Prove : ∣u⋅v∣⩽∣u∣∣v∣
∣u+v∣⩽∣u∣+∣v∣

Answer:

2 + 2 + 2 + 2 + 2 + 2 = 4 × 3

Step-by-step explanation:

Answer:

a. parallel    b. neither      c. neither      d. perpendicular

Step-by-step explanation:

Find the gradient of the line in the graph

Choose 2 coordinates, I choose (0,1) and (3,3)

Use the formula

(y2 - y1)/(x2 - x1)

(3 - 1) / (3 - 0)

2/3

Gradient of a parallel line is the same

Gradient of a perpendicular line formula m1m2 = -1

(2/3)m2 = -1

m2 = -3/2

The gradient of the perpendicular line will be -3/2

The gradient of the parallel line will be 2/3

Any other gradient will be neither parallel nor perpendicular.

In linear equation, The function we get (f.g)(x) =-3x+2

What is  a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                            The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that,

The linear function are f(x)=x-2 and g(x)=-3x+4

= (f ⋅ g)(x).

= f(g(x))

= f(-3x+4)

= (-3x+4)-2

= -3x+4-2

= -3x+2

Therefore, The function we get (f.g)(x) =-3x+2

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The number of degrees of freedom for the Student's t-test of a population mean is always 1 less than the sample size.

The correct answer is (a) sample size. In the context of the Student's t-test, the degrees of freedom represent the number of independent observations available to estimate the population parameter. For a one-sample t-test, the sample size determines the number of observations used to calculate the test statistic.

In the t-test, we compare the sample mean to a hypothesized population mean and assess whether any difference observed is statistically significant. The degrees of freedom in the t-test are calculated as n - 1, where n is the sample size. Subtracting 1 accounts for the loss of one degree of freedom due to estimating the sample mean. This adjustment is necessary because the sample mean is used to estimate the population mean.

By reducing the degrees of freedom by 1, the t-distribution becomes more concentrated around the mean, which affects the critical values and the calculation of p-values. This adjustment is specific to the t-distribution and is a key difference from the normal distribution, where degrees of freedom are not involved.

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Answer:

C. mental set

Step-by-step explanation:

A mental set generally refers to the brain's tendency to stick with the most familiar solution to a problem and stubbornly ignore alternatives. This tendency is likely driven by previous knowledge (the long-term mental set) or is a temporary by-product of procedural learning (the short-term mental set).

The standard equation of the sphere with the given characteristics, center (-1, -6, 3), and radius 5 is

\((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).

The standard equation of a sphere is \((x-h)^{2} +(y-k)^{2}+ (z-l)^{2} =r^{2}\), where (h, k, l) is the center of the sphere and r is the radius.
Using this formula and the given information, we can write the standard equation of the sphere:
\((x-(-1))^{2}+ (y-(-6))^{2} +(z-3)^{2}= 5^{2}\)
Simplifying, we get:
\((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).
Therefore, the standard equation of the sphere with center (-1, -6, 3) and radius 5 is \((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).

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The value of x in the similar triangles is 11.4.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore,

ΔACB ~ ΔEFD

Hence,

AC / EF = CB / FD = AB / ED

Therefore, let's find x

x = AB

ED = 3.8

BC = 15

FD = 5

x / 3.8 = 15 / 5

cross multiply

5x = 15 × 3.8

5x = 57

divide both sides of the equation by 5

x = 57 / 5

x = 11.4

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The two main ways in which marketers address the competition with their strategies are by satisfying a need better than the competition and by positioning the product . The correct option is B

Positioning is the process of forming a picture of the product in the target market's minds. To do this, a unique selling proposition (USP) must be developed that sets the product apart from the competition. A statement describing the advantages of the product and why it is superior to the competition is known as the USP.

Marketers use a variety of tools to position their products such as :

Therefore, the correct answer is B. positioning the product.

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Answer:

offering a lower price

Step-by-step explanation:

Answer:

13.7

Step-by-step explanation:

The computation of the volume of toy A is shown below:

7 × k^2=9

k^2= 9 ÷ 7

k=√9 ÷ 7

k = 1.133893419

Now

= 20 ÷ 1.133893419³

=13.7

Answer:

5 blocks south and 1 block west ( I think that's right sorry if its wrong I'm heading off to bed)

_______________

I'm reading your question

___________________

According to the Pythagorean theorem

Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2

The hypotenuse is the case (Square 1 )

area of the sqaure= side of the square^2

________________________

That means the area of 1 is = area of square 2 + area fo square3 (J is false)

_______________________________

We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)

______________________________

G is true

______________________________

Answer

G

Each side of cube is 100 cm.

In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

Given that,

Volume of cube = 1 cubic meter

We know that,

1 m = 100 cm

Also  volume of cube = \(a^{3}\)

Then,

Volume of cube = 1000000 cm

                   \(a^{3}\)  = \(100^{3}\)

                   a = 100 cm

Hence, Each side of cube is 100 cm.

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Answer:

Its the second table

Step-by-step explanation:

we dunno, hmmm let's check for the slope for PQ

\(P(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-10})\qquad Q(\stackrel{x_2}{-5}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-10)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-8)}}} \implies \cfrac{-12 +10}{-5 +8} \implies \cfrac{ -2 }{ 3 } \implies - \cfrac{2 }{ 3 }\)

keeping in mind that perpendicular lines have negative reciprocal slopes, then if both are truly perpendicular, then line RS will have a slope of

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2} \implies \cfrac{3}{ 2 }}}\)

let's see if that's true

\(R(\stackrel{x_1}{9}~,~\stackrel{y_1}{-6})\qquad S(\stackrel{x_2}{17}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-5}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{17}-\underset{x_1}{9}}} \implies \cfrac{-5 +6}{8} \implies \cfrac{ 1 }{ 8 } ~~ \bigotimes ~~ \textit{not perpendicular}\)

Answer:

Step-by-step explanation:

No they are not perpendicular.

Perpendicular lines have slopes that are negative reciprocals of each other.

PQ slope = -12 - -10/-5 --8 = -2/3

RS slope = -5 - -6/17 -9 = 1/8

Slope are not negative reciprocals - the lines are not perpendicular.

Slope formula is m = y2 - y1/x2 - x1

Use this to determine slope.

For example if the the slope of RS was 3/2 - the lines would be perpendicular.

Parallel lines have equal slope so

Lets check

Now

Lines are parallel

Answer:

The two lines are parallel

Step-by-step explanation:

If two lines are parallel, they have the same slope.

If two lines are perpendicular, the slopes will be negative reciprocals (the product of the slopes will be -1).

Given slopes:

\(\sf m_1=\dfrac{3}{4}\)

\(\sf m_2=\dfrac{12}{16}\)

Reduce m₂ to its simplest form by dividing the numerator and denominator by the largest common factor:

\(\sf m_2=\dfrac{12 \div 4}{16\div 4}=\dfrac{3}{4}\)

Therefore,

\(\sf as \quad \dfrac{3}{4}=\dfrac{3}{4} \implies m_1=m_2 \quad\)

As the given slopes are the same, the two lines are parallel.

The cost is the cost per pound times the number of pounds minus the coupon.

If \(p\) pounds are purchased, she will pay \(3.50p-3.25\).

If 3 pounds are purchased, she will pay 3.50(3)-3.25=7.25.

Check the picture below.

Make sure your calculator is in Degree mode.

\(\tan(\alpha )=\cfrac{\stackrel{opposite}{5}}{\underset{adjacent}{4}}\implies \alpha=\tan^{-1}\left( \cfrac{5}{4} \right)\implies \alpha \approx 51.3^o\)

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Both because they are all the same triangle

We are given two expressions to simplify. In the first expression, 6.1 sin 10° cos 440 + tan(360°-0), we need to simplify it to a single trigonometric term. In the second expression, sin(60° + 2x) + sin(60° - 2x), we are asked to evaluate it. By using trigonometric identities and properties, we can simplify and evaluate these expressions.

6.1 sin 10° cos 440 + tan(360°-0):

Using the trigonometric identity tan(θ + π) = tan(θ), we can rewrite tan(360° - 0) as tan(0) = 0. Therefore, the expression simplifies to 6.1 sin 10° cos 440 + 0 = 6.1 sin 10° cos 440.

sin(60° + 2x) + sin(60° - 2x):

Using the angle sum identity for sine, sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we can rewrite the expression as sin(60°)cos(2x) + cos(60°)sin(2x). Since sin(60°) = √3/2 and cos(60°) = 1/2, the expression simplifies to (√3/2)cos(2x) + (1/2)sin(2x).

Note: The given expression sin(60° + 2x) + sin(60° - 2x) cannot be further simplified to a single trigonometric term. However, we can rewrite it in terms of cosine using the identity sin(x) = cos(90° - x), which results in (√3/2)cos(90° - 2x) + (1/2)cos(90° + 2x).

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Answer:

1. 5/6

2. 5/8

3. 29/44

4. 3/8

5. -8/15

The value of K that moves both original poles back onto the real axis is 0. By setting K to zero, we eliminate the quadratic term and obtain a single pole at \( s = -2 \), which lies on the real axis.

The value of K that moves both original poles back onto the real axis can be found by setting the characteristic equation equal to zero and solving for K.

The transfer function of the plant is given by \( G(s) = \frac{1}{(s+2)^2} \). To move the original poles, we introduce a PD-controller with transfer function \( D_c(s) = K(s+7) \), where K is a positive constant.

The overall transfer function, including the controller, is obtained by multiplying the plant transfer function and the controller transfer function: \( G_c(s) = G(s) \cdot D_c(s) \).

To find the new poles, we set the characteristic equation of the closed-loop system equal to zero, which means we set the denominator of the transfer function \( G_c(s) \) equal to zero.

\[

(s+2)^2 \cdot K(s+7) = 0

\]

Expanding and rearranging the equation, we get:

\[

K(s^2 + 9s + 14) + 4s + 28 = 0

\]

To move the poles back onto the real axis, we need to make the quadratic term \( s^2 \) zero. This can be achieved by setting the coefficient K equal to zero:

\[

K = 0

\]

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when getting a bearing, we're referring to the angle from the North line moving clockwise, so of D from C?  well, the "from" point gets the North line and we check the angle from that North line clockwise to the other point, Check the picture below.

Answer:

1 . Chicken curries - £6.20 X 2 =  £12.40  15% of  £ 12.40 is £1.86 off = £10.54  +

2 .Onion Soups - £4.00 x 2 = £8.00    15% OF £8.00 is £ 1.20 off =       £6.80

3. One Naan bread = £.2.80    15% of £ 2.80 is £ 0.42 p  off  =              £2.38

4. One mint parfait = £ 3.80     15% of £ 3.80 is £ 0.57 p off  =               £ 3.23

5 .One ice cream delight = £2.60  15% of £ 2.60 is £0.39 p off             £ 2.21

                                                                                                           =      £ 25.16

Step-by-step explanation:

1. to find out 15% from £12.40 you can divide 12.40 / 100 = 0.124 and then times 0.124 by the percentage = 0.124 x 15 = £ 1.86

2 . to find out 15% from £8.00 you divide again £8.00 / 100 =0.08 and then times 0.08 by the percentage 15 %= 0.08 x 15 = £1.20 off

3.  £ 2.80 / 100 =0.028 x 15% =  £0.42 p off

4.    £ 3.80 /100 = 0.038 x 15% = £ 0.57 p off

5.     £ 2.60 /100 = 0.026 x 15% = £ 0.39 p off

Hope that helped !

Answer:

-70

Step-by-step explanation:

f(x)=x^3 - 6

f(-4) = (-4)^3 - 6

f(-4) = -64 -6

f(-4) = -70

According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.

Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.

Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.

Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.

So, Will could have put 8 ounces of water in each cup.

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Answer:

612 Children's dresses

Step-by-step explanation:

837 + 958 = 1795

2407 - 1795 = 612