if u1 and u2 are orthogonal unit vectors, and v=au1 bu2, find v•u1.

Answer:

x<10/7

Step-by-step explanation:

-7x>10

divide both sides by -7

-7x/-7>10/-7

x>-10/7

so,

x<10/7

Answer:

[tex]\boxed{\tt x=-\cfrac{10}{7}\: or\:\tt -1.428571}[/tex]

Step-by-step explanation:

[tex]\tt -7x > 10[/tex]

Divide both sides by -7:-

[tex]\tt \cfrac{-7x}{-7} > \cfrac{10}{-7}[/tex]

[tex]\tt x=-\cfrac{10}{7}[/tex]

or

[tex]\tt -1.428571[/tex]

________________________

Hope this helps!

Answer:

258

Step-by-step explanation:

divide the shape into more manageable pieces to find the area

Answer:264.32

Step-by-step explanation:    multiply 4.72 x 56 to get the answer of 264.32

Answer:

hdhdieidjdjjdjdjdufufifuififif

Answer:

  906 square feet

Step-by-step explanation:

You want to know the area of the patio with the composite shape shown in the figure.

We can divide the shape into two trapezoids and one parallelogram. Each has a height of 12 ft.

The top trapezoid has bases of 13 ft and 23 ft. The parallelogram has a base of 23 ft. The bottom trapezoid has bases of 37 ft and 32 ft.

The relevant area formulas are ...

  A = 1/2(b1 +b2)h . . . . . . area of a trapezoid

  A = bh . . . . . . . . . . . . . area of a parallelogram

Working from the top down, the areas of the composite parts are ...

  A = 1/2(13 +23)(12) = 6(36) = 216 . . . . square feet

  A = (23)(12) = 276 . . . .  square feet

  A = 1/2(37 +32)(12) = 6(69) = 414 . . . . square feet

Then the total area of the walkway and patio is ...

  216 +276 +414 = 906 . . . . square feet

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The probability of getting 2 spades, 3 diamonds, 3 clubs and 2 hearts in the given experiment is 1/16777216.

In the given question, it is said that an experiment of drawing a random card from an ordinary playing cards deck is done with replacing it back. This was done ten times. The probability of getting 2 spades, 3 diamonds, 3 clubs and 2 hearts can be calculated as follows:

Total number of cards in a deck = 52

Number of spades in a deck = 13

Number of diamonds in a deck = 13

Number of clubs in a deck = 13

Number of hearts in a deck = 13

Number of times an experiment was done = 10

We are to find the probability of getting 2 spades, 3 diamonds, 3 clubs and 2 hearts in the given experiment.

Let's calculate the probability of getting each of these:

Probability of getting a spade = 13/52 = 1/4

Probability of getting a diamond = 13/52 = 1/4

Probability of getting a club = 13/52 = 1/4

Probability of getting a heart = 13/52 = 1/4

We need to find the probability of getting 2 spades, 3 diamonds, 3 clubs and 2 hearts.

Let's calculate the probability of getting each of these:

Probability of getting 2 spades = (1/4)² = 1/16

Probability of getting 3 diamonds = (1/4)³ = 1/64

Probability of getting 3 clubs = (1/4)³ = 1/64

Probability of getting 2 hearts = (1/4)² = 1/16

Now, let's calculate the probability of getting 2 spades, 3 diamonds, 3 clubs and 2 hearts:

Probability of getting 2 spades, 3 diamonds, 3 clubs and 2 hearts= (1/16) × (1/16) × (1/64) × (1/64) = 1/16777216

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The area under the curve is then approximated by the sum of the areas of n rectangles of height [(2 + (3i/n))³] and width (3/n), which represents the Riemann sum.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

The correct Riemann sum to find the area under the graph of the function f(x) = x³ from x = 2 to x = 5 is:

the limit as n goes to infinity of the summation from i equals 1 to n of the product of the 3rd power of the quantity 2 plus 3 times i over n and 3 over n

This can be written as:

lim(n → ∞) ∑(i=1 to n) [(2 + (3i/n))³ * (3/n)]

Here, the interval [2, 5] is divided into n subintervals of equal width (Δx) = (5 - 2)/n = 3/n.

The right endpoint of each subinterval is represented by (2 + (3i/n)), and the function value at that endpoint is given by [(2 + (3i/n))³].

The area under the curve is then approximated by the sum of the areas of n rectangles of height [(2 + (3i/n))³] and width (3/n), which represents the Riemann sum.

As n approaches infinity, the width of the rectangles approaches zero, and the sum becomes an integral that represents the exact area under the curve.

Hence, The area under the curve is then approximated by the sum of the areas of n rectangles of height [(2 + (3i/n))³] and width (3/n), which represents the Riemann sum.

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Answer:

-1 ≤ x ≤ 4

-3≤ y ≤ 4

Step by Step

See the coordinate of first point and the last point

the solution to the equation [tex]4(1.7)^(x) = 7(1.08)^(x)[/tex]  is approximately

x = 8.732.

The other technique to write exponents in mathematics is using logarithms. A number's base-based logarithm is equal to another number. A logarithm performs exponentiation's exact opposite function. For instance, log10 100 = 2 if 102 = 100.

from the question:

By separating the variable on one side of the equation and then taking the logarithm of both sides, we can find the value of x.

Starting with:

[tex]4(1.7)^(^x^) = 7(1.08)^(^x^)[/tex]

Dividing both sides by [tex]7(1.08)^(x)[/tex], we get:

[tex](4/7)(1.7)^(^x^) = (1.08)^(^x^)[/tex]

Taking the logarithm of both sides (with any base), we get:

[tex]log[(4/7)(1.7)^(^x^)] = log[(1.08)^(^x^)][/tex]

Using the properties of logarithms, we can simplify this to:

log(4/7) + xlog(1.7) = xlog(1.08)

Subtracting x*log(1.7) from both sides, we get:

log(4/7) = xlog(1.08) - xlog(1.7)

Factoring out x, we get:

log(4/7) = x*[log(1.08) - log(1.7)]

Dividing both sides by [log(1.08) - log(1.7)], we get:

x = log(4/7) / [log(1.08) - log(1.7)]

We can evaluate this statement with a calculator and obtain:

x ≈ 8.732

As a result, x = 8.732 is about the answer to the equation 4(1.7)(x) = 7(1.08)(x).

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Answer:

78

Step-by-step explanation:

[tex]75+3[/tex]

All we have to do is add 3 to the number 75.

We can do this by counting.

76, 77, 78
So 75 + 3 = 78

Answer:

3 + 75 = 78

Step-by-step explanation:

Split the 75 to make 70 and 5. Now add 3 to the 5.

3 + 5 = 8

Now add the 70 back to the 8. Now you have 78.

You could also count up from 70 3 times. 76 77, 78

The measure of ∠BOD = ∠AOC = 90 since opposite angles of a parallelogram are equal. m∠cab = m∠cdb as they are corresponding angles since AC ∥ DB.

To find ∠BOD, we can use the fact that opposite angles of a parallelogram are equal. Since AC ∥ DB, we have:

∠BOD = ∠AOC

Now, we can use the fact that the sum of angles in a triangle is 180 degrees to find ∠AOC:

∠AOC = 180 - ∠CAB - ∠CDB

∠AOC = 180 - 35 - 55

∠AOC = 90

Therefore, we have:

∠BOD = ∠AOC = 90

So, ∠BOD is a right angle.

To compare m∠cab and m∠cdb, we can use the fact that corresponding angles are equal when two parallel lines are intersected by a transversal. Since AC ∥ DB, we have:

m∠cab = m∠cdb

Therefore, the measures of the two angles are equal.

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_____The given question is incomplete, the complete question is given below:

Line segments AB and CD intersect at O such that AC ∥ DB. It ∠CAB = 35 and ∠CDB= 55. Find ∠BOD. Compare m∠cab and m∠cdb from question 1. how are the measures of the two angles related?

Answer:

9, - 1

Step-by-step explanation:

Let the number be a

a² - 9 = 8a

a² - 8a - 9 = 0

(a - 9) (a + 1) = 0

a - 9 =0, a = 9

a + 1 =0, a = - 1

The set {1, x, x2,...,xn} is linearly independent in Pn(F) if the only linear combination that produces the zero vector is the trivial one, where all coefficients are equal to zero.

Let's consider a linear combination of the set:

c0*1 + c1*x + c2*x2 + ... + cn*xn = 0

We need to show that the only solution to this equation is c0 = c1 = c2 = ... = cn = 0.

Let's assume that there is a non-trivial solution, where at least one of the coefficients is not equal to zero.

Without loss of generality, let's assume that cn is not equal to zero. Then we can rearrange the equation to isolate the term with the highest power of x:

cn*xn = -c0*1 - c1*x - c2*x2 - ... - cn-1*xn-1

Now we can divide both sides of the equation by cn*xn to get:

1 = (-c0/cn)*1/xn + (-c1/cn)*x/xn + (-c2/cn)*x2/xn + ... + (-cn-1/cn)*xn-1/xn

The right-hand side of this equation is a polynomial of degree n-1, while the left-hand side is a constant. This means that the equation can never be true for any value of x, which contradicts our assumption that there is a non-trivial solution.

Therefore, the only solution is the trivial one, where all coefficients are equal to zero. This means that the set {1, x, x2,...,xn} is linearly independent in Pn(F).

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The shortest length that Adrian’s cable could be is 3cm.

To find the shortest length of Adrian's cable, we need to find the greatest common divisor (GCD) of 9cm and 15cm.

The GCD is the largest positive integer that divides both 9 and 15 without leaving a remainder.

We can use the Euclidean algorithm to find the GCD:

15 = 1 x 9 + 6

9 = 1 x 6 + 3

6 = 2 x 3 + 0

Since the remainder is 0 when we divide 6 by 3, the GCD of 9 and 15 is 3cm.

Therefore, Adrian's cable must be a multiple of 3cm in length in order to be cut into either 9cm or 15cm lengths.

The shortest possible length of the cable that satisfies this condition is 3cm.

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Answer:

7/8 x 1/3 is 7/24

Step-by-step explanation:

Multiple: 7/8 * 1/3 = 7 · 1/8 · 3 = 7/24

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(7, 24) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven eighths multiplied by one third is seven twenty-fourths.  

Answer:

45.

Step-by-step explanation:

Given: 3×5x when x = 3.

First write in x:

3×5×3, when two digits, or variables are together, there's always a multiplication sign.

Then calculate:

3×5×3

15×3

= 45

Answer:

4.5 liters

Step-by-step explanation:

1 liter = 1000 milliliters

4500 milliliters = ? liters

We take

4500 / 1000 = 4.5 liters

So, 4,500 milliliters is equivalent to 4.5 liters.

Answer:

4.5 liters

Step-by-step explanation:

1 liter = 1000 milliliters

To get your answer, just divide by 1000.

4500 / 1000 = 4.5 liters

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

Answer:

Step-by-step explanation:

1. (3/4)^2 = 3/4 * 3/4

2. numerator * numerator so 3 * 3 = 9

3. denominator * denominator so 4 * 4 = 16

Hence, the answer is 9/16

Step-by-step explanation:

(3/4)² = 3²/4² = 9/16

(a×b×c×d×...×z)² = a²×b²×c²×d²×...×z²

Answer:

No

Step-by-step explanation:

Plug it in to check. 36 is not equal to 4(11) becuase 4(11)=44.

36 never equals 44.

Answer:

0.58

Step-by-step explanation:

0.5809

0.0009 is the ten thousandths

0.000 is the thousandths

0.08 is the hundreds

0.5 is the tens

so the answer must only have two decimal places:

0.5809 rounded to the thousandth is 0.581, because 9 is closer to 10 then 0

0.581 rounded to the hundredth is 0.58, because 1 is closer to 0 then 10

Answer:

its true

Step-by-step explanation:

maths may be difficult, but if you practice it, you'll be able to solve any maths question

Denise makes $12.18 an hour.

Step-by-step explanation:

Hannah earns $12 dollars per hour and Jimmy makes 30% less.

We can use percent proportions to do this.

$12 is our whole, 30% is our percent, and 100

[tex]\frac{x}{12} =\frac{30}{100}[/tex]

12 x 30 = 360

360/100 equals 3.6

Jimmy makes $ 3.6 less than Hannah or $8.40 an hour.

Denise makes 45% more than Jimmy.

Again, we will use percent proportions

[tex]\frac{x}{8.4} =\frac{45}{100}[/tex]

8.4 x 45 = 378

378/100 = 3.78

After adding $8.4 + $3.78

You get $12.18

You can do this anyway you like but I find it more easier for me to use percent proportions while doing this.

Answer:

Denise makes $12.18 per hour.

Step-by-step explanation:

Jimmy:

12 x .3 = 3.60

12 - 3.60 = 8.40

Jimmy makes $8.40 per hour.

Denise:

8.40 x .45 = 3.78

3.78 + 8.40 = 12.18

Denise makes %12.18 per hour.

Helping in the name of Jesus.

For the MSE loss of a linear model, the critical point is a minimizer. The second derivative test shows that any deviation results in a higher loss.

The mean squared error (MSE) loss of a linear model f(x) = yx, given the observed data {li, Yi}, i = 1,...,n, is given by:

L(y) = (1/n) * ∑i=1 to n (Yi - y*li)^2

To find the critical point of this function, we need to differentiate it with respect to y and set it equal to zero:

dL(y)/dy = (1/n) * ∑i=1 to n 2*(Yi - yli)(-li) = 0

Simplifying this expression, we get:

∑i=1 to n (Yi * li) - y * ∑i=1 to n (li^2) = 0

Rearranging the terms, we get:

y = (∑i=1 to n (Yi * li)) / ∑i=1 to n (li^2)

This is the critical point of the MSE loss function for the given linear model. To show that this critical point is indeed the minimizer of the loss, we can use the second derivative test. Taking the second derivative of the loss function with respect to y, we get:

d2L(y)/dy2 = (2/n) * ∑i=1 to n (li^2)

Since the second derivative is positive for all values of li, this means that the critical point is a minimum.

Intuitively, this makes sense because the MSE loss measures the average squared difference between the predicted values (y*li) and the actual values (Yi). By minimizing this difference, we are finding the best fit line for the given data points. The critical point is indeed the minimizer of the loss.

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Answers

πr^2h

Step-by-step explanation:

because this is the volume of a

Step-by-step explanation:

the volume of a cone is

base area × height / 3

pi×r² × height / 3

pi×10² × 12 / 3 = 100pi × 4 = 400pi in²

for the first cone

pi×5² × 12 / 3 = 25pi × 4 = 100pi in²

The value of h that causes the system to be inconsistent is h = 15. the value of h that causes the system to be inconsistent, we can use the determinant method.

The determinant of a system of equations is given by : [tex]| a b c || d e f || g h i |[/tex]
Where a, b, c, d, e, f, g, h, and i are the coefficients of the variables in the system of equations. If the determinant is equal to zero, then the system is inconsistent.

For the given system of equations:[tex]x + y - 2z = -12x + hy - z = 3x + 3y + 2z = 1[/tex]
The determinant is:
[tex]| 1 1 -2 || 2 h -1 || 1 3 2 |[/tex]
Determinant by using the formula:
[tex]D = aei + bfg + cdh - ceg - bdi - afh[/tex]


Plugging in the values from the determinant:
[tex]D = (1)(-1)(2) + (1)(-1)(3) + (-2)(2)(3) - (-2)(-1)(3) - (1)(2)(2) - (1)(h)(-1)[/tex]
Simplifying:
D = -2 - 3 - 12 + 6 - 4 + h
D = -15 + h

For the system to be inconsistent, the determinant must be equal to zero: -15 + h = 0, Solving for h: h = 15. Therefore, the value of h that causes the system to be inconsistent is h = 15.

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The maximum displacement is A, the frequency is ω/2π, the value of d when t = 5 is A * cos(ω*5 + φ), and the least positive value of t for which d = 0 is (π/2 - φ)/ω.

The equation for simple harmonic motion is d = A * cos(ωt + φ), where d is the displacement, A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase shift.

To find the maximum displacement, we need to find the value of A. The maximum displacement occurs when cos(ωt + φ) = 1, so A is the maximum displacement.

To find the frequency, we need to find the value of ω. The frequency is given by f = ω/2π, so we can rearrange this equation to find ω = 2πf.

To find the value of d when t = 5, we can simply plug t = 5 into the equation for d and solve.

To find the least positive value of t for which d = 0, we need to find the value of t that makes cos(ωt + φ) = 0. This occurs when ωt + φ = π/2 + 2πn, where n is an integer. We can rearrange this equation to find t = (π/2 + 2πn - φ)/ω. The least positive value of t will occur when n = 0, so we can plug n = 0 into the equation and solve for t.

Finally, we can use a graphing utility to verify our results. We can graph the equation for d and look at the maximum displacement, the frequency, the value of d when t = 5, and the least positive value of t for which d = 0.

Overall, the maximum displacement is A, the frequency is ω/2π, the value of d when t = 5 is A * cos(ω*5 + φ), and the least positive value of t for which d = 0 is (π/2 - φ)/ω.

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The possible values of angle J is 76 degrees

Given that

Triangle = Triangle HIJ

j = 91 inches

i = 90 inches

Angle I = 106 degrees

The possible values of angle J can be calculated using the following law of sines

sin(J)/j = sin(I)/i

By substituion, we have

sin(J)/91 = sin(106)/90

So, we have

sin(J) = 0.9719

Take the arc sin of both sies

J = 76 and 104 degrees

The measure 104 degrees is not possible because a triangle cannot have two obtuse angles

Hence, the measure of J is 76 degrees

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The least-squares solution of the linear system AX = b, x1 = -1.2 and x2 = 0.8.

To solve for the least-squares solution of the linear system AX = b, we need to use the formula X = VΣ^(-1)U^Tb.

First, we need to calculate the inverse of Σ by taking the reciprocal of the non-zero diagonal elements and setting the zero diagonal elements to zero. So,

Σ^(-1) = [1/5 0]

[0 1/5]

Next, we calculate U^Tb by multiplying U^T and b:

U^Tb = [-3]

[ 1]

[-4]

[ 3]

Now, we can calculate X:

X = VΣ^(-1)U^Tb

= [ 0.8 0.6][1/5 0][-3]

[-0.6 0.8][0 1/5][ 1]

[0 0 ][-4]

[0 0 ][ 3]

= [-1.2]

[ 0.8]

[ 1.6]

[ 0.6]

Therefore, the least-squares solution are x1 = -1.2 and x2 = 0.8.

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Answer:the percentage increase is 14%

Step-by-step explanation:the difference between 57000 and 50000=7000

so therefore

% increase=7000/50000*100%

                  =14%  

The surface area of this triangular prism is 258 square units

Given parameter is

The triangular prism

The surface area of triangular prism is calculated as

Surface area = Perimeter * Length + 2 * Base area

Using the given dimensions, we have

Surface area = (5 + 6.5 + 6.5) * 11 + 2 * 5 * 6

Evaluate

Surface area = 258

Hence, the surface area is 258 square units

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