find y when y = 3x^2 -2x+5 and x = -1

Answer:

110

Step-by-step explanation:

Rate or proportion shows the relationship between the variation in the  number of two variables.

Given that the ratio of alternative songs to total songs is 9:14.

Total songs = 308

Since the to every 14 total songs, there is 9 alternative songs.

Thus,

Number of alternative songs = \(\frac{9}{14}\) x 308

                                                = 198

There are 198 alternative songs in the music library.

The number of songs that are NOT alternative songs = 308 - 198

                                                                                         = 110

Thus, there are 110 songs that are NOT alternative songs.

The exact value of cos(-510°) is approximately -0.866. The reference angle for -510° is 150°.

To find the exact value of the expression cos(-510°), we can use the periodicity property of the cosine function. The cosine function has a period of 360°, which means that cos(x) = cos(x + 360°) for any angle x. Therefore, we can find an equivalent angle within one full revolution (360°) that has the same cosine value.

To find an equivalent angle within one full revolution, we add or subtract multiples of 360° to the given angle -510° until we get an angle within the range of 0° to 360°:

-510° + 360° = -150° (Equivalent angle within one full revolution)

Now, we need to find the cosine of the equivalent angle, which is -150°:

cos(-150°)

The cosine function of -150° can be found using a trigonometric identity:

cos(-θ) = cos(θ)

So, cos(-150°) = cos(150°)

We can use a unit circle or a calculator to find the cosine of 150°. On a unit circle, the cosine of an angle is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.

On the unit circle, the point corresponding to 150° is:

( cos(150°), sin(150°) )

To find cos(150°), we look at the x-coordinate:

cos(150°) ≈ -0.866

Therefore, the exact value of cos(-510°) is approximately -0.866.

Reference angle or coterminal angle for -510°:

The reference angle is the positive acute angle between the terminal side of an angle and the x-axis. To find the reference angle for -510°, we take the positive equivalent angle within one full revolution, which is 150°. The reference angle for -510° is 150°.

Since -510° is already its terminal side, it is also a coterminal angle with itself. Another coterminal angle can be obtained by adding or subtracting multiples of 360°:

-510° + 360° = -150° (positive coterminal angle)

-510° + 720° = 210° (positive coterminal angle)

So, the reference angle for -510° is 150°, and the positive coterminal angles are 150°, -150°, and 210°.

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Answer:

Of the equations given, y = 2x - 5 best represents the table of values. However, the equation that fits the table of values perfectly would be \(y = \frac{2}{3}x - 5\).

Step-by-step explanation:

If you plug the equations into a graphing calculator along with the points on the table of values, you can see that (of the equations given) y = 2x - 5 is the closest line to fitting on the points.

Of the equations given, y = 2x - 5 best represents the table of values. However, the equation that fits the table of values perfectly would be .

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.  Although the linear functions are also represented in terms of calculus as well as linear algebra. The only difference is the function notation. Knowing an ordered pair written in function notation is necessary too. f(a) is called a function, where a is an independent variable in which the function is dependent. Linear Function Graph has a straight line whose expression or formula is given by;   y = f(x) = px + q      

It has one independent and one dependent variable. The independent variable is x and the dependent one is y. P is the constant term or the y-intercept and is also the value of the dependent variable. When x = 0, q is the coefficient of the independent variable known as slope which gives the rate of change of the dependent variable.

If you plug the equations into a graphing calculator along with the points on the table of values, you can see that (of the equations given)

y = 2x - 5 is the closest line to fitting on the points.

Hence, y = 2x - 5 equation best represents the linear function

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Using the distributive property we have that multiplying by some terms grouped in parenthesis is the same as multiplying each term.

On one hand:

2(x+3) = 2 · x + 2 · 3

= 2x + 6

On the other:

(x+4)​ = x + 4

Then

2(x+3) + (x+4)​ = 2x + 6 + x + 4

We combine like terms in the expression

2x + 6 + x + 4

terms with x: 2x and x

numbers: 6 and 4

adding them we have that:

terms with x: 2x + x = 3x

numbers: 6 + 4 = 10

Then

2x + 6 + x + 4

= 3x + 10

Answer: 2(x+3) + (x+4)​ = 3x + 10

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

0.41666666, to round up, the answer is 0.42

Step-by-step explanation:

\( \frac{3}{8} + \frac{1}{8} - \frac{1}{3} + \frac{1}{4} = \frac{4}{8} - \frac{1}{3} = \frac{4}{24} + \frac{1}{4} = \frac{10}{24} = \frac{5}{12} \)

Answer is 7:9

Explanation:

To find this answer, you write the two given numbers in the order presented. Separate them with a colon. So we have 14:18

Afterward, divide both parts by the GCF 2 so we go from 14:18 to 7:9

A quadratic equation is in the form of ax²+bx+c. The time for which the stone was in the air is 3.526.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

As the height of the stone will be zero or can say that the stone will be at the ground in only two conditions. When the stone will be just thrown and when the stone will complete its flight. Therefore, we can substitute the value of heigh h in the function as 0 to get those two timings.

\(h(t) = 5 + 50t - 16t^2\\\\0 = 5+50t - 16t^2\)

Substitute the quadratic equation in the formula of the root of the quadratic function,

\(x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\t = \dfrac{-50\pm\sqrt{(50)^2-4(-16)(5)}}{2(-16)}\\\\t= -0.089, 3.526\)

Hence, the time for which the stone was in the air is 3.526.

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Answer:

25°

Step-by-step explanation:

First, Half of a full circle is 180°. So You want to add 125 + 35, which will get you 155. Now, You need to subtract 180 - 155. You will get 25. Hope this helps!

Answer:

Hello! answer: x = 20

Because 20 + 20 + 35 + 35 + 125 + 125 = 360

Hope that helps!

Step-by-step explanation:

Image 1:

1. It doesn't tell much, but it could either be a reflection or a translation.

2. It can either be reflection or rotation.

3. Can either be rotation or reflection, although it looks much more like reflection.

4. This is dilation, the process of making something smaller.

Image 2:

Blank 1: (0,-3)

Blank 2: (0,0)

Blank 3: (-2,0)

Blank 4: (-3,-2)

Image 3:

Blank 1: (-6,5)

Blank 2: (-4,-2)

Blank 3: (-2,2)

Note: you may need to graph it all out.

Answer: 42 gallons

Step-by-step explanation:

given data:

average gas mileage/day = 29miles/gallon

distance travelled each day by James = 87miles

How much gas does he use in 14days drive.

solution:

james drives 87miles daily, so in 14 days he would have travelled

= 87miles * 14

= 1218miles travelled.

gas used in 14days

1218miles distance traveled in 14 days

29miles/gallon

= 1218miles / 29miles

= 42gallons of gas have been used by janew to fuel his truck in 14days.

Answer:

p=2

Step-by-step explanation:

10 – (8p + 3) = 9(2p - 5)

(rearrange and distribute) -8+7=18−45

(Subtract and combine) −26=−52

(Divide and find p) p=2

Answer:

2

Step-by-step explanation:

10-(8p+3)=9(2p-5)

10-8p-3=18p-45

26p=52

p=2

The cost of goods sold for the year can be calculated by adding the beginning finished goods inventory to the cost of goods manufactured, and then subtracting the ending finished goods inventory.

Therefore, the cost of goods sold for the year for Branson Books is: $400,000 (beginning finished goods inventory) + $860,000 (cost of goods manufactured) - $990,000 (ending finished goods inventory) = $270,000.

This means that the total cost of goods sold for the year was $270,000. Cost of goods manufactured represents the total cost incurred by the company to manufacture the goods during the year. Beginning work-in-process inventory represents the cost of goods that were partially completed at the beginning of the year, while ending work-in-process inventory represents the cost of goods that were partially completed at the end of the year.

By subtracting the beginning work-in-process inventory from the total cost of goods manufactured and adding the ending work-in-process inventory, the cost of goods completed during the year can be calculated. This cost, when added to the beginning finished goods inventory, represents the total cost of goods available for sale. By subtracting the ending finished goods inventory, the cost of goods sold can be calculated. In this case, we have calculated the cost of goods sold for Branson Books to be $270,000.

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Answer:

A) \(-\dfrac{1}{8}x\right + \dfrac{3}{16}\)

Step-by-step explanation:

We can simplify the expression using the Distributive Property, which states that:

\(A(B+C) = AB + AC\)

Applying this to the problem at hand...

\(-\dfrac{1}{2}\left(\dfrac{1}4x - \dfrac{3}{8}\right)\)

\(= \left(-\dfrac{1}{2}\cdot\dfrac{1}4x\right) - \left(-\dfrac{1}2\cdot\dfrac{3}{8}\right)\)

\(= -\dfrac{1}{8}x\right + \dfrac{3}{16}\)

So, option A is correct.

Based on the given information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own graphing TI calculators so it can be estimated that the proportion of students who do not own a TI graphing calculator is 50%.

To estimate the proportion of students who do not own a TI graphing calculator, we can use the information provided that out of the 4 students who owned a TI calculator, 2 had graphing calculators. Since we know that all graphing calculators are TI calculators, we can assume that the 2 students with graphing calculators are included in the total count of students who own TI calculators. Therefore, the remaining 2 students who own TI calculators must have non-graphing calculators.

Based on this information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own non-graphing TI calculators. Therefore, we can estimate that the proportion of students who do not own a TI graphing calculator is 50%.

It's important to note that this is an estimation based on the limited information provided. To obtain a more accurate estimate, a larger sample size or more comprehensive data would be needed. Additionally, this estimation assumes that the sample of 4 students is representative of the entire student population in terms of calculator ownership. If there are any biases or limitations in the sampling method or if the sample is not representative, the estimate may not accurately reflect the true proportion of students who do not own a TI graphing calculator.

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Answer:

2y - 3 < -13

Hope this helps

1/3

because there are 15 balls total and 5 are red, so 15/5 = 3 meaning 1/3 and also being that there are three different colors, so yeah, 1/3

Volume of cone is, 83.73 cm³

The curved surface area of cone is, 47.1 cm²

The total surface area​ of coin is, 75.4 cm²

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The base radius and slant height of a cone is 3cm and 5cm respectively.

Now, We know that;

⇒ Volume of cone = πr²h/3

Here, Radius (r) = 3 cm

Slant height ( l ) = 5 cm

Hence, we get;

h = √l² - r²

h = √5² - 3²

h = √25 - 9

h = √16

h = 4

Hence, We get;

⇒ Volume of cone = πr²h/3

⇒ Volume of cone = 3.14 × 4² × 5 / 3

⇒ Volume of cone = 83.73 cm³

We know that;

The curved surface area of cone is,

⇒ CSA = πrl

⇒ CSA = 3.14 × 3 × 5

⇒ CSA = 47.1 cm²

We know that;

The total surface area​ of cone is,

TSA = πr² + πrl

TSA = 3.14 × 3² + 3.14 × 3 × 5

TSA = 28.3 + 47.1

TSA = 75.4 cm²

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The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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The cell potential (E⁰ cell) of the given reaction Cr₂O₇²⁻ (aq) + 14H⁺ (aq) + 6I⁻ (aq) → 2Cr³⁺ (aq) + 7H₂O (l) + 3I₂ (s) is 0.79 volts.

The given reaction is a redox reaction involving the following species: Cr₂O₇²⁻ (aq) + 14H⁺ (aq) + 6I⁻ (aq) → 2Cr³⁺ (aq) + 7H₂O (l) + 3I₂ (s) .

To determine the cell potential (E⁰) of the reaction, we need to know the reduction potentials (E⁰) of the species involved. The reduction half-reactions involved in this reaction are:

Cr₂O₇²⁻ (aq) + 14H⁺ (aq) + 6e⁻→ 2Cr³⁺ (aq) + 7H₂O (l)

(1) I2 (s) + 2e⁻ → 2I⁻ (aq)

(2) The standard reduction potentials (E⁰) for these half-reactions are: E⁰(Cr₂O₇²⁻/Cr³⁺) = 1.33 V

E⁰(I2/I⁻) = 0.54 V

To calculate the cell potential (E⁰cell), we subtract the reduction potential of the anode reaction (oxidation half-reaction) from the reduction potential of the cathode reaction (reduction half-reaction):

E⁰cell = E⁰cathode - E⁰anode

In this case, the reduction half-reaction (1) involves Cr₂O₇²⁻/Cr³⁺ and has a higher reduction potential (1.33 V) compared to the reduction half-reaction (2) involving I2/I⁻ (0.54 V).

Therefore, the reduction half-reaction (1) is the cathode reaction, and the reduction half-reaction (2) is the anode reaction. Substituting the values into the equation, we get:

E⁰cell = 1.33 V - 0.54 V = 0.79 V

Therefore, the cell potential (E⁰cell) of the given reaction is 0.79 volts.

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Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Answer:

Step-by-step explanation:

hello :

f(x) = 5x - 7 and f(x) = -3

5x - 7  = -3

5x=7-3

5x=4

x=4/5

Answer:

x = 4/5

Step-by-step explanation:

5x - 7 = -3

5x = -3 + 7

5x = 4

x = 4/5

Check:

5*4/5 - 7 = -3

4 - 7 = -3

To determine the degree of the Maclaurin polynomial required for the error in the approximation of the function f(x) = -x+1 at the indicated value of x to be less than 0.001, we can use the formula: N ≥ ln(error)/ln(absolute value of x) + 1.

For our given function, the error is 0.001, and the value of x is 0.2. Plugging these values into the formula, we get: N ≥ ln(0.001)/ln(0.2) + 1, which is equivalent to N ≥ 6.64 + 1 = 7.64. Therefore, we need the degree of the Maclaurin polynomial to be 7.64 in order for the error in the approximation of the function at the indicated value of x to be less than 0.001.

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Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.

Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5   =  $29600

Median income of country A = (5+1)/2 th term = 3rd term = $29000

Mean to median ratio = 29600/ 26000= 1.02

Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800

Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000

Mean to median ratio of country B = 49800/29000 = 1.71

Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.

If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.

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Answer:

6.2

Step-by-step explanation:

I don't think you need my explanation anymore.

The Z score that is equivalent to the raw score 92.5 is B. -1.25.

A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:

Z = (92.5 - 100) / 15

Z = -7.5 / 15

Z = -0.5

Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.

The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.

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A. 70in³ i hope this helps!

Answer:

D. Alkali Metals

Step-by-step explanation:

Answer:

alkali metals