calculate the cross product. (7−5)×(4 )= (give your answer using standard basis vectors. express numbers in exact form. use symbolic notation and fractions where needed.)

The vectors v = 6i - 3j and w = i + 2j are orthogonal.

To determine if the vectors v and w are orthogonal, we need to find their dot product. If the dot product is 0, the vectors are orthogonal.

Here are the steps to find the dot product of v = 6i - 3j and w = i + 2j,

1. Identify the components of the vectors: v = (6, -3) and w = (1, 2)

2. Multiply the corresponding components of the vectors:

\((6 \times 1) + (-3 \times 2) = 6 - 6 \)

3. Add the products: 6 - 6 = 0 Since the dot product is 0, the vectors v = 6i - 3j and w = i + 2j are orthogonal.

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Correct question is " Are these vectors orthogonal? v = 6i - 3j and w = i+2j"

Answer: 7.3x + 5

Step-by-step explanation:

For us to solve the question, we have to solve 5.2x+8+2.1x-3 and the answer gotten will allow us know the equivalent expression.

= 5.2x+8+2.1x-3

= 5.2x + 2.1x + 8 - 3

= 7.3x + 5

Therefore, the correct answer is 7.3x + 5

Therefore, the answer is -8. The simplified expression involving h is -8. The difference quotient is the formula used in calculus to compute the derivative of a function.

The given function is f(x) = -8x +9.The difference quotient h for the given function is calculated as follows: f(x+h)-f(x) / hf(x+h) = -8(x+h) + 9 = -8x - 8h + 9f(x) = -8x + 9

So, the numerator is given by: f (x+h) - f(x) = [-8 ( x+h) + 9] - [-8x + 9]= -8x - 8h + 9 + 8x - 9= -8h

On substituting the numerator and denominator values in the given equation we have:(-8h) / h= -8

Therefore, the answer is -8.

The simplified expression involving h is -8. The difference quotient is the formula used in calculus to compute the derivative of a function.

The quotient formula is used to calculate the average rate of change in a function, with h representing the change in the input variable x.

The difference quotient formula is also used to calculate the slope of a curve at a given point.

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The equation for the tangent to the graph of y = arcsin(x/2) at the origin is y = x. This means that for any given x-value, the corresponding y-value is equal to that x-value, creating a line with a slope of 1. This line is tangent to the graph of y = arcsin(x/2) at the origin, which is (0, 0).

To find the equation for the tangent to the graph of y = arcsin(x/2) at the origin, we must first find the slope at the origin. We can do this by taking the derivative of the function y = arcsin(x/2) with respect to x.

The derivative of

y = arcsin(x/2) with respect to x is y' = (1/2)cos(x/2).

At the origin, x = 0, so the slope of the tangent at the origin is

y' = (1/2)cos(0) = 1.

Therefore, the equation for the tangent to the graph of

y = arcsin(x/2) at the origin is y = x, which has a slope of 1.

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The average speed of the second car was 60 miles per hour.

1. Let's calculate the time difference between when the first car started and when the second car caught up. The second car started two hours after the first car, therefore it travelled for five hours (9:00 PM - 4:00 PM).

2. We know that the first car traveled for a longer period than the second car, as it started at 2:00 PM and was overtaken at 9:00 PM. Therefore, we need to find the total distance traveled by the first car during this time.

  Time traveled by the first car = (9:00 PM - 2:00 PM) = 7 hours.

The first car's speed is 40 miles per hour.

Distance travelled by the first automobile = Speed Time = 40 mph per hour 7 hours = 280 miles.

3. Since the second car caught up with the first car, we can conclude that the distance traveled by the second car is equal to the distance traveled by the first car, which is 280 miles.

4. We know that the second automobile drove for 5 hours. 280 miles is the distance travelled by the second automobile. The second automobile travelled for 5 hours.

5. To get the average speed of the second vehicle, divide the distance travelled by the time required: The second car's average speed = Distance Time = 280 miles 5 hours = 56 miles per hour.

As a result, the second car's average speed was 56 miles per hour.

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Given :-

To find :-

We know :-

SP > CP

.°. There is a profit

Increase % = 42.86(approx) %

Solution:

We know that:

\(\large\tex\text{Profit percentage:} \ \dfrac{S.P - C.P}{C.P} \times 100 \\\\ \tex\text{The cost price of the shirt is the cost the storeowner bought.} \\\\ \ \ \tex\text{The selling price of the shirt is the price the store owner is selling it.}\)

We can make the following points:

Now, let's find the profit percent by plugging the C.P and the S.P.

Step-by step calculations:

\(\large\tex\text{Profit percentage:} \ \dfrac{S.P - C.P}{C.P} \times 100\)

\(\large\tex\text{Profit percentage:} \ \dfrac{50 - 35}{35} \times 100\)

\(\large\tex\text{Profit percentage:} \ \dfrac{15}{35} \times 100\)

\(\large\tex\text{Profit percentage:} \ \dfrac{3}{7} \times 100\)

\(\large\tex\text{Profit percentage:} \ \dfrac{300}{7} \%\)

\(\boxed{\bold{\large\tex\text{Profit percentage \ =} \ 42.86\% \ (Estimate)}}\)

Thus, the percent increase is about 42.86%.

Answer:

The answer is <U , <T , <V.

Step-by-step explanation:

There is no need to show work. You can show work by solving for the angles using Sin, Cos, and Tan.

Usually, the small side length is the smallest angle degree and the big side length is the larger angle degree.

VT = 18 , UV = 20 , TU = 23.

Answer:

26

Step-by-step explanation:

a^2-(b+c)= (-8)^2-(17+21)=64-38=26

The correct probabilities are P(at least two tails) = 0. 5 and P(at least one heads) = 0. 875.

Let's calculate the probabilities based on the given sample space:

Total number of outcomes (sample space) = \(2^{3}\) = 8

P(one tails):

From the sample space, there are four outcomes that have exactly one tails: HTT, THT, TTH, TTT.

So, P(one tails) = 4/8 = 0.5

P(three heads):

From the sample space, there is only one outcome that has three heads: HHH.

So, P(three heads) = 1/8 = 0.125

P(one heads and two tails):

From the sample space, there are three outcomes that have one heads and two tails: HHT, HTH, THH.

So, P(one heads and two tails) = 3/8 = 0.375

P(at least two tails):

From the sample space, there are four outcomes that have at least two tails: TTH, THT, HTT, TTT.

So, P(at least two tails) = 4/8 = 0.5

P(at least one heads):

From the sample space, there are seven outcomes that have at least one heads: HHH, HHT, HTH, THH, THT, TTH, TTT.

So, P(at least one heads) = 7/8 = 0.875

Therefore, the correct probabilities are:

P(one tails) = 0.5

P(three heads) = 0.125

P(one heads and two tails) = 0.375

P(at least two tails) = 0.5

P(at least one heads) = 0.875

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Answer:

1

Step-by-step explanation:

From -3 to -7 the distance is 4 (-3--7=4). Midpoint means that point -3 bisects the segment into two equal parts. So, the other endpoint is 4 units away from -3. Since -3+4=1, 1 is answer.

The volume trapped below the cone and over the semicircular disk can be calculated using the given equation z = Vx^2 + y^2 = r. The integral to evaluate the volume is ∫∫(0 to 1)(0 to 0.5 + √(7/2 - r^2))(r dr do).

To find the volume, we first need to understand the geometry of the problem. The equation z = Vx^2 + y^2 = r represents a cone with its vertex at the origin and its axis along the z-axis. The parameter V determines the slope of the cone, while r represents the radial distance from the origin. The semicircular disk lies in the xy-plane and is defined by the inequality 0 ≤ r ≤ 0.5 and 0 ≤ θ ≤ π.

To calculate the volume, we need to express the volume element in terms of the cylindrical coordinates r, θ, and z. In cylindrical coordinates, the volume element is given by dV = r dr do dz. However, in this case, since we are integrating over a semicircular disk, the range of θ is limited to π. Thus, the volume element becomes dV = r dr do dz, where r ranges from 0 to 0.5, θ ranges from 0 to π, and dz ranges from 0 to 0.5 + √(7/2 - r^2).

Now, we can set up the integral to evaluate the volume trapped below the cone and over the semicircular disk. The integral becomes ∫∫∫(0 to 1)(0 to π)(0 to 0.5 + √(7/2 - r^2))(r dr do dz). Evaluating this integral will give us the desired volume.

In conclusion, the volume trapped below the cone z = Vx^2 + y^2 = r over the semicircular disk is given by the integral ∫∫∫(0 to 1)(0 to π)(0 to 0.5 + √(7/2 - r^2))(r dr do dz), where V is the slope of the cone and r ranges from 0 to 0.5.

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PDF of Y is  (1/π + л) × (1/w) × (-1/R) × sin((1/w) × (arccos(y/R) - o)). CDF of Y is (1/π + л) × [(1/w) × (arccos(y/R) - o) + л]. Mean of the transformed random variable Y is ∫[(-R, R)] y × [(1/π + л)×(1/w)×(-1/R)×sin((1/w)×(arccos(y/R) - o))]dy.

a. To find the cumulative distribution function (CDF) and probability density function (PDF) of the transformed random variable Y = g(X) = Rcos(wX + o), we need to consider the properties of the cosine function and the distribution of X.

Since X is uniformly distributed in the interval (-л, π), its PDF is given by:

f_X(x) = 1/(π + л), for -л ≤ x ≤ π

To find the CDF of Y, we can use the transformation method:

F_Y(y) = P(Y ≤ y) = P(Rcos(wX + o) ≤ y)

Solving for X, we have:

cos(wX + o) ≤ y/R

wX + o ≤ arccos(y/R)

X ≤ (1/w) × (arccos(y/R) - o)

Using the distribution of X, we can express the CDF of Y as:

F_Y(y) = P(Y ≤ y) = P(X ≤ (1/w) × (arccos(y/R) - o))

        = (1/π + л) × [(1/w) × (arccos(y/R) - o) + л]

To find the PDF of Y, we can differentiate the CDF with respect to y:

f_Y(y) = d/dy [F_Y(y)]

      = (1/π + л) × (1/w) × (-1/R) × sin((1/w) × (arccos(y/R) - o))

b. To find the mean of the transformed random variable Y, we integrate Y times its PDF over its entire range:

E[Y] = ∫[(-R, R)] y × f_Y(y) dy

     = ∫[(-R, R)] y × [(1/π + л) × (1/w) × (-1/R) × sin((1/w) × (arccos(y/R) - o))] dy

c. To find the variance of the transformed random variable Y, we need to calculate the second central moment:

Var[Y] = E[(Y - E[Y])^2]

      = ∫[(-R, R)] (y - E[Y])² × f_Y(y) dy

The standard deviation of Y is then given by taking the square root of the variance.

d. The moment generating function (MGF) and characteristic function of the transformed random variable Y can be found by taking the expectation of \(e^{(tY)} and e^{(itY)}\), respectively, where t and θ are real-valued parameters:

\(MGF_{Y(t)} = E[e^{(tY)}]\)

      \(= \int [(-R, R)] e^{(ty)} \times f_Y(y) dy\)

If the MGF does not exist, we can use the characteristic function instead:

φ_Y(θ) = \(E[e^{(i\theta Y)}]\)

       =\(\int [(-R, R)] e^{(i\theta y)} \times f_Y(y) dy\)

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List the following words in order from smallest to

largest

C. DNA, Gene, Chromosome, Nucleus

Answer:

A. Gene, DNA, Chromosome, Nucleus

Step-by-step explanation:

Hope this helps. Please give Brainest if it did. Good luck

Answer:

True, she would need to order 48.

Step-by-step explanation:

If you divide the expected number of people (120) by the number of balloons per person (120 divided by 5) then multiply that by 2 you get 48.

if she sells 38 books we get that

she earns $89

Answer:

124.4

Step-by-step explanation:

Perimeter of ∆HIJ = IJ + HJ + HI

IJ = 40

HJ = 37.6

HI = ?

Let's find HI

∆HIJ and ∆EFG are similar. Since they have equal corresponding angles. Therefore, the ratio of their corresponding sides would be equal.

Thus:

EF/HI = FG/IJ

EF = 117 (given)

HI = ?

FG = 100 (given)

IJ = 40 (given)

Plug in the values

117/HI = 100/40

117/HI = 2.5

117 = HI*2.5

117/2.5 = HI

HI = 46.8

✔️Perimeter of ∆HIJ = IJ + HJ + HI

= 40 + 37.6 + 46.8

= 124.4

Answer:

53

Step-by-step explanation:

first put it in least to greatest

42,42,53,60,78

the middle value is the median

The estimated area under the graph of y = x^2 on the interval [0, 6] using Riemann sums is approximately 40.

Let's evaluate the estimation of the area under the graph of y = x^2 on the interval [0, 6] using Riemann sums.

Given that we are dividing the interval into three equal subintervals, the width of each subinterval is Δx = (6 - 0) / 3 = 2.

The left endpoints for each subinterval are as follows:

x1 = 0

x2 = 2

x3 = 4

To calculate the areas of the rectangles, we need to determine the corresponding y-values for each left endpoint.

y1 = (0)^2 = 0

y2 = (2)^2 = 4

y3 = (4)^2 = 16

Now, we can compute the areas of the rectangles using the formula: Area = Δx * y.

Area of the first rectangle: Δx * y1 = 2 * 0 = 0

Area of the second rectangle: Δx * y2 = 2 * 4 = 8

Area of the third rectangle: Δx * y3 = 2 * 16 = 32

The total estimated area under the curve is the sum of the areas of the three rectangles:

Estimated area ≈ (0 + 8 + 32) = 40

Based on the calculations, the estimated area under the graph of y = x^2 on the interval [0, 6] using Riemann sums is approximately 40.

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EXPLANATION

Given the system of equations:

(1) 3x + 5y = -17

(2) 2x + 4y = 6

Multiplying (1) by 2 and (2) by 3:

(1) 6x + 10y = -34

(2) 6x + 12y = 18

Subtracting (2) to (1):

(2) 6x + 12y = 18

-

(1) 6x + 10y = -34

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

2y = 52

Dividing both sides by 2:

y = 52/2

Simplifying:

y = 26

Simplify:

Divide both sides by 6:

Simplify:

The solutions to the system of equations are:

Answer:

90/n

Step-by-step explanation:

There are 90 cans, and each bag MUST have an equal amount of cans, so if we had, let's say 2 bags, then there would be 45 bags. We got this by doing 90/2. 2 being n, the expression would be 90/n.

Answer:

y=55x

given y=385

x=gallons of gas = 385/55 = 7 gallons

inverse function

y=55x

change x to y and y to x

x=55y

y=x/55

inverse function is x/55

Step-by-step explanation:

We will find the sum of 3+ 1 1/2 with help of a

Answer: I think the correct answers are 6:9, 3:2, and 18:12.

Step-by-step explanation: Well all these numbers are equivalent to 9:6.

Answer:

x=0.0000−3.0000i

x=0.0000+3.0000i

Hoped I helped

Answer:

x  = 3√3 - 3

x  = -3√3 - 3

Step-by-step explanation:

(3+x)² + 9 = 36

(x + 3)² + 9 - 9 = 36 - 9

(x + 3)² = 27

x + 3 = 3√3

x + 3 = -3√3

therefore,

x  = 3√3 - 3

x  = -3√3 - 3

If one bead were randomly selected, the likelihood that it would be green is 40.9090%.

According to the question, given that

10 red beads, 3 blue beads, and 9 green beads are all contained in a bag. if just one bead was chosen at random

The likelihood that the bead will be green

⇒ \(\frac{9}{10 + 3 + 9}\)

⇒  \(\frac{9}{22}\)

⇒ 0.409 ≈ 40.9090 %

Therefore, probability of  one bead was chosen at random that the bead is green = 40.9090 %

determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Probability is an important subject for Class 10 students because it teaches all of the subject's essential concepts. Every event's probability in a sample space is one.

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The probability that a single bead would be green if chosen at random is 40.9090%.

In response to the query, assuming that

A bag contains ten red beads, three blue beads, and nine green beads. suppose a single bead were picked at random

a bead's chance of being green

= 9/10+3+9

= 9/22

= 0.409 ≈ 40.9090 %

Therefore, probability of  one bead was chosen at random that the bead is green = 40.9090 %

Utilize probability to ascertain the likelihood of something happening. Many things are difficult to foresee with absolute confidence. Using it, we can only predict the likelihood of an event occurring or how likely it is. On the scale of probabilities, 0 denotes impossibility and 1 denotes certainty. For pupils in Class 10, probability is a crucial subject because it covers all of the subject's key ideas. In a sample space, the chance of each event is 1.

To determine the domain of a function, we need to identify any values of x that would make the denominator equal to zero, as division by zero is undefined.

The given function is:

f(x) = (x^2 - 16) / (x^2 - 4x - 12)

To find the values of x that would make the denominator zero, we can set it equal to zero and solve the quadratic equation:

x^2 - 4x - 12 = 0

This quadratic equation can be factored as:

(x - 6)(x + 2) = 0

Setting each factor equal to zero:

x - 6 = 0 --> x = 6

x + 2 = 0 --> x = -2

Therefore, the domain of the function f(x) is all real numbers except x = 6 and x = -2, since these values would make the denominator zero. In interval notation, the domain is (-∞, -2) ∪ (-2, 6) ∪ (6, +∞).

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The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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The equation of the level curve described above that contains the points (3,5) is -2u/[u + v]²

F(x1, y1)  = = √[x² + y²]

contains

f(3, 5)

F(3, 5) = √(3² + 5²)

= √34

= 5.83095

g(u,v) = [u-v]/[u+v]

gu = [(1) (u + v) - (u-v) (1)]/(u+v)²

= 2v/(u+v)²

gv =  [(-1) (u + v) - (u-v) (1)]/(u+v)²

= -2u/(u + v)²

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Full Question:

Find an equation of the level curve of f(x y) = √x² + y² that contains the point (3, 5)