Find all values of c for which the vectors are linearly independent. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) v1 = 1, c , v2 = โ1, 2 c does not equal?

The equation that represents the scatterplot is: y = -0.8x + 30

From the scatterplot, we see that when x = 25, y = 10

Option A: The equation is given as:

y = -0.8x + 30

At x = 25, we have:

y = -0.8(25) + 30

y = -20 + 30

y = 10

Option B: The equation is given as:

y = -1.5x + 50

At x = 25, we have:

y = -1.5(25) + 30

y = -37.5 + 30

y = -7.5

Option C: The equation is given as:

y = -2.8x + 73

At x = 25, we have:

y = -2.8(25) + 73

y = -70 + 73

y = 3

Option D: The equation is given as:

y = -3.5x + 82

At x = 25, we have:

y = -3.5(25) + 82

y = -87.5 + 82

y = -5.5

Thus, only option A is correct

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The equation for the linear equation perpendicular to y - 9 = - x is:

y = x +1

Two linear equations are perpendicular if the product betwen the slopes is -1.

Here we want a line perpendicular to:

y - 9 = -x

isolating y:

y = -x + 9

Then the slope is -1, thus, the slope of the perpendicular line a is:

a*-1 = -1

a = -1/-1

a = 1

Then our line is:

y = x + c

Now we want our line to pass through (2, 3), replacing these values we will get:

3 = 2 + c

3 - 2 = c

1 = c

The linear equation is:

y = x +1

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15) The height of the hotel is given as follows: 250 foot.

16) A reasonable estimate would be for the height of the building to be taller than the height of the tower, as it casts a larger shadow.

The height of the hotel is obtained applying the proportions in the context of the problem.

The proportions are applied by a rule of three, between the height of the building and it's shadow, as follows:

x foot - 25 feet

120 foot - 12 feet

The height of the building is the height of the shadow multiplied by 10, hence the height is given as follows:

25 x 10 = 250 foot.

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We want to find the probability of seeing more than 500 shooting stars in one night, when the average is 50 shooting stars per night.

Using the Poisson distribution, we can approximate the probability using a normal distribution with a mean of 50 and a standard deviation of √50. Standardizing for x=500, we get a result of about 30.14.

Using standard normal distribution tables, we know that the probability of a standard normal variable greater than 3 is less than 0.0013. The upper limit of the probability of seeing more than 500 shooting stars in one night is less than 0.0013.

If we assume that the average number of shooting stars seen per night is 50, then the parameter λ for the Poisson distribution is also 50. Therefore, the probability of seeing more than 500 shooting stars in one night is very low and can be considered negligible.

1. "Stars" - In this context, "stars" refer to the shooting stars you see at night.
2. "Average" - This is the mean value of a set of numbers, representing the typical or central value.
3. "Probability" - The measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1.

Now, let's consider the given information: you see an average of 50 shooting stars per night. To find an upper bound on the probability of seeing more than 500 shooting stars in one night, we can use the Poisson distribution as an approximation.

The Poisson distribution is used for counting the number of events (shooting stars) in a fixed interval (one night). The formula is:

P(X=k) = (e^(-λ) * λ^k) / k!

where:
- P(X=k) is the probability of observing k events (shooting stars)
- λ is the average number of events (50 shooting stars)
- k is the number of events we want to find the probability for (more than 500 shooting stars)
- e is the base of the natural logarithm (approximately 2.71828)
- ! denotes the factorial function

To find the upper bound on the probability of seeing more than 500 shooting stars, we can calculate the complementary probability, which is the probability of seeing 500 or fewer shooting stars, and then subtract it from 1:

To find the probability of seeing more than 500 shooting stars in one night, we can use the cumulative distribution function (CDF) of the Poisson distribution. The CDF gives the probability that the number of shooting stars seen in a night is less than or equal to a certain value. To find the probability that the number of shooting stars seen is greater than 500, we can subtract the probability that it is less than or equal to 500 from 1.

Using a calculator or statistical software, we can calculate that the probability of seeing 500 or fewer shooting stars in one night is approximately 2.2 x 10^-16. Subtracting this from 1, we get an upper bound on the probability of seeing more than 500 shooting stars in one night of approximately 1.

P(X>500) = 1 - P(X≤500)

Since it's highly unlikely to see more than 500 shooting stars when the average is only 50, the upper bound on the probability of seeing more than 500 shooting stars in one night would be close to 0. Note that computing the exact probability using the Poisson formula for such large numbers can be computationally challenging.

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If we compare price, length and number of plies in each "paper-towel-roll" from six different manufacturers, then "degree-of-freedom" is 5.

The "Degree-of-freedom" is defined as a statistical concept which is used in calculations to account for variability in the data.

In comparing price, length, and "number-of-plies" in each paper "towel-roll" from 6 different manufacturers, the "degree-of-freedom" will depend on the specific statistical test used.

The degree-of-freedom is = "total sample size" - 1,

The total sample-size is the number of different manufacturers, and we know that there are 6 different manufacturers,

So, Degree Of Freedom is = 6 - 1 = 5,

Therefore, the required "degree-of-freedom" is 5.

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The probability of picking 6 from the cards at first is  1/4 (or, 0.25) and  then picking a number less than 7 is 0.

You pick a card at random and without putting the first card back you pick a second card at random.

The given number of cards are picked from 6, 7, 8, 9

Total number of cards is = 4

The total number of  6 in the cards is 1.

Thus, the probability of picking a 6 is = 1/4 , at first pick.

Number of cards less than 7 is only 6 here in the given problem.

After picking a 6 at first, the probability of picking a card less than 7 is 0 since once a card drawn is not put back in the shuffle.

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The height of the tower is about 250 feet.

We can use trigonometry to determine the height of the tower.

Let's label the height of the tower as "h". Then we can use the sine function:

sin(39) = h/400

Multiplying both sides by 400, we get:

h = 400 × sin(39)

h = 250.11.

Hence, the height of the tower is about 250 feet.

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The value of the missing fraction for the given expression 1-  (3/7) - ___=  ( 5 /14 ) is equal to ( 3 /14).

Expression is equal to,

1-  (3/7) - ___=  ( 5 /14 ).

Let us consider 'y' represents the missing fraction .

Rewrite the expression as ,

⇒ 1 - ( 3 / 7) - y = ( 5 / 14 )

Simplify the expressions by taking the least common multiple.

⇒ ( 7 - 3 ) / 7 - y = ( 5 / 14 )

⇒ ( 4 / 7 ) - y = ( 5 / 14 )

Subtract ( 4 /7 ) from both the sides we get,

⇒ ( 4 / 7 ) - y  - ( 4 /7 ) = ( 5 / 14 ) - ( 4 /7)

⇒ -y = ( 5  - 8 ) / 14

⇒ y = 3 /14

Therefore, the value of the missing fraction is equal to ( 3/14) .

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The above question is incomplete, the complete question is:

Fill in the missing fraction 1-  (3/7) - ___=  ( 5 /14 ).

Answer:

5 is rounded to 5.0

Step-by-step explanation:

Susan would need 6(3/8) yards of fabric.

5/8 yards of fabric are left over after making the aprons.

Susan does not have enough fabric left to make another apron

We have,

Part A:

To make one apron, Susan needs 1 3/4 + 3/8 = 2 1/8 yards of fabric.

To make 3 aprons, Susan would need 3 × 2 1/8 = 6 3/8 yards of fabric.

Part B:

Susan needs 6 3/8 yards of fabric to make 3 aprons.

If she originally had 7 yards of fabric, then the amount of fabric left after making the aprons would be:

7 - 6 3/8 = 5/8 yards of fabric.

So, 5/8 yards of fabric are left over after making the aprons.

Part C:

Susan needs 2 1/8 yards of fabric to make one apron.

She has 5/8 yards of fabric left over after making 3 aprons.

Therefore, Susan does not have enough fabric left to make another apron because 5/8 yards is less than 2 1/8 yards required to make one apron.

Thus,

Susan would need 6(3/8) yards of fabric.

5/8 yards of fabric are left over after making the aprons.

Susan does not have enough fabric left to make another apron

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The number of children and the adults present at the pool in the day was 223 and 351 respectively.

Given that, there are 574 people in a day swimming at public pool, the daily prices are $1.75 for children and $2.25 for adults.

The receipts for admission totaled $1180.00.

Let the number of adults be a and that the children be c,

So,

a + c = 574

a = 574 - c.........(i)

2.25a + 1.75c = 1180............(ii)

Put eq(i) in eq(ii)

2.25(574-c) + 1.75c = 1180

1291.5 - 2.25c + 1.75c = 1180

0.5c = 111.5

c = 223

Put the value of c in the eq(i)

a = 574-223

a = 351

Hence, the number of children and the adults present at the pool in the day was 223 and 351 respectively.

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The total cost of the fruits she bought​ is 3p + 5n + 4

Given that

We have

9 pears = 3 * 3 pears

So, we have

9 pears = 3 * p

9 pears = 3p

Also, we have

n + 2 apple = 2 * (n + 2)

n + 2 apple = 2n + 4

We simply add the total of each together

So, we have

Total = 3p + 2n + 4 + 1.50 * 2n

Total = 3p + 2n + 4 + 3n

Evaluate

Total = 3p + 5n + 4

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Answer:

36

Step-by-step explanation:

A function that you can use to find the cost C of buying S songs is C = 0.90S.

In order to write a linear equation or function to describe this situation, we would assign variables to the cost of buying songs and the number of songs respectively, and then translate the word problem into a linear equation as follows:

Since this online music store sells songs for $0.90 each, a linear equation or function to describe this situation can be written as follows;

C = 0.90S

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The next three terms of the sequence would be:

-20, - 27 , -34

The rule is to subtract 7 from the every term that is on the question in other to get the next term

Lets assume the rule =

T = a - 7

we have

15 - 7 = 8

8 - 7 = 1

1 - 7 = -6

- 6 - 7 = - 13

- 13 - 7 = - 20

-20 - 7 = -27

- 27 - 7 = - 34

- 34 - 7 = -41

-41 - 7 = -48

The next three terms of the sequence would be:

-20, - 27 , -34

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Answer:

3% of 350 is 10.5. Because we're only calculating simple interest we multiply this by 5 to give $52.50 interest after 5 years. Therefore Frances will have earned $52.50.

Step-by-step explanation:

Not og answer credits to annikad

Well let’s start with what 3% of 350. It is 10.5 so at the end of 5 years the interest will be 52.50$. Your welcome btw!

The margin of error is approximately 0.014 grams, rounded to three decimal places.

To construct a 98% confidence interval for the mean of repeated measurements of the weight, we can use the following formula:

CI = x ± z × (σ/√n)

Where:
x = mean result = 10.230 grams
σ = standard deviation of scale readings = 0.020 gram
n = number of repeated measurements = 40
z = z-score for 98% confidence interval = 2.326

Plugging in the values, we get:

CI = 10.230 ± 2.326×(0.020/√40)
CI = 10.230 ± 0.014
CI = (10.216, 10.244)

Therefore, the 98% confidence interval for the mean of repeated measurements of the weight is (10.216, 10.244) grams.

The margin of error is the difference between the upper and lower bounds of the confidence interval divided by 2, so:

Margin of error = (10.244 - 10.216)/2
Margin of error = 0.014

Thus, the margin of error is 0.014 grams.

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The jet plane taking off is 100 million / 1 million = 100 times louder than the conversation.

According to the decibel scale, a sound that is 10 decibels higher is 10 times as loud. Therefore, a sound that is 20 decibels higher is 10 times 10, or 100 times as loud. This means that a 120-dB jet plane taking off is 100 times as loud as a sound that is 20 decibels lower, which is a 40-dB conversation.

To find out how many more times louder a 120-dB jet plane taking off is than a 40-dB conversation, we can divide the loudness of the jet plane by the loudness of the conversation

120 dB / 40 dB = 3

This means that a 120-dB jet plane taking off is 3 times as loud as a 40-dB conversation. However, we need to remember that the decibel scale is logarithmic, which means that each increase of 10 decibels represents a tenfold increase in loudness. Therefore, a 30-dB increase represents a thousandfold increase in loudness (10 to the power of 3).

Since the difference between 120 dB and 40 dB is 80 dB, which is 8 times 10 dB, the loudness of the jet plane taking off is 10 to the power of 8, or 100 million, times as loud as the conversation.

Therefore, the jet plane taking off is 100 million / 1 million = 100 times louder than the conversation.

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Using trigonometric functions, note that the value of x, in this case, is 4√3. See the explanation below.

We can use trig functions since this is a right triangle

The side opposite the right angle is 8, that is the hypotenuse

We know the opposite side is x

sin theta = opp/ hyp

sin 60 = x/8

Multiply each side by 8

8 sin 60 =x

sin 60 = √(3)/2

8√3/2 =x

4 √3 =x

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Full Question:

What is the value of x?

a: 4

b: 43√

c: 8

​ d: 83√ ​

The figure contains a right triangle. The side opposite the right angle is 8. The side opposite the 60 degree angle is x.

See attached image.

The distance traveled by train would be 300 miles.

The relation between speed, distance, and time:

You can use the equivalent formula d = rt which means distance equals rate times time. To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

A train travels for 3.75 hours at 80 miles per hour.

The distance traveled = speed * time

                                    = 3.75 * 80

                                    = 300 miles.

Hence, the distance traveled by train would be 300 miles.

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complete question;

A train travels for 3.75 hours at 80 miles an hour. Use the formula d = r. t, where

d = distance, r = rate, and t = time, to find the distance the train traveled.

The distance traveled is

miles.

The solution is

If three candidates A, B and C in a school election got 153, 245, and 102 votes respectively, then the percentage of votes got by the winner is (B) 49%.

The percentage of votes obtained by the winning Candidate in the school election is the total votes obtained divided by the total votes.

The percentage is always obtained as the quotient of two values multiplied by 100.

The votes obtained by Candidate A = 153

The votes obtained by Candidate B = 245

The votes obtained by Candidate C = 102

The total number of votes = 500

The percentage of votes obtained by the winner, Candidate B = 49% (245 ÷ 500 × 100)

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The distance between the given points is equals to 7.21 units ( approximately).

Coordinates of the two points are.

( x₁ , y₁ ) = ( -3, 1 )

( x₂ , y₂ ) = ( 3, 5 )

The distance formula to find the distance between the points (-3,1) and (3,5) is equal to ,

Distance 'd' =  √( y₂ - y₁ )² + ( x₂ - x₁ )²

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

And d is the distance between them.

Substitute the coordinates of the given points, we have,

⇒ Distance 'd'= √((3 - (-3))²+ (5 - 1)²)

⇒ Distance 'd'= √((6)²+ (4)²)

⇒ Distance 'd'= √(36 + 16)

⇒ Distance 'd'= √(52)

⇒ Distance 'd'= 2√13

⇒ Distance 'd'=  7.21 units.

Therefore, the distance between the points (-3,1) and (3,5) is  approximately equals to 7.21 units.

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Answer: [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

      We will use the formula, or rise over run, to solve for the slope.

Formula:

      [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Coordinate points we will use:

      (-8, 0) and (0, -4)

Substitute values and evaluate:

      [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

      [tex]\displaystyle \frac{-4-0}{0--8}=\frac{-4}{8} =-\frac{1}{2}[/tex]

Answer:  -1/2

Step-by-step explanation:

You can count the slope from the graph   m=rise/run

if you started on point (-8, 0) and counted to (0,-4)

went down 4  = -4

you went right 8 = 8

m = [tex]\frac{-4}{8}[/tex]  = [tex]-\frac{1}{2}[/tex]

The equation of the function that models the data is y = x² + 2x - 1

Given that

x    y

-2    -1

-1    -2

0    -1

1    2

2    7

A quadratic function is represented as

y = ax² + bx + c

Where c = y when x = 0

So, we have

y = ax² + bx - 1

Using the other points, we have

a + b - 1 = 2

4a + 2b - 1 = 7

So, we have

a + b = 3

4a + 2b = 8

When solved, we have

a = 1 and b = 2

So, the equation is

y = x² + 2x - 1

See attachment for the plot of the dataset

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Since the two lines above are parallel, if the slope of the red line is 5, then the slope of the green line is equal to 5.

In Mathematics and Geometry, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Mathematics and Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

This ultimately implies that, the slope of these two lines are equal and the same, and as such, we have the following:

Slope of red line = Slope of green line

5 = 5

In conclusion, we can reasonably infer and logically deduce that the slope of the green line is equal to 5.

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There are 12 different choices of pens available with this brand, obtained by multiplying the number of colors (3) by the number of writing tips (4).

To calculate the number of different choices of pens with this brand, you can use the multiplication principle of counting, which states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

Using this principle, the number of different choices of pens can be calculated as

Number of colors x Number of writing tips = 3 x 4 = 12

Therefore, there are 12 different choices of pens available with this brand.

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The slope of the line that passes through the points (6, 545) and (4, 225) is equal to 160.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (225 - 545)/(4 - 6)

Slope (m) = -320/-2

Slope (m) = 160.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 160.

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Therefore, the distance of the submarine from P is approximately 1035.5 m.

Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is particularly concerned with the measurement of angles, the computation of trigonometric functions such as sine, cosine, and tangent, and their applications to real-world problems, including engineering, physics, and astronomy. Trigonometry also includes the study of trigonometric identities and equations, as well as the use of trigonometric formulas to solve problems involving triangles and angles.

Here,

Let the distance between P and X be d and the distance between X and S be x. We are given that:

The bearing of S from P is 030°.

The bearing of S from Q is 085°.

The distance between P and Q is 1000 m.

To find x, we can use the Law of Sines, which states:

sin A / a = sin B / b = sin C / c

where A, B, and C are the angles of a triangle and a, b, and c are the lengths of the opposite sides. In our case, we have:

A = 180° - 30° = 150° (angle XPQ)

B = 180° - 85° = 95° (angle XQP)

C = 180° (angle XPS)

We also have:

a = 1000 m (PQ)

b = d (PX)

c = x (XS)

Using the Law of Sines, we can write:

sin 150° / 1000 = sin 95° / d = sin 180° / x

Solving for d, we get:

d = sin 95° / sin 150° * 1000

= 893.3 m (approx)

Solving for x, we get:

x = sin 180° / sin 150° * 893.3

= 1035.5 m (approx)

To make a scale drawing, we can choose a suitable scale, such as 1 cm = 100 m. We can then draw a line segment of length 10 cm to represent the distance between P and Q, and draw perpendiculars from P and Q to represent the bearings of the submarine. We can then use a protractor to measure the angles and draw the lines for the bearings, and measure the distance between the lines to find the distance of the submarine from P.

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There are 130 shark cookies should they order this month.

We have to given that;

Last month, they sold 65 shark cookies and 85 clown fish cookies.

Hence, If they plan to order 170 clown fish cookies this month.

Then, Number of shark cookies should they order this month is, x

Hence, We get;

65 / 85 = x / 170

x = 130

Thus, There are 130 shark cookies should they order this month.

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