Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165. The equation represents the $495 total cost that Barbara paid to Dance Unlimited. 495 = 165 + 55 m How many months, m, did Barbara receive dance lessons from Dance Unlimited? F. 2.25 months G. 6 months H. 12 months J. 9 months

Answer:

Let's find the discriminant to see if there are any solutions at all. When ax² + bx + c = 0 the discriminant (D) is b² - 4ac. In our case, a = -2, b = -16 and c = -44 so D = (-16)² - 4(-2)(-44) = -96 which is less than 0. Since D < 0 the answer is no real solutions or x ∉ R.

Answer:

x = -4 + i√6 and

x = -4 - i√6

Step-by-step explanation:

Divide all four terms by 2 to reduce the equation:  -x^2 - 8x - 22 = 0.

Change all four signs:  x^2 + 8x + 22

Complete the square of x^2 + 8x:

x^2 + 8x  =>  x^2 + 8x + 16 - 16

Then our x^2 + 8x + 22 from above becomes  x^2 + 8x + 16 + 22 - 16, or

(x + 4)^2 + 6 = 0, or (x + 4)^2 = -6

Taking the square root of both sides, we obtain:

x + 4 = ±√-6, or x + 4 = ±i√6

Solving for x, we get x = -4 ±i√6, and so the roots are:

x = -4 + i√6 and

x = -4 - i√6

The option C is correct.

In the given statement is:

Solve the inequality for x and identify the graph of its solution.

|x+2|<2

Here, The question is :

|x+2|<2

The modulus sign means that the absolute value of x + 2 is less than 2. This means that

-2 < x + 2 < 2

This is what is called double inequality. We must treat it as two separate inequalities.

From the left we get -2 < x + 2 and by subtract 2  to both sides we obtain

-4 < x.

On the right we have x + 2 < 2 , and by subtract 2 to both sides we get,

x < 0

We can write these solutions together as :

-4 < x < 0

and this range of values of x is illustrated on the number line see the image :

Hence, The option C is correct.

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m =4e-3 is the equation represents the number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions.

Two or more expressions with an Equal sign is called as Equation.

Let the multiple questions be denoted by m.

The essay questions be denoted by e.

The given sentence is the number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions.

In the sentence there is less than which means a value is subtracted and it has times which is meant by product.

m =4e-3 is the required equation of the given sentence.

Hence, m =4e-3 is the equation represents the situation.

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The number of stocks that went up yesterday given the stocks that went down yesterday is 618.

Ratio is used compare two or values together. It shows the number of times that one value is contained in another value or values. According to the information provided in the question,  the ratio of stocks that go up and the stock that goes down is 6 : 7.

The number of stocks that went up yesterday = (ratio of stocks that went up x number of stocks that went down yesterday) / ratio of stocks that went down yesterday

The number of stocks that went up yesterday =(6 x 721) / 7 = 618

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1) Always be polite and professional.

2) Specifically address the points that you disagree with.

3) Provide Evidence.

4) Close with a brief summary of your rebuttal.

Answer:

Although I believe ______, some may think that _______. However (evidence against their claim) shows that (explanation of evidence in 2-3 sentences)

Answer:

b.

Step-by-step explanation:I think so

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

20 ton

Step-by-step explanation:

We created a system of two separate equations to answer these questions.

"y" will be the total cost to transport the sugar

"x" will be the amount of sugar transported

Therefore, we have to:

y = 3995 + 225.50 * x

y = 6500 + 100.25 * x

We must establish these equations equal to each other because it asks how much of x is necessary to make the same amount of y, therefore:

3995 + 225.50 * x = 6500 + 100.25 * x

solved we have:

225.50 * x - 100.25 * x  = 6500 - 3995

125.25 * x = 2505

x = 2505 / 125.25

x = 20

which means that when the amount of sugar transported is 20 tons, the price is the same

The surface area of an ice cube with 4 cm sides is 96 square centimeters.

It is a measurement of the sum of all the areas of the faces, sides, and any other surfaces of an object. For example, a cube has six square faces, each with the same area.

To find the surface area of an ice cube with 4 cm sides, we need to add up the areas of all six faces. Each face is a square with side length 4 cm, so the area of each face is:

Area of one face = (side length)² = 4 cm × 4 cm = 16 cm²

Since there are six faces on a cube, the total surface area of the ice cube is:

Total surface area = 6 × (area of one face) = 6 × 16 cm² = 96 cm²

Therefore, the surface area of an ice cube with 4 cm sides is 96 square centimeters.

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Answer:

-3

Step-by-step explanation:

Biles' score was 3.26 standard deviations above the mean score for the women's competition, while Verniaiev's score was 2.43 standard deviations above the mean score for the men's competition.

First we need to calculate their z-scores based on the mean and standard deviation of their respective competitions.

For Simone Biles:

z-score = (62.366 - 57.275) / 1.563 ≈ 3.26

For Oleg Verniaiev:

z-score = (91.964 - 87.229) / 1.946 ≈ 2.43

Since the z-score measures the number of standard deviations above the mean score, we can see that Simone Biles had a stronger performance compared to the average in the women's all-around competition than Oleg Verniaiev had in the men's all-around competition.

Therefore, Biles' score was 3.26 standard deviations above the mean score for the women's competition, while Verniaiev's score was 2.43 standard deviations above the mean score for the men's competition.

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Answer:

30.5

Step-by-step explanation:

here :

n represents the number of trials

p represents the probability of success

 In a binomial distribution, The mean

 is equal to the product of those two values.

In other words,

The mean = n × p

                 = 122 × 0.25

                 = 30.5

Answer:

they're equal

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Inverse proportionality relationship

Step-by-step explanation:

SInce I equals 50 divided by t, we see "t in the denominator, which corresponds to an INVERSE proportionality between these variables (I and t)

As the counselor recommends that the client reconsider marrying her fiancé based on his belief discretion, this is an example of harmful use of bias.

The counselor's personal beliefs against interfaith marriages are influencing their professional advice, which can be harmful to the client's well-being and may even violate ethical guidelines for mental health professionals.

The counselor should provide unbiased and objective guidance to the client based on their specific needs and circumstances, rather than imposing their own beliefs or values onto the client's decision-making process.

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Check the picture below.

Answer: Its high

Step-by-step explanation: It just is

The probability that Brent draws mismatched socks is 32/153.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since Brent is drawing two socks without replacement, there are 18 choices for the first sock and 17 choices for the second sock.

Therefore, there are 18 x 17 = 306 possible ways Brent could draw two socks.

For Brent to have mismatched socks, he needs to draw a white sock first and a black sock second, or a black sock first and a white sock second.

Let's consider the first case.

There are 16 white socks and 2 black socks, so there are 16 x 2 = 32 ways Brent could draw a white sock first and a black sock second.

For the second case, there are 2 black socks and 16 white socks, so there are 2 x 16 = 32 ways Brent could draw a black sock first and a white sock second.

Therefore, the probability of Brent drawing mismatched socks is:

= (32 + 32) / 306

= 64 / 306

= 32 / 153

Thus, the probability that Brent draws mismatched socks is 32/153.

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Answer:

subtract 265 from 305 and get 40 (305 - 265 = 40) then divide that by 8 and get 8 (40/8 = 5). so F=5 (each party favor is 5 dollars)

Step-by-step explanation:

Which year group is this question from?

When the object is located at a location in front of the focal point, the image will always be located somewhere on the same side of the lens as the object. In this case, the image is enlarged; in other words, the image dimensions are greater than the object dimensions.

The combined balance of both bank accounts at the end of 3 years is closest to $1039.76.

To calculate the combined balance of both bank accounts after 3 years, we'll calculate the balance for each account separately and then add them together.

For Bank A, we can use the compound interest formula:

A =\(P(1 + r/n)^(nt)\)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount

r = annual interest rate (as a decimal)

n = number of times that interest is compounded per year

t = number of years

In this case, Wanda deposited $370 at a 2.25% interest rate compounded annually, so we have:

P = $370

r = 2.25% = 0.0225 (as a decimal)

n = 1 (compounded annually)

t = 3 years

Using the formula, we can calculate the balance for Bank A:

A_A = \(370(1 + 0.0225/1)^(1*3)\)

=\(370(1.0225)^3\)

= 370(1.0678450625)

= $394.76

For Bank B, we can use the simple interest formula:

A = P(1 + rt)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount

r = annual interest rate (as a decimal)

t = number of years

In this case, Wanda deposited $600 at a 2.5% simple interest rate, so we have:

P = $600

r = 2.5% = 0.025 (as a decimal)

t = 3 years

Using the formula, we can calculate the balance for Bank B:

A_B = 600(1 + 0.025*3)

= 600(1.075)

= $645

Finally, we can calculate the combined balance of both bank accounts:

Combined Balance = A_A + A_B

= $394.76 + $645

= $1039.76

Therefore, the combined balance of both bank accounts at the end of 3 years is closest to $1039.76.

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Answer:

x = 5

y = 1

Step-by-step explanation:

2x - y = 9

3x + 4y = 19

We multiply the first equation by 4

8x - 4y = 36

3x + 4y = 19

11x = 55

x = 5

Now we put 5 in for x and solve for y

2(5) - y = 9

10 - y = 9

-y = -1

y = 1

Let's Check the answer

2(5) - 1 = 9

10 - 1 = 9

9 = 9

So, x = 5 and y = 1 is the correct answer.

Answer:

91 degrees

Step-by-step explanation:

Sum of angles in a quadrilateral: 360 degrees

87, 89, 91, 93 are four consecutive odd numbers that add up to 360

third angle is 91 degrees

Answer:

64.8 ft

Step-by-step explanation:

A square has all its sides equal

Therefore to get one side from its area is simply finding the square root of its area

√262.44=16.2ft

Having the one side then perimeter= to the four equal sides × the dimensions of one side

=4×16.2

=64.8 ft

Answer:

\(x=\dfrac{2}{3},-\dfrac{3}{2}\)

Step-by-step explanation:

Given equation:

\(6x^2+5x-6=0\)

First, factor the left side of the given equation.

To factor a quadratic in the form \(ax^2+bx+c\) find two numbers that multiply to \(ac\) and sum to \(b\):

\(\implies ac=6\cdot-6=-36\)

\(\implies b=5\)

So the two numbers are: 9 and -4

Rewrite \(b\) as the sum of these two numbers:

\(\implies 6x^2+9x-4x-6=0\)

Factorize the first two terms and the last two terms separately:

\(\implies 3x(2x+3)-2(2x+3)=0\)

Factor out the common term \((2x+3)\):

\(\implies (3x-2)(2x+3)=0\)

To solve for x:

\(\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}\)

Therefore:

\(x=\dfrac{2}{3},-\dfrac{3}{2}\)

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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