Use the quadratic function to predict y if x equals 7. Y=2x^2 -3x +3

To find side b in the triangle, we use the fact that angles in a triangle sum up to 180° to find angle B, and then apply the Law of Sines to solve for b using angles B and C and side c.

To determine b in a triangle where angle A = 63°, angle C = 49°, and side c = 3, first, we need to find angle B using the fact that the sum of angles in a triangle is 180°. Therefore, B = 180° - A - C. Calculating this gives us B = 180° - 63° - 49° = 68°. Since angles A, B, and C are known, we can use the Law of Sines to find side b:

b/sin(B) = c/sin(C)

Rearranging this for b yields:

b = c * sin(B) / sin(C)

We substitute the known values to find b:

b = 3 * sin(68°) / sin(49°)

By solving this, we get the length of side b is 3.68

Answer:

  [0, ∞)  or  0 ≤ x

Step-by-step explanation:

You want to know the domain of the function y = √x.

The domain of a function is the set of values of the independent variable for which the function is defined. The square root function is defined for all non-negative real numbers. So, ...

The domain of

 y = √x

is all real numbers greater than or equal to zero.

  0 ≤ x . . . . domain of y=√x

In interval notation, this is ...

  [0, ∞) . . . . domain of y=√x

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Additional comment

The inequality for the domain of y=√x can also be written as x ≥ 0.

It is sometimes useful to write the inequality with a left-pointing inequality symbol so the limit and the variable map directly to a region of the number line. Here, the limit (0) is at the left end of the ray on the number line that identifies the domain of x.

The "practical" domain of a function is the set of values the function may be expected to utilize in the real world. A function may be defined for all values of mass, for example, but is of no practical use for negative mass or values of mass greater than that of the known universe.

Final answer:

The domain of the function y = √x consists of all real numbers greater than or equal to 0. The function is non-differentiable only at x = 0. The restriction ensures that the square root is of a non-negative number, conforming to real-valued outputs.

Explanation:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. Considering the function y = √x, the domain is all real numbers greater than or equal to 0 because we cannot take the square root of a negative number in the real number system. This ensures that the values under the square root are non-negative, allowing the function to produce real number outputs. When we consider functions like l(x) = x² √√x, we must also consider that while x² is defined for all real numbers, the part √√x restricts the domain since x must be greater than or equal to 0 for the function to be real-valued. Thus, the domain of l(x) is also limited to x values greater than or equal to 0.

When seeking nondifferentiable points within the domain, we look for values of x where the derivative of the function does not exist. For the function y = √x, all points in the domain are differentiable except at x = 0, where the function has a cusp and is, therefore, not differentiable.

To summarize, the domain of y = √x is all x ≥ 0, and with the function l(x), we are careful to include only those x-values where the square root and the entire expression are defined, which also turns out to be x ≥ 0.

 Answer: Y-48

If the median of the values in the data set is Y, it means that Y is the value in the middle of the data set. If 48 will be deducted from each of all values in the data set including Y, then the median of the resulting value will be Y-48. 

To find the total bill including the service charge, multiply the original meal cost by 15% to calculate the service charge. Then, add this to the original meal cost to get the total of £75.21.

The question involves Mathematics as it requires calculating the total bill including the service charge which is essentially calculating a percentage of the original amount. To determine the total amount to be paid, one must first calculate the 15% service charge on the £65.40 meal and add it to the original amount. The service charge is calculated by converting the percentage to a decimal and multiplying it by the meal cost: 0.15 × £65.40.

Let's do the calculation:

The total bill after adding the 15% service charge to the £65.40 meal cost is £75.21.

Answer:

the final answer is the last option, D

Step-by-step explanation:

Team A won 3g - 7 games, where g is the number of games won by Team C. To determine the number of games Team A won, multiply the number of games Team C won by 3 and subtract 7.

Let's denote Team C's number of wins as g. According to the information provided, Team B won three times as many games as Team C, which can be expressed as 3g. It is also stated that Team A won 7 fewer games than Team B. So, if Team B won 3g games, then Team A won 3g - 7 games.

To find the number of games Team A won, simply multiply the number of games Team C won by 3 and subtract 7 from that total. This can be represented by the algebraic expression A = 3g - 7, where A represents the number of games won by Team A and g represents the number of games won by Team C.

Answer:

  D.  $877.96

Step-by-step explanation:

You want the amount saved if a 20 year loan of $60,000 at 4.4% is paid off 3 years early.

The monthly payment on the loan can be found from ...

  [tex]A=\dfrac{Pr}{12(1-(1+r/12)^{-12t})}[/tex]

where P is the loan amount at rate r for t years.

For the 20 year loan of $60,000 at 4.4%, the payment is calculated as ...

  [tex]A=\dfrac{60000(.044)}{12(1-(1+0.044/12)^{-12\cdot20})}=\dfrac{220}{0.584549}=376.3585[/tex]

After 204 payments on the loan, the remaining balance due is ...

  [tex]A=P\left(1-\dfrac{(1+r/12)^n-1}{(1+r/12)^{12t}-1}\right)\\\\\\A=60000\left(1-\dfrac{1.0036667^{204}-1}{1.0036667^{240}-1}\right)=12671.04[/tex]

The remaining 36 payments on the loan come to about ...

  36 × 376.3585 ≈ 13548.91

So, the savings from early payoff is about ...

  13548.91 -12671.04 ≈ 877.86

Choice D, $877.96, is the best match for this value.

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Additional comment

The actual savings will depend on the details of rounding of intermediate values in the calculation, and on the timing of the early payment. If the loan is amortized over 17 years, so more is paid each month, the savings can be more than $5000.

Here, we have calculated the savings on the assumption that payment number 204 includes the payoff amount.

Using the loan formula, monthly payments are $458.14. Remaining balance after 17 years is approximately $58,214.19. The savings would be approximately $1,785.81. The closest option to this calculation is  C. $376.36

To calculate the amount saved by paying off the loan 3 years early, we need to find out the remaining balance of the loan after 17 years (20 years - 3 years). Then, we compare the remaining balance to the original balance to find the savings.

Let's break down the steps:

1. Find the monthly interest rate (r):

[tex]\[ r = \frac{4.4\%}{12} = \frac{0.044}{12} \][/tex]

2. Calculate the total number of payments (n):

[tex]\[ n = 20 \times 12 = 240 \text{ months} \][/tex]

3. Use the formula for the monthly payment (PMT) of a loan:

[tex]\[ PMT = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \][/tex]

where:

P = principal amount (loan amount)

r = monthly interest rate

n = total number of payments

We'll use PMT to find out the monthly payment Arthur has to make.

4. Use the monthly payment (PMT) to find the remaining balance after 17 years (204 months).

5. Finally, calculate the savings by comparing the remaining balance to the original loan amount.

Let's do the calculations:

1. Monthly interest rate:

[tex]\[ r = \frac{0.044}{12} = 0.00367 \][/tex]

2. Total number of payments:

[tex]\[ n = 20 \times 12 = 240 \text{ months} \][/tex]

3. Monthly payment (PMT):

[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot (1 + 0.00367)^{240}}{(1 + 0.00367)^{240} - 1} \][/tex]

[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot (1.00367)^{240}}{(1.00367)^{240} - 1} \][/tex]

[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot 1.937}{1.937 - 1} \][/tex]

[tex]\[ PMT = \frac{429.33}{0.937} \][/tex]

[tex]\[ PMT= 458.14 \][/tex]

4. Remaining balance after 17 years (204 months):

[tex]\[ PV = \frac{PMT \cdot (1 - (1 + r)^{-n})}{r} \][/tex]

[tex]\[ PV = \frac{458.14 \cdot (1 - (1 + 0.00367)^{-204})}{0.00367} \][/tex]

[tex]\[ PV = \frac{458.14 \cdot (1 - 0.533)}{0.00367} \][/tex]

[tex]\[ PV = \frac{458.14 \cdot 0.467}{0.00367} \][/tex]

[tex]\[ PV = \frac{213.94}{0.00367} \][/tex]

[tex]\[ PV = 58214.19 \][/tex]

5. Savings:

Savings = 60000 - 58214.19

Savings ≈ 1785.81

So, Arthur would save approximately $1785.81 by paying off the loan 3 years early.

The closest option to this calculation is  C. $376.36

The best point estimate for the true mean weight of all packages received by a parcel service, given a sample mean of 20.6 pounds and a standard deviation of 3.2 pounds, is 20.6 pounds.

In this problem, we are given that a sample of 41 packages were randomly selected. This sample provided a mean weight of 20.6 pounds and a standard deviation of 3.2 pounds. It is asked what the best point estimate for a confidence interval estimating the true mean weight of all packages is.

The best estimate of the true mean weight (µ) of all packages would be the mean of the sample that was taken, assuming that the sample was randomly selected and is representative of the entire population. This is due to the fact that in statistics, the sample mean is the best point estimate of the population mean.

Therefore, the best point estimate for the true mean weight of all the packages received by the parcel service is 20.6 pounds.

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Try the first table value and see what you get from the various choices. For x = 1, the answer choices give you

... A: y = 5×1 = 5

... B: y = 1 + 1 = 2

... C: y = 1 + 2 = 3

... D: y = 2×1 = 2

Both B and D give the correct value (2), so we need to try another table entry. For x = 3 (the second table entry), the answer choices give you

... B: y = 3 + 1 = 4

... D: y = 2×3 = 6

Only selection D gives you the correct value (6). The appropriate choice is

... D. y = 2x

Final answer:

The quantity with units of (kg*m²)/(s²*c) is closely related to the energy concept in physics, specifically within the framework of Einstein's mass-energy equivalence formula, E = mc², albeit with an added factor of the speed of light in the denominator.

Explanation:

The quantity with units of (kg*m^2)/(s^2*c) is related to the concept of mass-energy equivalence, as seen in Albert Einstein's famous equation, E = mc².

In this equation, E represents energy in joules, m represents mass in kilograms, and c represents the speed of light in meters per second.

The units of c² are m²/s², making the units of energy (when mass is given in kilograms) equivalent to kg*m²/s², or joules.

However, the specific units you mentioned, (kg*m²)/(s²*c), seem to incorporate an additional factor of the speed of light in the denominator, suggesting a possible deviation or specific application within the broader context of relativistic physics or energy conversions where the factor of c is explicitly considered.

Answer:

Angela's board is a rectangle.

Step-by-step explanation:

As we know rectangle follow two properties.

1). All angles of a rectangle are right angle.

2). Opposite sides of a rectangle are equal in measure.

Since all angles of a rectangle are 90°. Therefore, right angle triangle formed by length, width and diagonal will follow Pythagoras theorem.

For Angela

20² + 21² = 841 = 29²

Therefore Angela's board is a rectangle.

For Bradley

9² + 9² = 162 ≈ 9²

So Bradley's board is not a rectangle.

For Carlton

25² + 30² = 1525 ≠ 35²

Carlton's board is not a rectangle.

For Della

10² + 12² = 244 ≠ 15²

Della's board is not a rectangle.

Therefore, Angela's board is a rectangle.

Answer:

  11 cm by 15 cm

Step-by-step explanation:

The perimeter is double the sum of length and width, so that sum is 26 cm. The area is the product of length and width, so you want to find two numbers whose product is 165 and whose sum is 26.

  165 = 1·165 = 3·55 = 5·33 = 11·15

The numbers in the last factor pair total 26. These are the dimensions.

The dimensions are 11 cm by 15 cm.

Answer:

Your answer would be a. or the first problem.

Step-by-step explanation:

The probability that the average mosquito count in a randomly chosen square meter of the pond is more than 68 mosquitoes is approximately 59.87%.

To find the probability that the average count of mosquitoes in a randomly chosen square meter of the pond is more than 68 mosquitoes per square meter, we can use the normal distribution properties.

Given:

We need to find P(X > 68). To do this, we convert the raw score to a Z-score using the formula:

Z = (X - μ) / σ

Substitute the given values:

Z = (68 - 70) / 8 = -2 / 8 = -0.25

Next, we need to find the probability corresponding to Z > -0.25 using the standard normal distribution table.

Looking up Z = -0.25, we find the cumulative probability (P(Z < -0.25)) is approximately 0.4013.

To find P(Z > -0.25):

P(Z > -0.25) = 1 - P(Z < -0.25) = 1 - 0.4013 = 0.5987

Therefore, the probability that the average mosquito count in a randomly chosen square meter is more than 68 mosquitoes per square meter is approximately 0.5987 or 59.87%.

The expected number of responses after offering a discount leads to an 80% increase from 23,000 is 41,400.

The student's question relates to predicting email response rates when a discount is offered. Since the history suggests an 80% increase in responses when a discount is included and the last email got 23,000 responses, we can expect:

Thus, the answer is (a) 41,400 responses expected with a discount offer.