this week
36. Britney practiced the piano a total of 7 hours this week. This is 3 hours
less than she practiced last week. Select the correct labels to complete
the bar diagram that is used to find the number of hours w Britney
practiced last week.
last week, w
3 hours
4 hours
7 hours
10 hours
How many hours did Britney practice the piano last week?

translating phrases and sentences into expressions, equations, and inequalities is an important skill in mathematics. It involves identifying key words and phrases that indicate mathematical operations and relationships. By understanding these key words, we can represent real-world problems using mathematical language and symbols, making it easier to solve and analyze them.

translating phrases and sentences into expressions, equations, and inequalities

When solving mathematical problems, it is often necessary to translate phrases and sentences into mathematical expressions, equations, and inequalities. This process involves identifying key words and phrases that indicate mathematical operations and relationships.

For example, let's consider the following sentence:

'The sum of a number and 5 is equal to 12.'

In this sentence, the key words 'sum,' 'number,' 'equal to,' and '12' indicate that we need to perform addition and find the value of the unknown number. We can represent this sentence as the following equation:

x + 5 = 12

Here, 'x' represents the unknown number.

Similarly, let's consider the following sentence:

'Twice a number decreased by 7 is greater than 15.'

In this sentence, the key words 'twice,' 'decreased by,' 'greater than,' and '15' indicate that we need to perform multiplication, subtraction, and comparison. We can represent this sentence as the following inequality:

2x - 7 > 15

Here, 'x' represents the unknown number.

By understanding key words and phrases, we can effectively translate real-world problems into mathematical language and solve them using expressions, equations, and inequalities.

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1) An inequality to represent the given phrase is 5q>30.

2) An equation to represent the given phrase is 2b²=8.

1) The given phrase is "The product of 5 and q is greater than 30."

Here, the product of 5 and q = 5×q

= 5q

Now, the product is greater than 30.

Thus, 5q>30

q>30/5

q>6

2) The given phrase is "Twice the square of b is equal to 8."

Here, the square of b = b×b

= b²

Twice the square of b = 2b²

So, the product is equal to 8.

That is. 2b²=8

b²=4

b=±2

Therefore,

1) An inequality to represent the given phrase is 5q>30.

2) An equation to represent the given phrase is 2b²=8.

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"Your question is incomplete, probably the complete question/missing part is:"

Translate phrases and sentences into expressions, equations and inequalities.

1) The product of 5 and q is greater than 30.

2) Twice the square of b is equal to 8.

To compute the cosine of the angle between the two planes with normals 1=⟨1,0,1⟩ and 2=⟨10,7,3⟩, we first need to find the dot product of the two normal vectors.
1⋅2 = ⟨1,0,1⟩⋅⟨10,7,3⟩ = 1(10) + 0(7) + 1(3) = 13

Next, we need to find the magnitudes of the two normal vectors.
|1| = √(1^2 + 0^2 + 1^2) = √2
|2| = √(10^2 + 7^2 + 3^2) = √174
Finally, we can use the dot product formula to find the cosine of the angle between the two normal vectors:
cosθ = (1⋅2) / (|1|⋅|2|) = 13 / (√2 ⋅ √174) ≈ 0.692
Therefore, the cosine of the angle between the two planes is approximately 0.692.
To compute the cosine of the angle between the two planes with normals 1=⟨1,0,1⟩ and 2=⟨10,7,3⟩, you need to find the dot product of the normal vectors and divide it by the product of their magnitudes.
The dot product of the normal vectors is:
(1)(10) + (0)(7) + (1)(3) = 10 + 0 + 3 = 13
The magnitudes of the normal vectors are:
||1|| = √((1)^2 + (0)^2 + (1)^2) = √(1 + 0 + 1) = √2
||2|| = √((10)^2 + (7)^2 + (3)^2) = √(100 + 49 + 9) = √158
Now, divide the dot product by the product of the magnitudes:
cosine(angle) = 13 / (√2 * √158) = 13 / (√316)
So the cosine of the angle between the two planes is 13/√316.

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The difference in the amount of interest paid the first month between the average and worst score is given as follows:

$94.58.

The average interest rate would allow you to do so while paying the least amount of money, due to the lower rate compared to the poor.

The equation to model the interest accrued after t years is given as follows:

I(t) = Prt

.

In which the parameters of the equation are explained as follows:

For the average score, the parameters are given as follows:

P = 25000, r = 0.0535, t = 1/12. (as one month = 1/12 of a year).

Hence the interest accrued is of:

I = 25000 x 0.0535 x 1/12

I = 111.46.

For the poor score, the parameters are given as follows:

P = 25000, r = 0,0989, t = 1/12. (as one month = 1/12 of a year).

Hence the interest accrued is of:

I = 25000 x 0.0989 x 1/12

I = 206.04.

Hence the difference is of:

206.04 - 111.46 = $94.58.

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Answer:$

94.58

Step-by-step explanation:

Answer:

$53.70

Step-by-step explanation:

I worked it out I think this is the answer

Answer:

85/135 -> 17/27.

50/135 -> 10/27.

Step-by-step explanation:

135 - 50 orange = 85 R.

50 O + 85 R = 135 total.

85/135 -> 17/27.

50/135 -> 10/27.

Given:

Radius of the circle = 4 meters

Measure of arc = 135 degrees

To find:

The area of the sector bounded by the given arc.

Solution:

Formula for area of a sector is:

\(A=\pi r^2\times \dfrac{\theta}{360^\circ}\)

Where, r is the radius and \(\theta\) is the central angle or measure of intercepted arc.

Putting \(r=4,\ \theta =135^\circ\) in the above formula, we get

\(A=\pi \times (4)^2\times \dfrac{135^\circ}{360^\circ}\)

\(A=\pi \times 16\times \dfrac{3}{8}\)

\(A=\pi \times 2\times 3\)

\(A=6\pi \)

Therefore, the exact area of the given sector is \(6\pi \) square meters.

Answer:

the answer is just 6π

Step-by-step explanation:

Answer:

7x - 3)

Step-by-step explanation:

Given

3x - 7 + 2(2x - 7) ← distribute parenthesis

= 3x - 7 + 4x - 14 ← collect like terms

= 7x - 21 ← factor out 7 from each term

= 7(x - 3)

The expression 3x - 7 + 2(2x - 7) can be written as the product of 7 and the factor (x - 3).

We have write the expression 3x - 7 + 2(2x - 7) as the product of 7 and another factor.

we can simplify the expression first and then factor out the common factor of 7.

Let's simplify the expression step by step:

3x - 7 + 2(2x - 7)

= 3x - 7 + 4x - 14 (distributing the 2 to the terms inside the parentheses)

= (3x + 4x) + (-7 - 14)

= 7x - 21

Now, let's factor out the common factor of 7:

= 7(x - 3)

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Step-by-step explanation:

Let's call the number of girls in the school "g". We know that there are 1000 boys, so the total number of students is 1000 + g.

The problem states that 48% of the total number of students were successful in the examination. Therefore, we can write an equation:

0.48(1000 + g) = 0.5(1000) + 0.4(g)

Simplifying and solving for g:

480 + 0.48g = 500 + 0.4g

0.08g = 20

g = 250

Therefore, the number of girls in the school is 250.

Answer:

250

Step-by-step explanation:

Hi dear,

Firstly, let the girls be G

1000 + G = Total number of students

50% of boy = 1000 × 0.5 = 500

40% of girls = G × 0.4 = 0.4G

0.48 • (1000 + G) = 480 + 0.48G

480 + 0.48G = 500 + 0.4G

Collect Like Terms

0.48G - 0.4G = 500 - 480

0.08G = 20

G = 20/0.08

G = 250

Therefore, the girls are 250( two hundred and fifty)in the school

Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

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Answer:

8.1

Step-by-step explanation:

3 x 27 = 81

8.1

3 x 2.7 = 8.1

Answer:

Step-by-step explanation:

V=m/d

V=8.4g/(2g/cm³)=4.2cm³

V=4 π R³/3 ;  π≅3.14

R³ =3V/(4 π)=3*4.2cm³/(4*3.14)=12.6cm³/12.56 ≅ 1.0 cm³

=>R=∛(1.0 cm³) =1.0 cm

The radius of the spherical grape is 1.0 cm.

Density refers to the measurement of the amount of mass of a substance per unit of volume.

This measurement of a pure substance has the same value as its mass concentration. Densities vary with different materials or substances.

i.e., V=m/d

Given that, the mass of a spherical grape is 8.4 grams and its density is 2 grams per cubic centimeter.

V = 8.4g/(2g/cm³) = 4.2cm³

V = 4 π R³/3  

R³ =3V/(4 π) = 3*4.2cm³/(4*3.14)=12.6cm³/12.56 ≅ 1.0 cm³

R =1.0 cm

Hence the radius of the spherical grape is 1.0 cm.

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A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.

A slant asymptote exists of the form y = mx + b where m ≠ 0.

Vertical lines go up and down and are in the form of x = a, where a stands for the common x-coordinate of all locations, whereas horizontal lines go left to right and take the shape of y = b, where b stands for the y-intercept.

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's domain, the graph can never cross it. There may be multiple vertical asymptotes for a given function. All common factors are cancelled in the denominator, D(x).

A horizontal asymptote exists of the form y = k where x→∞ or x→ -∞ if the value of the one/both of the limits lim ₓ→∞ f(x) and lim ₓ→ -∞ f(x).

A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.

A slant asymptote exists of the form y = mx + b where m ≠ 0.

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can see picture but i tried sorry

Answer:

what are the choices so I could help

Answer:

see explanation

Step-by-step explanation:

∠ L = 180° - (60 + 60)° = 180° - 120° = 60° [ sum of angles in Δ = 180° ]

Since the 3 angles are 60° , then the triangle is equilateral with the 3 sides being congruent.

Then

5x - 3 = 4 ( add 3 to both sides )

5x = 7 ( divide both sides by 5 )

x = \(\frac{7}{5}\) = 1.4

and

2y + 6 = 4 ( subtract 6 from both sides )

2y = - 2 ( divide both sides by 2 )

y = - 1

Answer:

x=9/80

Step-by-step explanation:

Answer:

9/80

Step-by-step explanation:

\(1)\ x + \frac{9}{20} = \frac{9}{16}\)

\(2)\ x = \frac{9}{16} - \frac{9}{20}\)

\(3)\ x = \frac{9}{16} - \frac{9}{20}\)

\(4)\ x = \frac{45}{80} - \frac{36}{80}\)

\(5)\ x = \frac{9}{80}\)

Area of rectangle is 96/13 sq. units

Given the rectangular area bounded by the x-axis and semicircle y = √36 – x²,

To find the dimensions of the rectangle and the area of the rectangle.

We can use calculus to solve the problem.

Let the length and width of the rectangle be L and W respectively.

As the rectangle is bounded by the x-axis and the semicircle y = √36 – x², we get: L = 2xW = 2yAlso, y² + x² = 36, which is the equation of the given semicircle.

We need to maximize the area of the rectangle.

We know that the area of the rectangle is A = LW = 4xy.

Substituting L and W in terms of x and y, we get: A = 8xy = 8x(√36 – x²)

We differentiate A w.r.t. x to find the critical point.

dA/dx = 8(√36 – x²) – 16x²/√36 – x²³ = 8(36 – x²) – 16x²/6√36 – x² = 8(36 – 2x²)/6√36 – x²

At critical points dA/dx = 0:8(36 – 2x²)/6√36 – x² = 0√36 – x² = 3x/2

Therefore, y = 3x/2.

Substituting this value of y in y² + x² = 36, we get:

(3x/2)² + x² = 36

⇒ 9x²/4 + x² = 36

⇒ 13x²/4 = 36

⇒ x² = 144/13√36 – x²

= √(1296/13)A

= 8x(√36 – x²)

= 8(144/13)^(1/2) (36/13)^(1/2)

= 96/13 sq. units

Therefore, the area of the rectangle bounded by the x-axis and semicircle y = √36 – x² is 96/13 sq. units.

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It takes Sally 4 hours, working alone, to paint one room.

Let's use the variable "x" to represent the number of hours it takes Sally to paint one room. According to the problem, it takes Henry 8 hours longer, or "x + 8" hours, to paint one room.

When they work together, they can paint one room in 3 hours. This means that their combined rate of painting is 1/3 of a room per hour. We can use this information to set up an equation:

1/x + 1/(x+8) = 1/3

To solve for x, we first need to simplify the equation by finding a common denominator:

(3(x+8) + 3x) / x(x+8) = 1

(6x + 24) / x(x+8) = 1

6x + 24 = x^2 + 8x

0 = x^2 + 2x - 24

Using the quadratic formula, we get:

x = (-2 ± sqrt(2^2 - 4(1)(-24))) / (2(1))

x = (-2 ± sqrt(100)) / 2

We can ignore the negative solution since it doesn't make sense in the context of the problem:

x = (-2 + 10) / 2

x = 4

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5,5

Because x is moving it right so right 2 units would be 5

Because y is moving it up so up 4 units would be 5

Answer:

a) - 11x - 94y / 12    b)  x -4 / 5- 3x   c) 12x - 11 /10y

Step-by-step explanation:

a)  2x - 6y / 4    -  4y - x/ 12    -   4x - 20y /3

6x - 18y / 12 -     4y - x / 12              -  16x - 80y / 12

= 5x - 14y / 12     - 16x - 80y / 12

- 11x - 94y / 12

b) x /5 -    4/ 3x =  x -4 / 5- 3x

c) 2x -3/ 5y  -    5- 2x / 10y + x/y

4x - 6 /10y   -  5-2x/ 10y +  10x / 10y

2x - 11 / 10  + 10x / 10y

= 12x - 11 /10y

Answer:

answers of the question

Answer:

4x² - 12x + 9

Step-by-step explanation:

Use the foil method.

(2x - 3) (2x - 3)

= 4x²- 6x - 6x + 9

= 4x² - 12x + 9

Answer:

\(Square \ of \ (2x - 3) = 4x^2 - 12x + 9\)

Step-by-step explanation:

\((a +b)^2 = a^2 + b^2 + 2ab\)

  \((2x + (- 3))^2 = (2x)^2 + ( -3 )^2 + ( 2\times 2x \times - 3)\\\\\)

                    \(= 4x^2 + 9 + ( -12x)\\\\=4x^2 - 12 x + 9\)

In this case, you have 3 B's, 2 A's and 3 C's, so the total amount of cases are 3+3+2=8. If only one of these cases was an A, then the probability would be 1/8, but you have 2 A's, so the probability is 2/8. This in percentage is found by 100*2/8=25%

Answer:

8%

Step-by-step explanation:

9+3=12 (total number of students that write left handed)

90+60=150 (total number of 6th graders)

12/150 x 100% = 8%

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Solving the provided question, we can say that the highest number bouquets she can make without having any flowers left is calculated by Highest Common Factor so, HCF of 56, 48 and 16 is 8

In mathematics, the highest positive integer that divides the corresponding integers is known as the greatest common divisor of two or more non-zero integers. The greatest common factor (HCF) of two or more numbers is the sum of those two or more numbers. As a result, it is frequently referred to as the largest common divisor (GCF). Take the prime factors of the two (or more) integers and determine the shared prime factors to determine the greatest common divisor. Following that, the sum of common prime factors is the greatest common divisor. A specified number divided by the biggest integer results in the greatest common divisor.

the highest number bouquets she can make without having any flowers left is calculated by Highest Common Factor so, HCF of 56, 48 and 16 is 8

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Answer:

So the answer is 20/64=5/16

The probability of getting at least 3 heads when a fair coin is tossed 6 times is 3/64.

Here, correct answer will be 3/64

This means that there is a 3 in 64 chance that 3 or more heads will be obtained when the coin is flipped 6 times. This can be calculated by finding the total number of possible outcomes of flipping the coin 6 times and then subtracting the number of outcomes that contain fewer than 3 heads.

The total number of possible outcomes is 2^6, which is 64. The number of outcomes that contain fewer than 3 heads is 7, which is the total of 1 head, 2 heads, and 0 heads. Therefore, the probability of getting at least 3 heads when a fair coin is tossed 6 times is 3/64.

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Answer:

the solution to the system of nonlinear equations is C. (0,3)

A factory inspector found flaws in 3 out of 18 wooden boxes. What is the experimental probability that the next wooden box will be flawed?

Write your answer as a fraction or whole number.

-------------------------------------------------------------------------------------------------------------

Remember, The experimental probability is the number of times an event occurs out of the total number of trials.

-------------------------------------------------------------------------------------------------------------

Flawed Boxes / Total

=3/18

=1/6

So The Answer is 1/6

The experimental probability that the next wooden box will be flawed is 1/6=0.167.

The experimental probability of an event is the ratio of the number of outcomes in which a specified events occurs to the total trials.

Mathematically, Experimental probability= f/n, where f is the number of times an event occurs, n is the total number of trials.

Total number of wooden boxes= 18

Total number of boxes that are flawed= 3

Therefore, required experimental probability = 3/18

                                                           =1/6

Hence, the experimental probability that the next wooden box will be flawed= 1/6

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The total distance traveled over the interval 0 < t < 8 is: 32/3 + 16/3 + 176/3 = 224/3.

To find the displacement over the given interval, we need to integrate the velocity function:

∫v(t)dt = ∫(t^3 - 10t^2 + 24t)dt = (1/4)t^4 - (10/3)t^3 + 12t^2

Now we can evaluate the displacement over the different intervals:

0 < t < 4:

(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2 = 32/3

4 < t < 6:

(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2 - [(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2]

= -16/3

6 < t < 8:

(1/4)(8)^4 - (10/3)(8)^3 + 12(8)^2 - [(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2]

= 176/3

Therefore, the displacement over the entire interval 0 < t < 8 is:

32/3 - 16/3 + 176/3 = 64/3

To find the distance traveled over the given interval, we need to break down the motion into the different intervals of direction:

0 < t < 4: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 32/3.

4 < t < 6: The particle is moving in the negative direction, so the distance traveled is the absolute value of the displacement, which is 16/3.

6 < t < 8: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 176/3.

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The total distance traveled over the interval 0 < t < 8 is: 32/3 + 16/3 + 176/3 = 224/3.

To find the displacement over the given interval, we need to integrate the velocity function:

∫v(t)dt = ∫(t^3 - 10t^2 + 24t)dt = (1/4)t^4 - (10/3)t^3 + 12t^2

Now we can evaluate the displacement over the different intervals:

0 < t < 4:

(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2 = 32/3

4 < t < 6:

(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2 - [(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2]

= -16/3

6 < t < 8:

(1/4)(8)^4 - (10/3)(8)^3 + 12(8)^2 - [(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2]

= 176/3

Therefore, the displacement over the entire interval 0 < t < 8 is:

32/3 - 16/3 + 176/3 = 64/3

To find the distance traveled over the given interval, we need to break down the motion into the different intervals of direction:

0 < t < 4: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 32/3.

4 < t < 6: The particle is moving in the negative direction, so the distance traveled is the absolute value of the displacement, which is 16/3.

6 < t < 8: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 176/3.

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Answer:

V≈743.25

Step-by-step explanation:

V=5

12tan(54°)ha2=5

12·tan(54°)·4·182≈743.24624