what is the solution to the system of equations?
6x-2y=-14
4x-3y=-31​

The quotient is x^2 – 3, and the remainder is -1 when dividing x^6 – x^4 + 3x^2 – 3 by x^2 – 1 using long division.


To find the quotient and remainder using long division, we divide the polynomial x^6 – x^4 + 3x^2 – 3 by the divisor x^2 – 1.
We start by dividing the highest degree term of the dividend (x^6) by the highest degree term of the divisor (x^2), which gives us x^4. We then multiply the divisor (x^2 – 1) by x^4, which gives us x^6 – x^4. Subtracting this from the dividend, we get -2x^4 + 3x^2 – 3.

We repeat the process with -2x^4 + 3x^2 – 3 as the new dividend. Dividing -2x^4 by x^2 gives us -2x^2, and multiplying (x^2 – 1) by -2x^2 gives us -2x^4 + 2x^2. Subtracting this from the dividend, we get x^2 – 3.
Since the degree of the new dividend (x^2 – 3) is less than the degree of the divisor (x^2 – 1), we stop here. The quotient is x^2 – 3, and the remainder is -1.

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The matrix equation for the given data can be set up as follows:

A * [x, a, p;
       y, b, q;
       z, c, r] = [24;
                          27;
                          20]

To set up a matrix equation for the given data, we can use a matrix with three rows (representing the three types of nutrients: protein, fat, and carbohydrates) and three columns (representing the three foods). Let's call this matrix A.

The values in the matrix will correspond to the amount of each nutrient in each food.

Let's say food 1 has x grams of protein, y grams of fat, and z grams of carbohydrates. Similarly, food 2 has a grams of protein, b grams of fat, and c grams of carbohydrates, and food 3 has p grams of protein, q grams of fat, and r grams of carbohydrates.

The matrix equation for the given data can be set up as follows:

A * [x, a, p;
       y, b, q;
       z, c, r] = [24;
                          27;
                          20]

This equation represents the requirement to have a total of 24 grams of protein, 27 grams of fat, and 20 grams of carbohydrates in the meal.

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Answer:

is the line are perpendicular then the product of there slope is -1

the slope of the first equation is 2

Step-by-step explanation:

m1+m2=-1

2+m2=-1

m2=-1-2

m2=-3

so the second equation became y=-3x+C

then insert the point (-1,2)

2=-3*-1+C

2=3+C

C=2-3

C=-1

so y=-3x-1

Hope that helps

Answer:

6-inch board is cut into two pieces. One piece is two times the length of the other. Find the length

of the shorter pi

The type of automobile insurance coverage that is needed in this problem is of:

Liability coverage.

The types of car insurance coverage are listed as follows:

In this problem, the situation is that Harold caused a collision that resulted in injuries to Tyler, who has to pay the ambulance/hospital bill.

This means that Harold is liable to the injuries caused to Tyler, meaning that he needs liability coverage to help pay the hospital/ambulance bill, as collision coverage and personal injury coverages are for the victim and not for the person that caused an accident.

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The length of the displaced threshold for runway 22 at Toledo (TDZ) is 380 feet. Option C) is correct.

A displaced threshοld is a designated pοrtiοn οf a runway where the starting pοint fοr landing aircraft is mοved further dοwn the runway. It is typically marked by white arrοws οr οther markings οn the pavement. The purpοse οf a displaced threshοld is tο create a clear area fοr οbstacles, such as buildings οr terrain, at the beginning οf the runway, allοwing aircraft tο apprοach the runway at a safer pοint.

This can be necessary due tο the presence οf οbstructiοns οr tο meet certain οperatiοnal requirements. When a displaced threshοld is present, the pοrtiοn οf the runway befοre the threshοld is nοt available fοr landing and takeοff οperatiοns.

Displaced threshold is half of clearance,

Therefore, we calculate the clearance and divide it by 2

(1000 - 620) / 2 = 380

Thus, The length of the displaced threshold for runway 22 at Toledo (TDZ) is 380 feet. Option C) is correct.

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Complete question:

(Refer to Figure 63.) What is the length of the displaced threshold for runway 22 at Toledo (TDZ)?

A) 25 feet.

B) 100 feet.

C) 380 feet.

Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

Cost price is the amount we pay to buy an item at which it is available.

Here,

Selling price of a cake = 200 cedis

Discount because of sale = 10% on each unit.

                                              (Only if 4 cakes purchased at a time)

Amanda purchased 8 cakes

So, Amanda need to pay only 90 percent of the total amount.

Total cost price of 8 cakes for Amanda = (200 X 90%) X 8

                                                                  = 180 X 8

                                                                  = 1440

Thus, Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

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(A) The maximum likelihood estimate of lambda is 1.5.

(B) The maximum likelihood estimate that the next two calls will be completed without any accidental drops is e^(-3).

To find the maximum likelihood estimate of lambda in a Poisson distribution representing the number of dropped wireless phone connections per call, we can analyze the given data. From four calls with the number of dropped connections as 2, 0, 3, and 1, we can determine the lambda value that maximizes the likelihood of observing these specific outcomes. Using the maximum likelihood estimation, we can also estimate the likelihood of the next two calls being completed without any accidental drops.

(a) To find the maximum likelihood estimate of lambda, we need to determine the parameter that maximizes the likelihood of observing the given data. In a Poisson distribution, the probability mass function is given by P(X = x) = (e^(-lambda) * lambdaˣ) / x!, where X is the number of dropped connections and lambda is the average number of dropped connections per call.

Given the data: 2, 0, 3, 1, we calculate the likelihood function L(lambda) as the product of the individual probabilities:

L(lambda) = P(X = 2) * P(X = 0) * P(X = 3) * P(X = 1)

To find the maximum likelihood estimate, we differentiate the logarithm of the likelihood function with respect to lambda, set it equal to zero, and solve for lambda. However, for simplicity, we can directly observe that the likelihood is maximized when lambda is the average of the given data points:

lambda = (2 + 0 + 3 + 1) / 4

lambda = 6 / 4

lambda = 1.5

Therefore, the maximum likelihood estimate of lambda is 1.5.

(b) To estimate the likelihood of the next two calls being completed without any accidental drops, we can use the maximum likelihood estimate of lambda obtained in part (a). In a Poisson distribution, the probability of observing zero dropped connections in a call is given by P(X = 0) = (e^(-lambda) * lambda^0) / 0!, which simplifies to e^(-lambda).

Using lambda = 1.5, we can calculate the probability of zero dropped connections in a call:

P(X = 0) = e^(-1.5)

To estimate the likelihood of two consecutive calls without any drops, we multiply the individual probabilities:

P(X = 0 in call 1 and call 2) = P(X = 0) * P(X = 0) = (e^(-1.5))^2 = e^(-3)

Therefore, the maximum likelihood estimate that the next two calls will be completed without any accidental drops is e^(-3).

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Answer:

A. ≈31.1

B. ≈19.7

Step-by-step explanation:

A. 245/798

B. 157/798

Answer:

Look at step-by-step explanation

Step-by-step explanation:

14a.

There are 798 students total and 245 freshman. To find the percent of freshman, divide 245 by 798:

245/789= 31.1%

Same process for part b. There are 798 students and 157 seniors:

157/789= 20.0%

\(\bull\)Total number of seats in theatre = 4500

\(\bull\)Total number of seats left vacant = 3105

\(\longrightarrow\)Number of seats occupied = Total number of seats in theatre - Total number of seats left vacant

\(\longrightarrow\)Number of seats occupied

\(\quad\)= 4500 - 3105

\(\longrightarrow\) 1395

\(\\\)

Now,

\(\begin{gathered}\bull \sf Percentage \:of \:seats \:filled = \frac{Seats \: filled \: by \:6th \:grader }{Total \:number \:of \:seats} \times 100 \% \\\end{gathered} \)

\(\begin{gathered}\bull \sf Percentage \: of \:seats \: filled = \frac{1395}{45\cancel{00}} \times \cancel{100} \% \\\end{gathered} \)

\(\begin{gathered}\implies\quad \sf \frac{1395}{45} \% \\\end{gathered} \)

\(\begin{gathered}\implies\quad \sf 31 \% \\\end{gathered} \)

\(\longrightarrow\)Thus , 31 % of seats in the theater were filled by the 6th graders on the trip

Answer:

$6.20 is the cost of candy per pound.

5/31 lbs of candy would be for $1.

Step-by-step explanation:

With 98% confidence interval, all teenagers' mean number of hours watching TV per week will be (26.6,29.4).

98% confidence interval can be calculated as

Point estimate± Error margin

Point estimate=mean number of hours watching TV

students=28.

Error margin=1.4.

As per given data, the 98% confidence interval for all teenagers is

=28± 1.4

=(28-1.4,28+1.4)

=(26.6,29.4)

Statisticians use confidence intervals to assess the level of uncertainty in a sample variable. For instance, a researcher may select numerous samples at random from the same population and compute a confidence interval for each sample to estimate how each sample may correctly reflect the true value of the population variable. With certain intervals including the true population parameter and others not, each produced dataset is distinct. Confidence intervals are a set of values that are constrained by the mean of the statistic and are likely to include an unidentified population parameter. The confidence level is the proportion of likelihood, or certainty, that, after multiple draws from a random sample, the confidence interval would contain the true population parameter.

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Answer:

(x+4)^2-5

Step-by-step explanation:

To solve this we first need to shift the graph to the left 4 spots

We do this by adding 4 so we get

(x+4)^2

We then need the graph to go down 5 spots so we subtract by 5

This gives us

(x+4)^2-5

Answer:

C = (5F - 160)/9

Step-by-step explanation:

Given:

F = 9/5C + 32

Solve the formula for C in terms of F

F = 9/5C + 32

F - 32 = 9/5C

C = (F - 32) ÷ 9/5

C = (F - 32) × 5/9

= (5F - 160)/9

C = (5F - 160)/9

Answer:

The answer is III: 4.5

Step-by-step explanation:

It's not the first option since there has to be more than one person living in those houses. It's not the second since 3 is greater than 0, and median is in order from least to greatest. It's three since it's reasonable and is in order from least to greatest.

If the price of gasoline has increased from $2.00 per gallon to $3.00 per gallon. how would this price change be represented on the demand curve is: a movement from one point on the line to a higher point on the line.

Demand curve can be defined as the curve that show price of goods and services produced as well as the quantity demanded for the goods produce at a particular period of time.

The  price change can be represented on the demand curve when price increase and this happen when the price of goods move from one point on a line to a higher point on the line

Therefore  how would this price change be represented on the demand curve is: a movement from one point on the line to a higher point on the line.

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The function f(x) = 2x + 8x has a local maximum at x = 0 with a value of 0 and a local minimum at x = -2 with a value of -24.

To find the local maximum and minimum of the given function f(x) = 2x + 8x, we first differentiate it with respect to x. The derivative of f(x) is f'(x) = 2 + 8 = 10. Setting f'(x) = 0, we find the critical point at x = -2.

To determine if it is a local maximum or minimum, we evaluate the second derivative. The second derivative, f''(x), is a constant 0. Since the second derivative is zero, it indicates a point of inflection. Thus, x = -2 is a local minimum. Similarly, the function has no local maximum as it increases indefinitely.

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The greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.

Let's call the total distance that Oleg jogged z. Then z = 2x.

The total distance that Oleg bicycled was 30 - z - 2. Let's call this distance w. Then w = 30 - 2x - 2.

Since Oleg bicycled for 2 hours, the speed that he bicycled was w / 2. So, w / 2 = y.

Substituting the expressions for z and w, we have:

y = (30 - 2x - 2) / 2.

Since y must be the greatest possible speed that Oleg could have bicycled that day, x must be the smallest possible value.

Since Oleg jogged for 2 hours, the minimum value of x is 2 / 2 = 1.

Substituting x = 1 into the expression for y, we have:

y = (30 - 2 * 1 - 2) / 2 = (26) / 2 = 13.

So, the greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.

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The

speed

indicated in kilometers per hour is 85 km/h, as shown on the circular scale of the automobile

speedometer

.

The automobile

speedometer

is an instrument that measures the speed of a vehicle. It has a circular

scale

that reads both miles per hour (mph) and kilometers per hour (km/h). To determine the

speed

in kilometers per hour, the user must first locate the needle on the scale. The needle should be pointing to a specific number that corresponds to both mph and km/h. For example, if the needle is pointing to 85, then the speed indicated in kilometers per hour is 85 km/h. It is important to note that if the needle is located between two

numbers

, the user should determine the approximate speed by interpolating the two numbers. To find the speed in miles per hour, the user can simply look at the number that corresponds to the needle on the scale. In this case, the speed indicated in miles per hour is 53 mph.

The complete question: An automobile speedometer with circular scales reading both miles per hour and kilometers por hour is shown. What speed is indicated in miles per hour? 100 120 140 80 160 *60 180 200 40 20 220 Own 240 Express your answer in miles per hour v.2 mph

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Answer:

x=40

y=− 17 /6

Step-by-step explanation:

Therefore , the solution of the given problem of percentage comes out to be the estate agency will receive a commission of R 196,000.

A percentage in arithmetic is a number or a number expressed as a fraction of 100. The forms "pct.," "pct," and "pc" are also rarely used. However, the symbol for it, "%," is commonly employed. There are no dimensions; the percentage total is flat. Percentages are essentially integers because their numerator is 100. To indicate that a number is a percentage, it must be preceded either by percent symbol (%).

Here,

The estate agency receives a commission of 7% of the farm's selling price.

=> Commission = 7% of R 2,800,000

=> Commission = 0.07 x 2,800,000

=> Commission = R 196,000

So, when the farm is sold, the estate agency will receive a commission of R 196,000.

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Answer:

The product of (px + qy)(ax − by) is pax^2 + qaxby - pbx^2 - qby^2.

Step-by-step explanation:

Answer: apx^2-bpxy+aqxy-bqy^2

Step-by-step explanation: (px+qy)x(ax-by) Multiply each term in the first parenthesis by each term in the second parenthesis (FOIL). That would give you pxax-bpxy+aqxy-qyby. Then calculate the product pxax which would give you apx^2-bpxy+aqxy-qyby. Calculate the other product qyby which would give you apx^2-bpxy+aqxy-bqy^2.  

Answer:

0.81859

Step-by-step explanation:

We solve using z score method

The formula for calculating a z-score is is z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Mean 0.8 pound

Standard deviation 0.25 pound

For x = 0.55 pound

z = 0.55 - 0.8/0.25

= -1

Probability -value from Z-Table:

P(x = 0.55) = 0.15866

For x = 1.3 pounds

Z = 1.3 = 0.8/0.25

= 2

Probability value from Z-Table:

P(x = 1.3) = 0.97725

The probability that a randomly selected zucchini will weigh between 0.55 pound and 1.3 pounds is

P(x = 1.3) - P(x = 0.8)

0.97725 - 0.15866

0.81859.

Answer:

A

Step-by-step explanation:

2 standard deviations away

Answer:

22.5 pounds

Step-by-step explanation:

The computation of the weight of the block of gel is shown below:

As we know that

Volume = (length) (width) (height)

= (20) (6 ) (6)

= 720 cubic inches

Now we have to convert into cubic foot

As we know that

1 ft = 12 inches

So 1ft^3 = 12 inches^3

= 1728 inches ^3

Now

= 720 × 1 cubic foot ÷ 1728 cubic inches

= 5 ÷ 12

Now the weight is

= 54 × 5 ÷ 12

= 22.5 pounds

The lower bound for the perimeter of the rectangle when the length is 87. 3cm and the width is 51. 8cm is 278.24 cm.

Lower bound is the minimum valued number that have been before it was rounded to the nearest. As per the query, we need to find the perimeter of the rectangle whose length is 87.3 cm while its width is 51.8cm. The perimeter of a rectangle is given by the formula:

=2 (l + b)

=2 (87.3 + 51.8)

=2 (139.1)

=278.2 cm

Therefore, the perimeter of the rectangle, when the length is 87. 3cm and the width is 51. 8cm is, 278.2 cm.

We need to assume the lower bound value for this value. We can assume that 278.2 may have been 278.24cm before it was rounded to the nearest value, i.e., 278.2cm. Thus, the lower bound for the perimeter of the rectangle when the length is 87. 3cm and the width is 51. 8cm is 278.24 cm.

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From the graph, we get that:

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

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Answer: No Zeros

Domain: -4<=x<=4

Positive: -4<=x<=0

Negative: 0<x<=4

Step-by-step explanation: The other person had a good explanation but the problem needed a different format.