Determine the projection of u=1.6i+3.3j in the v=-2.1i-0.5j direction

ANSWER

The length of a Diameter is 3.714

EXPLANATION

The circumscribed triangle is shown in the attachment.

We use the cosine ratio to find the altitude of the isosceles triangle.

[tex] \cos(60 \degree) = \frac{altitude}{hypotenuse} [/tex]

[tex] \cos(60 \degree) = \frac{altitude}{8} [/tex]

Altitude =8cos(60°)

Altitude=4cm

Let the upper half of the altitude be y cm.

Then the radius of the circle is (y-4)cm

The upper radius meets the tangent at right angles.

From the smaller right triangle,

[tex] \sin(60 \degree) = \frac{4 - y}{y} [/tex]

[tex] y\sin(60 \degree) = 4 - y[/tex]

[tex]y\sin(60 \degree) + y= 4 [/tex]

[tex](\sin(60 \degree) + 1)y= 4 [/tex]

[tex]y= \frac{4}{\sin(60 \degree) + 1} [/tex]

[tex]y = 16 - 8 \sqrt{3} [/tex]

y=1.857

The diameter is 2y

[tex]d = 32 - 16 \sqrt{3} [/tex]

=2(1.875)

The length of a Diameter is 3.714

Answer:

Diameter of the circle is 16 cm.

Step-by-step explanation:

Given : The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm.

To find : The length of a diameter of the circle circumscribed about this triangle?

Solution :

We construct a circle in which an ABC isosceles triangle is formed.

Refer the attached figure below.

The measure of a vertex angle of an isosceles triangle is 120° .

The length of a leg is 8 cm, AC=8 cm

Vertex angle is divided by the line touching the center of the circle.

So, [tex]\angle A=60^\circ[/tex] and line AD=radius of the circle

Applying property of isosceles triangle,

Now, ∠DAC=∠ACD=∠CDA=60°

AC=DC=8 cm

The radius of the circle is 8 cm.

The diameter of the circle is twice the radius.

Therefore, The diameter of the circle is d=2(8)=16 cm.

Answer:

Statistic

Step-by-step explanation:

You are asking more than one people/persons so it would be statistic.

Answer:

x = 20

∠B = 92

∠C = 40

Step-by-step explanation:

im pretty sure

Answer:

x = 20. ∠B = 92° and ∠C = 40°

Step-by-step explanation:

Angles of a triangle are ∠A = 48°, ∠B = (6x - 28)° and ∠C = (2x)°

Since sum of all the angles of the triangle is 180°

So ∠A + ∠B + ∠C = 180°

48° + (6x - 28)° + (2x)° = 180°

48 + 6x - 28 + 2x = 180

8x + 20 = 180

8x = 180 - 20

8x = 160

x = [tex]\frac{160}{8}=20[/tex]

Now ∠B = (6x - 28) = 6×20 - 28

∠B = 120 - 28 = 92°

And ∠C = 2x° = 2×20 = 40°

Therefore, x = 20. ∠B = 92° and ∠C = 40° is the answer.

Answer: 58.86

Step-by-step explanation:

45(.068)= 3.06

3.06+45= 48.06

45(0.24)=10.8

48.06+10.8= 58.86

Answer:

6 miles

Step-by-step explanation:

Let the route length be r.  The distance the cyclist has already covered is then (5/7)r + 40.  This plus 0.75r - 118 must = r, the length of the entire route.

Then:

(5/7)r + 40 + (3/4)r - 118 = r

The LCD of the fractions 5/7 and 3/4 is 28.  We thus have:

(20/28)r + 40 + (21/28)r - 118 = r, or

(41/28)r - 78 = (28/28)r

Combining the r terms, we get 13r = 78, and so r = 78/13 = 6.

The cyclist's bike route is 6 miles long.

Answer:

168 miles

Step-by-step explanation:

Answer:

(4,470°)

Step-by-step explanation:

The representation that does not change the location of (4, 110°) in polar coordinates are all points that are coterminal with the given point.

The only point among the given options that is coterminal with (4, 110°) is (4, 470)°

The two points have the same magnitude and 470°-360°=110°.

Since 110° is coterminal with 470° and the two points have the same magnitude with the same sign, the two points represent the same location in polar coordinates.

The correct choice is (4,470°)

In the polar coordinate system, the point (4, 470°) is the representation that does not change the location of the given point (4, 110°). We obtain this by adding 360° to the given angle.

This question is based on the concept of polar coordinates. Polar coordinates represent a point in space by specifying its distance from a reference point, usually the origin, and the angle made with the positive x-axis. In polar coordinates, (r, θ), 'r' represents the distance and 'θ' is the angle.

Given point is (4, 110°). We can notice that by adding or subtracting multiples of 360° from the angle, we are not changing the location of the point. So, if we add 360° to the 110°, we will obtain 470°. Hence, the point that represents the same location is (4, 470°).

The point (-4, 200°) represents the point in the opposite direction and the points (4, 290°) and (-4, 470°) change the angle beyond or below what is allowable without changing the point's location.

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in the junior side it is 22 the middle is 8 the girl side is 20 the outside is 16

Answer:

In sequence: 6, 8, 12 and 16

Step-by-step explanation:

Ok, the Venn diagram has 4 sections:

A - Juniors, but excluding girls (so boys only)

B - Juniors, who are also girls (so girls only)

C - Girls only, who aren't Juniors

D - Then outside the circles, for those who are not juniors and who are not girls (senior boys).

So, in A, you place the junior boys (6)

in B, you place the junior girls (8)

in C, you place the senior girls (12)

and in D, you place the senior boys (16)

Answer:

option B

[tex]\frac{280}{\sqrt{L}\sqrt[3]{P}}[/tex]

Step-by-step explanation:

Step 1

S varies inversely of the cube root of P

s [tex]\alpha[/tex][tex]\frac{1}{\sqrt[3]{P} }[/tex]

s = [tex]\frac{k}{\sqrt[3]{P} }[/tex]

Step 2

S varies inversely with square root of L

s[tex]\alpha\frac{1}{\sqrt{L} }[/tex]

s = [tex]\frac{k}{\sqrt{L} }[/tex]

Step 3

Jointly

s = [tex]\frac{k}{\sqrt{L} \sqrt[3]{P} }[/tex]

Step 4

Plug values given in the question to find constant of proportionality

7 = [tex]\frac{k}{\sqrt{100}\sqrt[3]{64}}[/tex]

7 = k /(10)(4)

7 = k/40

k = 280

Step 5

General formula will be

s = [tex]\frac{280}{\sqrt{L}\sqrt[3]{P}}[/tex]

Answer:

2:5

it may be faster to google it

Answer:

Required ratio is 2:5.

Step-by-step explanation:

Given that number of female nurses = 250

Given that number of male nurses = 100

Now we need to find about what is the ratio of male nurses to female nurses.

So we just need to divide number of male nurses by the number of female nurses. That means divide 100 by 250. We get:

[tex]\frac{male}{female}=\frac{100}{250}[/tex]

[tex]\frac{male}{female}=\frac{10}{25}[/tex]

[tex]\frac{male}{female}=\frac{2}{5}[/tex]

Hence required ratio is 2:5.

Answer:

The volume of the larger pyramid is equal to [tex]7,133\ cm^{3}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z----> the scale factor

In this problem, the ratio of the height is equal to the scale factor

[tex]z=\frac{4}{7}[/tex]

step 2

Find the volume of the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> volume of the smaller pyramid

y----> volume of the larger pyramid

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{4}{7}[/tex]

[tex]x=1,331\ cm^{3}[/tex]

substitute

[tex](\frac{4}{7})^{3}=\frac{1,331}{y}\\ \\(\frac{64}{343})=\frac{1,331}{y}\\ \\y=343*1,331/64\\ \\y=7,133\ cm^{3}[/tex]

Answer:

(A) 1/.2.

Step-by-step explanation:

Experimental Probability = the total number of tails / total number of tosses

= 40 / 80

= 1/2 (answer).

Answer:

The answer is (A) 1/2 its correct on gradpoint

answer for this question is 5x-17

Answer:

87550

Step-by-step explanation:

Answer:

3788 + 83762 = 87,550

Answer:

I don't know the size of the pans, but I'd probably say the rectangle ones.  

Step-by-step explanation:

Y'know, you have to calculate volume and all that put based on the info given rectangular pans usually hold more...although there are two round pans...please add some numbers to clarify!

The answer is Ms Hernandez can bring up to 6 people to the zoo.

x -  the number of people that she can bring to the zoo

The parking will cost $7: a = 7

Admission tickets will cost $15.50 per person: b = 15.50x

She can spend on parking and admission tickets $100:

a + b ≤ 100

a = 7

b = 15.50x

7 + 15.50x ≤ 100

15.50x ≤ 100 - 7

15.50x ≤ 93

x ≤ 93 / 15.50

x ≤ 6

Answer:

Step-by-step explanation:

The definitions of rigid-motion transformations need to be precise as they entail more than physical descriptions of motions. They have unique mathematical definitions and are important for understanding and interpreting real-world movements and physical phenomena.

The definitions of each rigid-motion transformation, namely slides (translations), flips (reflections), and turns (rotations), need to be more precise because they are not solely about the physical manifestation of the motion. These transformations have distinct mathematical underpinnings. For instance, a translation involves moving the figure along a specified direction and distance in a straight line, without changing the orientation of the figure. A reflection involves 'flipping' the figure over a line of reflection, altering its orientation but not its shape or size. A rotation involves turning the figure around a specified point for a given angle.

Moreover, in both rotational and translational motion - two forms of rigid-body motion, there are accurate variables such as displacement, velocity, and acceleration related to translational motion and the corresponding angular variables in rotational motion. These specific definitions are crucial for the mathematics behind movement and interpreting the world around us. Understanding such concepts can also aid in studying physical phenomena as diverse as a spinning ballet dancer or a rotating planet.

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Answer:

x=3

y=21

Step-by-step explanation:

To use substitution method, first we need to decide which variable solve first, either x or y.

Here we decide to start by 'y' using equation y=x+18, which is already solved for 'y'

That same equation is then substitute into the first equation:

x+18= 10x-9

From here, we isolate 'x' variable and grouping terms, we have this:

27=9x

Resulting x=3

Now, we can use the above result in the second equation (y=x+18)

Leading to y=3+18=21.

Answer:663.95$

Step-by-step explanation:

Answer:

633.95

Step-by-step explanation:

Answer:

$1109.81

Step-by-step explanation:

$249.00 +$369.62= $618.62(ms. aguilars class)

$618.92-$430.43= $188.19(mr. barry's class)

$249.00+$618.62+$188.19=$1109.81(complete answer of all 3 classes combined)

Answer:

The final amount is $1109.81

Step-by-step explanation:

In order to find the total amount, start with the know amount, which is Ms. Moore's class. Her class raised $249. Now we can use that to find the amount from Ms. Aguilar's class.

$249 + $396.62 = $645.62

Now we can use the amount from Ms. Aguilar's class to find the amount from Ms. Barry's class

$645.62 - $430.43 = $215.19

Now we can add the three amounts together to find the total amount.

$249 + $645.62 + $215.19 = $1109.81

Answer:

5

Step-by-step explanation:

Mode means most, so it's the number you see most.

Answer:

sin Ф = 3/√13; cos Ф = 2/√13; and tan Ф = 3/2

Step-by-step explanation:

Let's assume we're limiting ourselves to Quadrant I.

Start with the tangent function.  tan Ф = opp / adj.

In this case opp = 3 and adj = 2.  

The length of the hypotenuse is found using the Pythagorean Theorem and is √(3² + 2²) = √13.

Then sin Ф = opp / hyp = 3/√13 or 3√13/13

and

cos Ф = adj / hyp = 2/√13 or 2√13/13

and (as before)

tan Ф =  opp / adj = 3/2

sin(θ) is approximately 0.832

cos(θ) is approximately 0.555

tan(θ) is 1.5

The given parameters are;

The location of point (2, 3) = The terminal side of angle θ in standard position

The required parameters;

sin of θ, cosine of θ, and tangent of θ

Strategy;

Draw angle θ on the coordinate plane based on definition showing point (2, 3) on the terminal side and find the required trigonometric ratio

Standard position is the position of an angle that has the vertex at the

origin, the fixed side of the angle is on the x-axis and the terminal side

which defines the angle is drawn relative to the initial fixed side to form

the given angle either clockwise or anticlockwise

We have the following trigonometric ratios with regards to the reference angle;

[tex]sin\angle X = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]

The hypotenuse length = √(2² + 3²) = √13

Therefore;

[tex]\mathbf{sin( \theta)} = \dfrac{3 - 0}{\sqrt{13} }= \dfrac{3}{\sqrt{13} } = \mathbf{\dfrac{3 \cdot \sqrt{13} }{13}}[/tex]

[tex]\mathbf{sin( \theta)} \ is \ \mathbf{\dfrac{3 \cdot \sqrt{13} }{13}} \approx 0.832[/tex]

[tex]cos\angle X = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}[/tex]

Therefore

[tex]\mathbf{cos( \theta)} = \dfrac{2 - 0}{\sqrt{13} }= \dfrac{2}{\sqrt{13} } =\mathbf{ \dfrac{2 \cdot \sqrt{13} }{13 }}[/tex]

[tex]\mathbf{cos( \theta)} \ is \ \mathbf{ \dfrac{2 \cdot \sqrt{13} }{13 }} \approx 0.555[/tex]

[tex]tan\angle X = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length}[/tex]

The hypotenuse length = √(2² + 3²) = √13

Therefore;

[tex]\mathbf{tan( \theta)} = \dfrac{3 - 0}{2 - 0 } \mathbf{=\dfrac{3}{2 }}[/tex]

tan(θ) = 1.5

Learn more bout trigonometric ratios here;

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Answer:

x = (19.5 - 6y - 6z) /6

y = (19.5 - 6x - 6z) /6

z = (19.5 - 6x - 6y) /6

Step-by-step explanation:

Let the Apples be X

           Oranges be Y

           Avocados be Z

Total cost of the Fruits = 19.5

So the equation would be as follows:

6x + 6y + 6z = 19.5

for Apples, equation would be:  

6x= 19.5 - 6y - 6z

x = (19.5 - 6y - 6z) /6

For Oranges, the equation would be:

6y= 19.5 - 6x - 6z

y = (19.5 - 6x - 6z) /6

For Avocados, the equation would be:

6z= 19.5 - 6x - 6y

z = (19.5 - 6x - 6y) /6

Answer:

simple answer

Step-by-step explanation:

Let x be the cost of one apple, y the cost of one orange, and z the cost of one avocado.

The first weekend, Ed buys 6 of each fruit and pays $19.50: 6x+6y+6z=19.5

The second weekend, Ed buys 12 apples, 2 oranges, and 1 avocado and pays $9.50: 12x+2y+z=9.5

The third weekend, Ed buys 2 apples, 4 oranges, and 5 avocados and pays $14: 2x+4y+5z=14.

Final answer:

The probability that three people independently select the same letter of the alphabet is 1/676.

Explanation:

The question asks about the probability that three people select the same letter of the alphabet independently. Since there are 26 letters in the alphabet, the first person can pick any letter with a probability of 1 (they are sure to pick some letters). The second person must pick the same letter as the first, which has a probability of 1/26. Similarly, the third person also has a probability of 1/26 to pick the same letter as the first two. To find the combined probability for all three events happening in sequence (all three picking the same letter), we multiply the individual probabilities: 1 * (1/26) * (1/26) = 1/676.

Factors of 16 :

1, 2, 4, 8, 16

1,2,4,8,16

16 is a composite number and it is 4 squared. 16= 1x16,2x8 or 4x4. So all the factors of 16 is 1,2,4,8,16

Answer:

150 square inch

Step-by-step explanation:

you want to calculate each rectangle area individually then add all together

A = lw

1st one....9*4 = 36 sq. in

2nd one..4*3 = 12 sq. in

3rd one...9*3 = 27 sq. in

4th one...4*3 = 12 sq. in

5th one...9 *4 = 36 sq. in

6th one...9*3 = 27 sq. in

____________________

add all = 150 sq. in.

Answer:

Choice C is the correct solution

Step-by-step explanation:

We can split up the terms under the cube root sign to obtain;

[tex]\sqrt[3]{32}*\sqrt[3]{x^{8} }*\sqrt[3]{y^{10} }\\\\\sqrt[3]{32}=\sqrt[3]{8*4}=\sqrt[3]{8}*\sqrt[3]{4}=2\sqrt[3]{4}\\\\\sqrt[3]{x^{8} }=\sqrt[3]{x^{6}*x^{2}}=\sqrt[3]{x^{6} }*\sqrt[3]{x^{2} }=x^{2}*\sqrt[3]{x^{2} }\\\\\sqrt[3]{y^{10} }=\sqrt[3]{y^{9}*y }=\sqrt[3]{y^{9} }*\sqrt[3]{y}=y^{3}*\sqrt[3]{y}[/tex]

The final step is to combine these terms;

[tex]2\sqrt[3]{4}*x^{2}*\sqrt[3]{x^{2} }*y^{3}*\sqrt[3]{y}\\\\2x^{2}y^{3}\sqrt[3]{4x^{2}y }[/tex]

The expression (2−2n)−(5n−27) is not positive for any natural values of n, because when simplified, the inequality n < −(25/7) suggests n would need to be a negative value, which is not possible for natural numbers.

To determine for which natural values of n the expression (2−2n)−(5n−27) is positive, we must solve for the values of n that make the expression greater than zero. Simplifying, we get:

2 − 2n − 5n − 27 > 0

−7n − 25 > 0

Since we have a negative coefficient for n, as n increases, the value of the left side of the inequality decreases. To find the values of n that satisfy the inequality, we isolate n:

−7n > 25

n < −(25/7)

Considering n must be a natural number (positive integer), there are no natural values of n that satisfy the inequality, as natural numbers are always non-negative, and our inequality requires n to be less than a negative number.

Answer:

d = 25 inches

Step-by-step explanation:

If the figures are similar, the dimensions have to be in proportion

diameter     diameter

------------- = ------------

height          height

10 ft            d inches

------------- = ------------

4 ft             10 inches

Using cross products

10 * 10 = 4 *d

100 = 4 d

Divide by 4

100/4 =4d/4

25 = d

d = 25 inches

Check the picture below.

bearing in mind that the large cylinder is using feet units, and thee are 12 inches to 1 foot, thus 10 feet  = 120 inches.

ANSWER

Option B is correct

EXPLANATION

On the interval,

[tex]x \: < \: 2[/tex]

The function is a straight line graph with x-intercept

[tex]x = 1[/tex]

and y-intercept

[tex]y = - 2[/tex]

The equation of this line is

y=2x-2

On the interval, 2≤x≤5,

The equation is the constant function, y=4

On the interval x>5,

The equation is y=x+1

The correct choice is B.

Answer:

Step-by-step explanation:

The clock on the left shows that there are 6 minutes needed to reach 4:00

The clock on the right shows that it is (5*7 + 1) =  36 minutes past 4:00

The time passed is 6 + 36 = 42 minutes.