chosen to form a triangle. Thus, if the third angle measure chosen is 70 degrees, then a triangle with three angle measures of 45 degrees, 65 degrees and 70 degrees can be formed. Similarly, if the third angle measure chosen is 30 degrees, then a triangle with three angle measures of 45 degrees, 65 degrees and 30 degrees can be formed.

Thus, it can be concluded that more than one triangle can be formed using the three angle measures of triangle QPC.

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25344 ft

We can use the conversion factors to convert 8 kilometers to another measure.

From the given conversion factors, we know that:

1 km ≈ 0.6 mi

1 mi = 5,280 ft

So, to convert 8 kilometers to feet, we can first convert it to miles and then convert miles to feet:

8 km x 0.6 mi/km = 4.8 miles

4.8 miles x 5,280 ft/mile = 25,344 ft

Therefore, 8 kilometers is equivalent to 25,344 feet.

The answer is option (C) 25,344 ft

Let V be a finite-dimensional vector space and let S1 and S2 be two bases of V. To show that S1 and S2 have the same number of elements, we will assume, without loss of generality, that S1 has more elements than S2, i.e., n > m. We will then derive a contradiction.

Since S1 is a basis of V, every vector in V can be expressed as a linear combination of the vectors in S1. In particular, for each j = 1, 2, ..., m, we can express βj as a linear combination of the vectors in S1:

βj = c1,jα1 + c2,jα2 + ... + cn,jαn

where c1,j, c2,j, ..., cn,j are scalars. We can write this in matrix form as

| β1 | | c1,1 c1,2 ... c1,m | | α1 |

| β2 | | c2,1 c2,2 ... c2,m | | α2 |

| ... | = | ... ... ... ... | * | ... |

| βm | | cm,1 cm,2 ... cm,m | | αn |

where the matrix on the right is the matrix whose columns are the vectors in S1, and the matrix on the left is the matrix whose columns are the vectors in S2.

Since S2 is also a basis of V, the matrix on the left is invertible. Therefore, we can multiply both sides of the equation by the inverse of the matrix on the left, giving

| α1 | | b1,1 b1,2 ... b1,m | | β1 |

| α2 | | b2,1 b2,2 ... b2,m | | β2 |

| ... | = | ... ... ... ... | * | ... |

| αn | | bn,1 bn,2 ... bn,m | | βm |

where b1,j, b2,j, ..., bn,j are scalars.

Now consider the determinant of the matrix on the left-hand side of this equation. Since this matrix is obtained by multiplying the matrix whose columns are the vectors in S2 by the inverse of the matrix whose columns are the vectors in S1, its determinant is equal to the product of the determinants of these two matrices:

det([α1 α2 ... αn]) * det([β1 β2 ... βm]^-1) = det([α1 α2 ... αn] [β1 β2 ... βm]^-1)

The left-hand side is nonzero, since S1 and S2 are both bases of V and therefore their vectors are linearly independent, so the determinant of each matrix is nonzero. However, the right-hand side is zero, since the product of the two matrices on the right-hand side is the identity matrix, and the determinant of the identity matrix is 1.

This is a contradiction, so our assumption that S1 has more elements than S2 must be false. Therefore, S1 and S2 have the same number of elements, and the proof is complete.

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Answer:Latasha should ask her mom for help

Step-by-step explanation:

The factored form of the given polynomial 9x^(2)y+9x^(2)-9x^(3)y is 9x^(2)(y+1-xy).

We can factor out the greatest common factor from this polynomial by finding the highest power of each variable that is common to all terms.

The greatest common factor of 9x^(2)y, 9x^(2), and 9x^(3)y is 9x^(2). Therefore, we can factor out 9x^(2) from the given polynomial.

[tex]9x^{2}y+9x^{2}-9x^{3}y = 9x^{2}(y+1-xy)[/tex]

Therefore, the answer is 9x^(2)(y+1-xy).

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