Andrea paid $9.99 to join an online music service. If she purchases 12 songs each month at a cost of $0.80 per song, what will be the total amount she has spent after 6 months?

Answer:

7/8

Step-by-step explanation:

7/8 is a larger fraction than 4/5, so the decimal must be larger. You can check this using a calculator, and dividing the numbers.

Answer:

  C.  0.625

Step-by-step explanation:

You want to know if the given decimals are correctly written as the given fractions.

It is generally easier to find the decimal equivalent of a fraction, but some calculators can go the other way, as well.

The decimal 0.625 corresponds to the fraction 5/8, not 7/8.

0.625 was converted incorrectly.

__

Additional comment

You can factor out 125 from numerator and denominator of the fraction equivalent of 0.625:

  \(0.625=\dfrac{625}{1000}=\dfrac{5(125)}{8(125)}=\dfrac{5}{8}\)

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Answer:

6

Step-by-step explanation:

its equivalent to root36 and root 36 is 6

Answer:

D. 6

Step-by-step explanation:

Its basically asking for the square root of 36, which is 6 because if you multiply 6 by itself you get 36.

The required equations are =

a) y = 3x + 2

b) 2y = -4x + 1

c) y = -2x + 2

a) System of Equations with One Solution:

To create a system of equations with one solution, we can introduce a second linear equation that intersects the first equation at a single point.

Let's consider the equation y = -2x + 0.5 and add another equation that doesn't have the same slope or intercept.

Let's say the second equation is y = 3x + 2. To create a system of equations with one solution, we can combine these two equations:

y = -2x + 0.5 (Equation 1)

y = 3x + 2 (Equation 2)

This system of equations will have one unique solution since the two lines intersect at a single point.

b) System of Equations with Infinitely Many Solutions:

To create a system of equations with infinitely many solutions, we can create two equations that represent the same line.

Let's consider the equation y = -2x + 0.5 and multiply it by a constant to create a second equation.

Multiplying the equation by 2, we get 2y = -4x + 1.

The system of equations will be:

y = -2x + 0.5 (Equation 1)

2y = -4x + 1 (Equation 2)

Both equations represent the same line, so any point on the line will satisfy both equations. This system will have infinitely many solutions.

c) System of Equations with No Solution:

To create a system of equations with no solution, we can create two parallel lines.

Let's consider the equation y = -2x + 0.5 and add a second equation with the same slope but a different intercept.

Let's say the second equation is y = -2x + 2. To create a system of equations with no solution, we can combine these two equations:

y = -2x + 0.5 (Equation 1)

y = -2x + 2 (Equation 2)

Since both equations have the same slope but different y-intercepts, the lines will never intersect.

Therefore, this system of equations will have no solution.

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The minimum value of the function \($f(x,y,z)=x^2+y^2+z^2$\) subject to the constraint \($g(x,y,z)=x+y+z-1=0$\) is \(\[f(1/3,1/3,1/3)=\frac13+\frac13+\frac13=\frac13.\]\)

The name of a surface of this type is an ellipsoid.

At the intersection of the surface with any plane parallel to the xy-plane, the curves of intersection are ellipses. At the intersection of the surface with any plane parallel to the xz-plane, the curves of intersection are hyperbolas. To find z_x and x_y, we differentiate the given equation with respect to x and y respectively:

\(\[\begin{aligned}\frac{\partial}{\partial x}(x^2+2y^2-3z^2)&=2x, \\ \frac{\partial}{\partial y}(x^2+2y^2-3z^2)&=4y. \end{aligned}\]\)

Therefore, z_x=0 and x_y=0.

The function to minimize is \($f(x,y,z)=x^2+y^2+z^2$\) subject to the constraint \($g(x,y,z)=x+y+z-1=0$\).

We will use the method of Lagrange multipliers. The objective function is $f(x,y,z)=x^2+y^2+z^2$, the constraint function is \($g(x,y,z)=x+y+z-1$\), and the Lagrange multiplier is \($\lambda$\).

We need to solve the system of equations:

\(\[\begin{aligned} \nabla f(x,y,z)&=\lambda\nabla g(x,y,z), \\ g(x,y,z)&=0. \end{aligned}\]\)

Using the given functions, we have

\(\[\begin{aligned} \nabla f(x,y,z)&=2x\mathbf{i}+2y\mathbf{j}+2z\mathbf{k}, \\ \nabla g(x,y,z)&=\mathbf{i}+\mathbf{j}+\mathbf{k}. \end{aligned}\]\)

Hence, we obtain the following system of equations:

\(\[\begin{aligned} 2x&=\lambda, \\ 2y&=\lambda, \\ 2z&=\lambda, \\ x+y+z&=1. \end{aligned}\]\)

Since 2x=2y=2z, we have x=y=z.

Substituting this into the last equation, we

\(\[\begin{aligned} 2x&=\lambda, \\ 2y&=\lambda, \\ 2z&=\lambda, \\ x+y+z&=1. \end{aligned}\]\)

get 3x=1, so x=y=z=1/3.

Therefore, the minimum value of the function \($f(x,y,z)=x^2+y^2+z^2$\) subject to the constraint \($g(x,y,z)=x+y+z-1=0$\) is\(\[f(1/3,1/3,1/3)=\frac13+\frac13+\frac13=\frac13.\]\)

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The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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Answer:

4

Step-by-step explanation:

I don't know how to explain this other than use a calculator.

Hope that this helps!

Answer:

\( sin \theta = \frac{\sqrt {19}}{10} \)

Step-by-step explanation:

\( ( \sin \theta) ^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \therefore \:( \sin \theta) ^{2} + { \bigg( \frac{{9} }{10} \bigg)}^{2}= 1 \\ \\( \sin \theta) ^{2} + \frac{81}{100}= 1 \\ \\ ( \sin \theta) ^{2} = 1 - \frac{81}{100} \\ \\ ( \sin \theta) ^{2} = \frac{100 - 81}{100} \\ \\ ( \sin \theta) ^{2} = \frac{19}{100} \\ \\ \sin \theta = \sqrt{\frac{19}{100} } \\ \\ \sin \theta = \frac{\sqrt {19}}{10} \)

No, because the test value 0.28 is in the noncritical region.

The null hypothesis (H₀) is the hospital's success rate is equal to the national average.

H₀: p = 0.78 (hospital's success rate is equal to the national average)

The alternative hypothesis (H₁) is the hospital's success rate is different from the national average.

H₁: p ≠ 0.78 (hospital's success rate is different from the national average)

We can use a significance level (α) of 0.05 for this test.

z = (p(hat) - p₀) / √(p₀(1 - p₀) / n)

P(hat) is the sample proportion (successful operations / total operations)

p₀ is the hypothesized proportion under the null hypothesis (0.78)

n is the sample size

p(hat) = 42 / 52 ≈ 0.8077

z = (0.8077 - 0.78) / √(0.78 × 0.22 / 52)

z = 0.28

Now, we compare the test statistic to the critical values. Since it is a two-tailed test, we divide the significance level (α = 0.05) by 2 to get α/2 = 0.025.

Looking up the z-value corresponding to α/2 = 0.025 in the standard normal distribution table, we find that the critical z-values are approximately -1.96 and 1.96.

Since the calculated test statistic (z = 0.28) falls within the noncritical region (-1.96 < z < 1.96), we fail to reject the null hypothesis.

A) No, because the test value 0.28 is in the noncritical region.

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From the given data of room ,ceiling , windows and door , the area of the four walls and ceiling to be painted is equal to 783.75 ft².

As given in the question,

Room is 14ft by 20 ft

Height of the room = 8ft

Two windows are of 3ft by 4ft

Door is 2.5ft by 6.5ft

Area of the four walls = 2 (14 × 8) + 2(20×8)

                                  = 224 +320

                                  = 544ft²

Area of the ceiling = 14 × 20

                             = 280ft²

Area of two windows = 2(3×4)

                                  =24ft²

Area of the door= 2.5 ×6.5

                         =16.25ft²

Total area to be painted = ( 544 + 280 -24-16.25 )

                                      = 783.75 ft²

Therefore, the total area of the four walls and ceiling to be painted is equal to 783.75 ft².

The complete question is :

A room is 14ft by 20ft. It needs to be painted. The ceiling is 8ft above the floor. There are two windows in the room, each one is 3ft by 4ft. The door is 2.5ft by 6.5ft.

a. find the total area of the four walls and ceiling to be painted?

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A) 500

B) 54 minutes

C) 68cents and 60 cents

D)

E) $40.95

A proportion is a statement that says that two ratios are equal. They can be used in many everyday situations like comparing sizes, cooking, calculating percentages, and more.

Proportions can be written as equivalent fractions or as equal ratios.

A) 42% = 210

100% = (210 x 100)/42

= 500 people

B) 135 berries = 15 minutes

    486 berries = ??minutes

= (486 x 15)/135

= 54 minutes

C) unit price = $6.75/10 = 0.675cents or 68cents

    ii) unit price = $7.25/12 = 0.604cents or 60cents

D) Inconclusive question.

E) 40% of 65 = $26

65 - 26 = $39

Tax = 5% = $1.95

Total = $39 + 1.95

Final Price of jacket = $40.95

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Answer:

18.84

Step-by-step explanation:

Answer:

18.8495559215

Step-by-step explanation:

In order to find circuference we use the formula

C= 2π(r)

c= circumference

r= radius

since they gave you the diameter, you first have to find the radius so you would divide the diameter by two since radius is half of a circle so 6 divided by 2 is 3. From here we would plug in 3 for "r" in the formula I wrote above. So C= 2π(3). then type this into a calculator to get the answer I wrote above. Then round as directed

The points A', B', and C' are  (3, 1), (0, 3) and (-2, 4) respectively. The solution has been obtained by using the concept of transformation.

What is transformation?

Transformations allow for the translation, rotation, and reflection of shapes on a coordinate plane. Any line, point, or vector can be rotated, translated, or reflected.

We are given coordinates of triangle ABC as A (1, -3), B (3, 0) and C (4, -2).

Now, we need to rotate the triangle ABC 90 degrees about the origin.

We know that the rotation rule for rotating 90 degrees about the origin is that (x, y) becomes (y, -x).

So, from this we get the coordinates as

A' (3, -1)

B' (0, -3)

C' (-2, -4)

Now, on reflecting it over the x - axis, we get

A' (3, 1)

B' (0, 3)

C' (-2, 4)

Hence, the points A', B', and C' are  (3, 1), (0, 3) and (-2, 4) respectively.

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Answer:

x² + 8x + 12

Step-by-step explanation:

Area of a rectangle = length × width

Original dimensions:

Width = x

Length = x + 4

James will increase both dimensions of the floor by 2 feet

New dimensions:

Width = x + 2

Length = x + 4 + 2

= x + 6

Area of the new rectangle = length × width

= (x + 2) × (x + 6)

= x² + 6x + 2x + 12

= x² + 8x + 12

Equation which represents the

new area, N, of the floor of the cage = x² + 8x + 12

Answer:

1) X =20° ,Y=60°

2) 7/5

3) first is correct

4) 2

Answer: 70%

Step-by-step explanation:

obviously 7/10 gives you 70%

Answer:

70%

Step-by-step explanation:

If 3 of the pins were knocked down, that means 7 pins were still standing.

Next, to find what percent 7 is of 10, divide 10 by 100 to get 0.1.

0.1 is 1% of 10, so we need to divide 7 by 0.1 to find the percentage, which is 70.

Answer:

y = 3x + 9

Step-by-step explanation:

y = mx + b

As the values of x increase by 1, the values of y increase by 3.

That means the slope, m, is 3.

m = 3

At x = 0, y = 9. That means the y-intercept, b, is 9.

b = 9

y = mx + b

y = 3x + 9

Answer:

40V

Step-by-step explanation:

If the peak value of a sine wave is 80 vac. The peak-to-peak value of this waveform is: D. 160V.

The difference between a sine wave's positive and negative peaks is known as the sine wave's peak-to-peak value. The negative peak value, which has the same magnitude but the opposite sign as the positive peak value (80V), will be expressed as -80V.

So,  

Peak-to-peak value is:

Peak-to-peak value = Positive peak value - Negative peak value

Peak-to-peak value = 80V - (-80V)

Peak-to-peak value = 80V + 80V

Peak-to-peak value = 160V

Therefore, the peak-to-peak value of this waveform is 160V.

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The cost of 1.20 kg of carrots is $2.09.

to convert the weight of carrots from pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram. Therefore, 1.20 kg of carrots is equivalent to 2.64555 pounds.

Next, we can use the given price of $0.79 per pound to calculate the cost of 2.64555 pounds of carrots.

Cost of 2.64555 pounds of carrots = 2.64555 x $0.79

Cost of 2.64555 pounds of carrots = $2.09 (rounded to the nearest cent)

Therefore, the cost of 1.20 kg of carrots is $2.09.

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Answer:

a - right trapezoid

b - isosceles triangle

c - equilateral triangle

d - kite

Answer:

A) \(\huge\boxed{Trapezoid }\)

Because of a pair of parallel lines.

B) \(\huge\boxed{Isosceles \ Triangle}\)

Because of two equal sides.

C) \(\huge\boxed{Equilateral \ Triangle}\)

Because of three equal sides.

D) \(\huge\boxed{Kite}\)

Having 2 pairs of equal adjacent sides.

Answer: -36

Step-by-step explanation:

the parameters we are estimating using the OLS method must be themselves linear

What are the Gauss Markov assumptions?

Gauss Markov Assumptions

Linearity: the parameters we are estimating using the OLS method must be themselves linear. Random: our data must have been randomly sampled from the population. Non-Collinearity: the regressors being calculated aren't perfectly correlated with each other.

What are the properties of Gauss Markov Theorem?

The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.

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The probability that the sum of the die rolls is odd is 1, which is equivalent to 100% (option a.)

To find the probability that the sum of the die rolls is odd, we need to consider the possible outcomes of the coin tosses and die rolls.

There are four possible outcomes for the coin tosses: HH, HT, TH, and TT.

For each head (H) that results, one fair die is rolled. The sum of the die rolls will be odd if there is an odd number of dice rolled.

Let's analyze each outcome:

1. HH: In this case, both coins show heads, so two dice will be rolled. The sum of the dice can only be even (2, 4, or 6). Probability = 0.

2. HT: One coin shows heads and the other shows tails. One die will be rolled. The sum of the die can be odd (1, 3, or 5) or even (2, 4, or 6). Probability of odd sum = 1/2.

3. TH: Similar to the previous case, one die will be rolled, and the sum can be odd or even. Probability of odd sum = 1/2.

4. TT: Both coins show tails, so no dice are rolled, and the sum is 0. Probability of odd sum = 0.

Now, let's calculate the overall probability of an odd sum:

Probability of HT = 1/2

Probability of TH = 1/2

Total probability of an odd sum = Probability of HT + Probability of TH = 1/2 + 1/2 = 1.

Therefore, the probability that the sum of the die rolls is odd is 1, which is equivalent to 100%.

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Complete Question:

Two fair coins are to be tossed once. for each head that results, one fair die is to be rolled. what is the probability that the sum of the die rolls is odd? (note that if no die is rolled, the sum is 0.)

\((a) $1 \\\\(b) $\frac{1}{2}$ \\\\(c) $\frac{43}{72}$ \\\\(d) $\frac{5}{8}$ \\\\(e) $\frac{2}{3}$\)

tried my best to show the steps!! all i did was isolate to find the missing widths attached to the respective lengths (divided surface area by width) and then multiply both sides by two and add them together to find the perimeter.

The dimensions of the garden that would require the least amount of fencing are 6 ft in length and 6 ft in width.

The dimensions are the sides of a geometric shape.

The lengths of the three gardens are given as 6 ft, 9 ft, and 12 ft respectively.

If the area of the garden is 36 feet squared, then the widths for the three lengths will be as follows:

The width of the garden with a length of 6 ft \(= \dfrac{36}{6} = 6\ ft\)

The width of the garden with a length of 9 ft \(= \dfrac{36}{9} = 4\ ft\)

The width of the garden with a length of 6 ft \(= \dfrac{36}{12} = 3\ ft\)

The parameters are calculated as:

The parameter of the garden with dimensions (6 ft, 6 ft) = 2(6 + 6) = 24 ft

The parameter of the garden with dimensions (9 ft, 4 ft) = 2(9 + 4) = 26 ft

The parameter of the garden with dimensions (12 ft, 3 ft) = 2(12 + 3) = 30 ft

The least of the parameter is of the garden with dimensions (6 ft, 6 ft).

Thus, the garden with dimensions (6 ft, 6 ft) would require the least amount of fencing.

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Answer:

12

Step-by-step explanation:

The Pythagorean theorem shows that 400 or 20² - 256 or 16² = 144 or 12² which means that the other side is 12

x=12

Answer:0.66

Step-by-step explanation:

hope this helps

Answer:0.66

Step-by-step explanation:33%50=0.66

Answer is a)  We have shown that:

cos((3π/2) + x) = -sin(x)

b) We have shown that:

cos(3x) = 4cos³x - 3cosx

c) We have shown that:

(tan(x) - sin(x)) / sin³(x) = sec(x) / (1 + cos(x))

a) Using the angle addition formula for cosine:

cos((3π/2) + x) = cos(3π/2)cos(x) - sin(3π/2)sin(x)

Since cos(3π/2) = 0 and sin(3π/2) = -1, we can simplify to:

cos((3π/2) + x) = -sin(x)

Therefore, we have shown that:

cos((3π/2) + x) = -sin(x)

b) Using the double angle formula for cosine:

cos(2x) = 2cos²x - 1

Substituting x with 3x:

cos(6x) = 2cos²(3x) - 1

Using the identity for cosine triple angle:

cos(3x) = 4cos³x - 3cosx

We can substitute this into our previous equation to get:

cos(6x) = 2(cos³(3x) - cos(3x)) + 1

Using the identity for cosine cubed:

cos³(3x) = (cos(3x))³ = (4cos³x - 3cosx)³

Expanding the cube:

cos³(3x) = 64cos⁹x - 96cos⁷x + 36cos⁵x - 3cos³x

Substituting this into the previous equation:

cos(6x) = 2(64cos⁹x - 96cos⁷x + 36cos⁵x - 3cos³x - (4cos³x - 3cosx)) + 1

Simplifying:

cos(6x) = 64cos⁹x - 96cos⁷x + 38cos⁵x - 5cos³x + 1

Therefore, we have shown that:

cos(3x) = 4cos³x - 3cosx

c) Starting with the left-hand side of the equation:

(tan(x) - sin(x)) / sin³(x)

Using the identity for tangent:

(sin(x)/cos(x) - sin(x))/sin³(x)

Combining fractions:

(sin(x) - sin(x)cos(x)) / sin⁴(x)

Factoring out sin(x):

sin(x)(1 - cos(x)) / sin⁴(x)

Simplifying:

(1 - cos(x)) / sin³(x)

Using the identity for secant:

sec(x) = 1/cos(x)

Substituting this into our previous expression:

(1 - cos(x)) / sin³(x) = (1/cos(x))(1 - cos(x)) / sin³(x)

Simplifying:

(1 - cos(x)) / sin³(x) = sec(x) / (1 + cos(x))

Therefore, we have shown that:

(tan(x) - sin(x)) / sin³(x) = sec(x) / (1 + cos(x))

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The area of the composite solid is 602.88m²

A composite solid is a solid that is composed, or made up of, two or more solids.

The solid consist of two cones. one big and one small cone

Area of a cone can be expressed as;

A = πr² + πrl

A = πr(r+l)

For the Big cone

A = πr(r+l)

A = 3.14 × 8 ( 8+10)

A = 25.12 × 18

A = 452.16m²

Area of the small cone

A = 3.14 × 4( 4 + 8)

A = 12.56 × 12

A = 150.72m²

Therefore the area of the composite solid

= 452.16 + 150.72

= 602.88 m²

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Answer:

x = 4

Step-by-step explanation:

log₃[1 + log₃(2ˣ - 7)] = 1

log₃[1 + log₃(2ˣ - 7)] = log₃(3)

1 + log₃(2ˣ - 7) = 3

log₃(2ˣ - 7) = 2

log₃(2ˣ - 7) = log₃(3)²

2ˣ - 7 = 9

2ˣ = 9 + 7

2ˣ = 16

2ˣ = 2⁴

x = 4

By putting x = 4 in the original equation,

log₃[1 + log₃(2⁴ - 7)] = 1

log₃[1 + log₃(16 - 7)] = 1

log₃[1 + log₃(9)] = 1

log₃[1 + log₃(3)²] = 1

log₃[1 + 2] = 1

log₃[3] = 1

1 = 1

Therefore, x = 4 is not the extraneous solution and there is no error in your answer.