Consider w₁ = -3i and w₂ = -2. What is the result of subtracting w₂ from w₁?

The probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.

Given that,

A survey of middle school students asked what is your favorite winter sport so they have given the result in the table we can see.

Below is a summary of the findings. A participant from this study is chosen at random from among these 545 students, who serve as the sample space.

We have to find what is the probability that the chosen student, a grade 8 student, likes skiing over ice skating.

The total 8th grade are 180

The skiing are 171

The ice skating are 163

Probability = 180/(171+163) = 0.5389 = 53.89%

Therefore, the probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.

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On solving the provided graph question, we got to know that - the area below the line will be taken into account.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph.

Given : equation  2x + 3y ≤ 6

Out of the options provided, we must select the graph that displays the graph of the solution set for the equation 2x + 3y 6.

Consider the given equation   2x + 3y ≤ 6

We first find the points where the equation cut x- axis and y-axis.

Thus,

[tex]For x - axis put y = 0 ,\\We get 2x + 3(0) \leq 6 =2x \leq 6 x \leq 3\\Thus, point (3,0)\\For y - axis put x = 0 ,\\We get 2(0) + 3y \leq 6 = 3y \leq 6 = y \leq 2\\Thus, point (0,2)[/tex]

For each region, we select a test point, determine the values of x and y there, and then determine whether or not the inequality is satisfied.

Take into account the point (0, 0), and inequality becomes,

[tex]2(0) + 3(0) \leq 6 = 0 \leq 6 (true)\\[/tex]

So, the area below the line will be taken into account.

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Answer:

53 candy

Step-by-step explanation:

The graph shows a polynomial function with a positive leading coefficient B.

The function will reach its maximum value of + in the case of a positive leading coefficient and its minimum value of - in the case of a negative leading coefficient. This indicates that even degree polynomials with positive leading coefficients have a range of  [ymin, ∞), where ymin stands for the global minimum that the function reaches.

When a variable in an equation like the quadratic equation, cubic equation, etc. has only non-negative integer powers or only positive integer exponents, the function is said to be polynomial.

Leading coefficients are the values listed before the variable with the biggest exponent. They can be positive, negative, real, imaginary, whole, fractional, or decimal, much like conventional coefficients, and they can also be positive, negative, real, or imaginary.

Therefore, the correct answer is option B.

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Answer:

these are the prime factors of 84

The method to determine the numbers is random only if the balls generate numbers in equal frequencies.

The entire process is random and is not generated by a computer or humans.

One of the most important requirements for a random number is independence, as this aids in the establishment of no correlations between successive numbers. It must be ensured that the frequency of occurrence of these random numbers is roughly the same. As a result, it is theoretically difficult to generate a long random number.

The frequency of a repeating event is the number of occurrences per unit of time. It is distinct from angular frequency and is sometimes referred to as temporal frequency. The frequency is expressed in hertz (Hz), which equals one event per second. Because the period is the time interval between events, it is the reciprocal of the frequency.

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For the study for investing the result of drugs in a particular diseases,

(1)This is an example of double blind experiment. So,correct option is option A

(2) The Correct option is option (C) i.e. the data can be treated as a random sample from the population of interest.

(3) The random variable X has approximately a normal distribution because of Central Limit Theorem i.e the Correct option is option (A).

Here , Spontaneous hydrostatic collapse is a disease in which teeth spontaneously turn into fluid. Jim Halpert decided to perform a study to find out if new drugs can prevent the development of this disease.

1. Since, neither researcher nor the employees were told who received which treatment, this is an example of a double-blind experiment.

2. In order to make thorough conclusions, the most important condition for statistical inference is usually that data can be treated as a random sample from the population of interest.

3. The sample mean age, X-bar of these residents has approximately a normal distribution because of the central limit theorem. Hence, we get all required answers for asking questions.

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As tickets are selling for a high school play. student tickets cost $4 and general admission tickets cost $6 and sell 31 tickets and collect $170.

Therefore, the system of equation is

8$4 + 23$6 = $32 + $138 = $170 total

A system of equations is a set of one or more equations with many variables. A solution to a system of equations is a variable map such that all component equations are satisfied. That is, the point where all those equations intersect.

Given that :

Ticket cost = $ 4 and $6

and collection = $170.

Now,

        4S+6G = 170                ------------------------ (1)

            S+G = 31                  -----------------------  (2)

Therefore,  subtract from 1st equation to eliminate one variable:

4S+ 4G = 124    ----------------------------- (3)

Now,

  2G = 46

⇒ G = 23 tickets

putting G = 23 in equation(2)

S = 31-23

  = 8 student tickets

The system of equation is:

8$4 + 23$6 = $32 + $138

                    = $170 total

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Answer:

3x-4=2x+7 thus: (D)

x = 11

Step-by-step explanation:

Solve for x:

3 x - 4 = 2 x + 7

Subtract 2 x from both sides:

(3 x - 2 x) - 4 = (2 x - 2 x) + 7

3 x - 2 x = x:

x - 4 = (2 x - 2 x) + 7

2 x - 2 x = 0:

x - 4 = 7

Add 4 to both sides:

x + (4 - 4) = 4 + 7

4 - 4 = 0:

x = 7 + 4

7 + 4 = 11:

Answer: x = 11

___________________________

Solve for x:

4 - 2 (x - 5) = x - 19

-2 (x - 5) = -2 x + 10:

(-2 x + 10) + 4 = x - 19

Add like terms. 4 + 10 = 14:

-2 x + 14 = x - 19

Subtract x from both sides:

(-2 x - x) + 14 = (x - x) - 19

-2 x - x = -3 x:

-3 x + 14 = (x - x) - 19

x - x = 0:

-3 x + 14 = -19

Subtract 14 from both sides:

(14 - 14) - 3 x = -14 - 19

14 - 14 = 0:

-3 x = -14 - 19

-14 - 19 = -33:

-3 x = -33

Divide both sides of -3 x = -33 by -3:

(-3 x)/(-3) = (-33)/(-3)

(-3)/(-3) = 1:

x = (-33)/(-3)

The gcd of -33 and -3 is -3, so (-33)/(-3) = (-3×11)/(-3×1) = (-3)/(-3)×11 = 11:

Answer: x = 11

Answer:3x-4=2x+7

Step-by-step explanation:

first,  4-2x+10=x-19

        14+19 =x+2x

           33=3x

               x=11

A. 2x+10=8

    2x= -18

      x=-9

B. 3x-9=9

       3x=18

         x=6

C. x+2=2x-3

      3x = 5

         x = 5/3

D. 3x-4 = 2x+7

    3x-2x=7+4

          x=11

Answer:

z = 11

Step-by-step explanation:

To find the answer we need to set up an expression with the two values they gave us:

8z = z + 77

This works because side IJ is the same length as side JK. So, all we have to do is solve for z:

8z = z + 77

-z    - z

7z = 77

/7     /7

z = 11

The coefficient and constant in the system of linear equations are identified below

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.

In this question, we are given two equations to define the variables.

3x + 7y = 18 ...eq(i)

2x - 4y = 9 ..eq(ii)

In the equations above;

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There is a 95% chance that the mean length of all term papers lies between confidence limits (11.58,17.82) for the given data:

14, 20, 25, 10, 16, 8, 15, 12, 18, 9

We assume the length of paper has an approximately normal distribution.

Sample size = 10

The sample mean for the given data = 14.7

The standard deviation for the given data = 5.04

Critical value is obtained from standard normal distribution at the level of significance 0.05.

The critical value is 1.96.

The 95% confidence interval for the mean length of all term papers is calculated as follows:

P(14.7 - (1.96 x (5.04/√10)) < µ < 14.7 + (1.96 x (5.04/√10))) = 0.95

P(11.58 < µ < 17.82) = 0.95

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The temperature at Tacoma WA is -26 5/12°F.

The temperature at 5pm in Juneau Alaska: temperature at noon + total change in temperature

-20 + (-1.25 x 5)

-20 - 6.25 = -26.25°F = -26 1/4°F

The temperature in Tacoma WA = termpature in Juneau + difference in temperature

-26 1/4°F - 2/3 = -26 5/12°F

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Answer: For problem a is 16 and problem b is 34 i wasn't sure which problem it was so i did both

Step-by-step explanation:

problem a                                                    problem b

(6²-4)/2                        or                              6²-4/2

     |                                                                      |

[tex]6^2=36\\[/tex]                                                            [tex]6^2=36[/tex]

36-4=32                                                         36-4/2

32/2=16                                                          36-2=34

   16                                                                    34

The movie claims that 40% of your brain is used for visual decoding.

Williams, the William G. Allyn Professor of Medical Optics, notes that processing visual information takes up more than 40% of the cortex, the surface of the brain.

Light and dark pixels in the eye are where our visual experience begins. These signals are sent to the V1 region in the rear of the brain, where they are changed to match to the borders of visual scenes.

The visual cortex processes information from the sensory periphery in accordance with a highly regulated hierarchy, according to experiments utilizing static stimuli, such as images. The information about visual sceneries is subsequently translated by deeper brain areas into more intricate forms, objects, and ideas.

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Using the slope-intercept form of the equation of a line, the correct statement are:

The slope of the line is 5/3

The y-intercept of the line is 0

From the question, we are to determine the statements about the given line that are correct

The given equation is

y/x = 5/3

To determine the statements that are correct, we will write the equation of the line the slope-intercept form of a line

The slope-intercept form of a line is given by

y = mx + b

Where m is the slope

and b is the y-intercept

Writing the equation in the slope-intercept form

y/x = 5/3

y = 5/3(x)

By comparing with the slope-intercept form of a line,

m = 5/3

c = 0

Thus,

The slope is 5/3

and the y-intercept is 0

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On solving the provided question, the equation will be [tex]y^2 = - 4ax[/tex] and the factors - This cannot be determined from the information given

When points on a curve are equally spaced from a fixed point and line, the curve is said to have a parabola as its equation. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. Remember that the fixed point is not on the fixed line as well. A parabola is the locus of any point that is equidistant from both a focus and a straight line. A conical curve of interest in coordinate geometry is a parabola.

The equation will be

=> [tex]y^2 = - 4ax[/tex]

=> [tex]y^2 = -24x[/tex]

Factors - This cannot be determined from the information given

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(a) There are 21 different ways to choose two different restaurants.

(b)There are 42 different ways to choose two different restaurants.

(c) There are 49 different ways to choose two different restaurants.

In the given question,  suppose Ches Tahoe restaurant is one of the 7 largest restaurants in x city.

a. We would like to choose two different restaurants from them. So we have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants.

So different ways:

n = [tex]^{7}C_{2}[/tex]

Using, [tex]^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]

n = [tex]\frac{7!}{2!(7-2)!}[/tex]

After solving

n = 21

There are 21 different ways to choose two different restaurants.

b. We would like to choose two different restaurants. one is for our lunch and the other one is for our dinner. We have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants one for our lunch and the other one for our dinner.

So different ways:

n = [tex]^{7}P_{2}[/tex]

Using, [tex]^{n}P_{r} = \frac{n!}{(n-r)!}[/tex]

n = [tex]\frac{7!}{(7-2)!}[/tex]

After solving

n = 42

There are 42 different ways to choose two different restaurants.

c. We would like to choose two restaurants. one is for your lunch and the other one is for your dinner. We are OK for going to the same restaurants. We have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants one is for your lunch and the other one is for your dinner OK to the same

So different ways:

n = (7)^2

n = 49

There are 49 different ways to choose two different restaurants.

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The measure of angle 1 is given as follows:

m < 1 = 150º.

From the image given at the end of the answer, we have that two Railroad tracks are transversal to the Olive Street.

Considering that Olive Street is transversal to the parallel lines, we have that the angle 2 forms a linear pair with the angle of 30º.

Linear pairs are supplementary angles, meaning that the sum of their measures is of 180º, hence the measure of angle 2 is given as follows:

m < 2 + 30º = 180º

m < 2 = 180º - 30º

m < 2 = 150º.

Now we have that angles 1 and 2 are alternate interior angles, as they are between the two parallel lines, on the opposite side of the transversal.

Alternate interior angles are congruent, meaning that the measure of angle 1 is given as follows:

m < 1 = 150º.

The diagram is given by the image shown at the end of the answer.

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Answer:

No

Step-by-step explanation:

Functions must have only one answer for each x. However, in all the x values in this graph there are two answers.

Answer:

The answer is 20

Step-by-step explanation:

6/8 = 15/y

(6) × y = (8) × (15)

6y = 120

6y/6 = 120/6

y = 20

Thus, The value of y is 20

Answer:

[tex] \sf \: y = 20[/tex]

Step-by-step explanation:

Given equation,

[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]

Now the value of y will be,

[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]

[tex] \sf \rightarrow \: 6y = 15 \times 8[/tex]

[tex] \sf \rightarrow \: 6y = 120[/tex]

[tex] \sf \rightarrow \: y = \frac{120}{6} [/tex]

[tex] \sf \rightarrow \boxed{ \sf y = 20}[/tex]

Hence, the value of y is 20.

Answer:

x = 2/3

Step-by-step explanation:

ln3^(9x-6)  = ln4^(12x-8)

9x - 6 = 12x - 8

12x - 9x = -6 + 8

3x = 2

3/3 x = 2/3

x = 2/3

The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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There is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

Given that,

Over 62% of a newsletter publisher's subscribers, in their estimation, own a Rolls-Royce. A potential advertiser wants to verify this claim for marketing purposes. The advertiser decides to reject the null hypothesis following a test with a significance threshold of 0.02 after executing the analysis.

We have to find what is the verdict in relation to the publisher's assertion.

We know that,

First we have to write the null hypothesis and alternative hypothesis for the hypothesis test.

H₀:P=0.62

H₁:P>0.62

At 0.02 level of significance, rejecting H₀ then accepting H₁.

That is sufficient evidence that percentage over 62%.

Therefore, there is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

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The volume of the smaller cone is 19.6cm³

From the question, we have the following parameters that can be used in our computation:

The above parameter mean that

Smaller cone

Side length = 2 cm

Volume = [?] cm³

Large cone

Side length = 3 cm

Volume = 66 cm³

The ratio of the cones can be represented as

Ratio = Side length³ : Volume

So, we have

2³ : Volume of smaller cone = 3³ : 66

Evaluate the exponents

8 : Volume of smaller cone = 27 : 66

Express as fraction

Volume of smaller cone/8 = 66/27

So, we have

Volume of smaller cone = 8 * 66/27

Evaluate

Volume of smaller cone = 19.6

Hence, the volume is 19.6cm³

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The correct option for the graph shown are-

The question's line traverses the origin and (4,-12).

The line's rate of change is;

m = -12 - 0 / 4 - 0

m = -3

The slope of the line or its rate of change is -3.

The line's equation is provided by;

y - 0 = -3(x - 0)

y = -3x

This relationship is linear as a result.

The relationship is proportionate if we take any value of x because there will only ever be one value of y.

Therefore, the following claims are accurate:

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Given √24−x when x = 6 in simple radical form is 3*√2.

Simply put, simplifying a radical eliminates the need to find any further square roots, cube roots, fourth roots, etc.

Additionally, it entails eliminating any radicals from a fraction's denominator.

The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414.

So, we have:

√24−x when x = 6
Thus we must now calculate the square root of 18.

The square root, if you're allowed to use a calculator, is 4.242.

If not, however, let's come as close as we can:

√(9 * 2)

Since 3 is the square root of 9:

3*√2

Therefore, given √24−x when x = 6 in simple radical form is 3*√2.

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To solve this expression, you can first simplify the fractions:

5/11 * -11/6 = (-5/6) * (-6/5)

Then, you can multiply the fractions:

(-5/6) * (-6/5) = (-30/30) = -1

So, the result of the expression is -1.

Answer: c

Step-by-step explanation: