What is the greatest common factor of 3 and 13?

The length of the unknown side of the right triangle is 13

A right triangle (American English), sometimes known as a right-angled triangle (British), is a triangle with one angle that is a right angle (i.e., a 90-degree angle), or two sides that are perpendicular. The link between is the basis of trigonometry.

between the right triangle's angles and sides.

The side across from the right angle is the hypotenuse (side c in the figure). Legs are the sides closest to the ideal angle (or catheti, singular: cathetus). The side a that is next to angle B and across from angle A is referred to as side b, and the side a that is next to angle A and across from angle B is referred to as side a.

Right triangles are referred to as Pythagorean triangles and their side lengths as Pythagorean if all three of their sides are integer lengths.

[tex]\sqrt{(12)^2+(5)^2}=13[/tex]

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Answer:

Step-by-step explanation:

if * means multiplication

the equivalent expression will be :

[tex]\frac{2.14}{2.2} = \frac{7}{7} = 7[/tex]

If the * means power :

then equivalent expression will be

[tex]\frac{2^{14} }{2^{2} } = 2^{(14-2)} =2^{12}[/tex]

The equation which represents the net profit of the charity organization is y = 45x-810.

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The square root of 255 is approximately 15.969.

Given,

Root 255, [tex]\sqrt{255}[/tex]

We have to find the square root of the number:

Square root of a number:

A number multiplied by itself is the square root of that number. Or we may say that after adding a number to itself, we must calculate its square root in order to go back to the original number. The square root of p, if it is a positive integer, is represented by p, so that p = q.

Now,

√255 = 15.9687194227

Which is approximately equals to 15.969

That is,

The square root of 255 is approximately 15.969

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Her commission for the week was $234.

It is given the total earning in past week = $3,925  and jean earns 4% for the first $2000

So, the commission = $2000 x 4/100  = $80

To find additional sales, the formula to refer is

Add –on sales = total sales – base sales

                          = 3,925 – 2000

                          = 1,925

For the $1,925 sales, Jeans earns 8% commission, Her commission

                                                     = 1,925*0.08    = $154

So, the total commission = $80 + $154  = $234

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answer:
Green t-shirt=profit of $1

White t-shirt=profit of $3

Black t-shirt=profit of $1.

To find the answer, selling price minus total money spent (shirt, printing) If the number is negative, it’s loss, and if it’s positive, it’s profit

Answer:

[tex]6.45*10^{-9}[/tex]

Step-by-step explanation:

Answer:

The number will be x

Step-by-step explanation:

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

2x + 8 = 3x - 6

14 = x

Using sampling concepts, the population being studied is all visitors that are flying to the state of Hawaii.

The problem is incomplete, but researching it on a search engine, it asks for us to identify who is the population of this study.

In this problem, a set of visitors traveling to Hawaii were sampled, hence the population being studied is all visitors that are flying to the state of Hawaii.

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Answer:

x = 1/2 or 0.5

Step-by-step explanation:

4 • ((2x • (2x - 1)) -  (2x - 1))  = 0

The rule says: To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (2x-1)  and the exponents are :

         1, as  (2x-1), is the same number as  (2x-1)1

and   1, as  (2x-1)  is the same number as  (2x-1)1

The product is therefore,  (2x-1)(1+1) = (2x-1)2

 4 • (2x - 1)2  = 0

4.2      Solve  :    (2x-1)2 = 0

 (2x-1) 2 represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means:   2x-1  = 0

Add  1  to both sides of the equation :

                     2x = 1

Divide both sides of the equation by 2:

                    x = 1/2 = 0.500

Answer:

x = 1/2.

Step-by-step explanation:

4 (2x (2x - 1) - 1 (2x - 1)) = 0

(2x (2x - 1) - 1 (2x - 1)) = 0

(2x - 1) is common to both parts.

(2x - 1)(2x - 1) = 0

2x - 1 = 0

x = 1/2.

Answer:

150 degrees

Step-by-step explanation:

Vertical angles

The solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3

The statement is given as:

5x+3 is greater than or equal to x-9

Express as an inequality

5x + 3 >= x - 9

Collect the like terms

5x - x >= -9 - 3

Evaluate the like terms

4x > = -12

Divide both sides by 4

x >= -3

Hence, the solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3

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Answer:

-7 i + 43

Step-by-step explanation:

Simplify the following:

(-4 i + 3) (6 i + 7) - (-3 i + 2)

(3 - 4 i) (7 + 6 i) = 3×7 + 3×6 i - 4 i×7 - 4 i×6 i = 21 + 18 i - 28 i + 24 = 45 - 10 i:

(-10 i + 45) - (-3 i + 2)

-(-3 i + 2) = 3 i - 2:

45 - 10 i + (3 i - 2)

45 - 10 i - 2 + 3 i = (45 - 2) + (-10 i + 3 i) = 43 - 7 i:

Answer:  -7 i + 43

If we shift the origin without changing the direction and point P(x, y) is changed to P(X, Y) then the new coordinates will be x = X + h and y = Y + k.

Shifting of origin is the phenomenon of changing the coordinates of the origin which is generally (0, 0) to another point which has coordinated (h, k). This phenomenon is usually carried out graphically. This is done when there is difficulty to solve the problems in coordinate geometry when we take the origin at (0, 0).

If we shift the origin which is at P(x, y) to another point (h, k) then the coordinates of new point P(X, Y) will be

x = X + h and y = Y + k

If h is positive, then coordinates will be x = X + h and if h is negative then coordinates will be x = X - h. If k is positive, then coordinates will be y = Y + k and if k is negative then coordinates will be y = Y - k.

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a)

[tex]z=4.658\\p_v=P(z > 4.65)=1-P(z < 4.65)=1.581x*10^{-6}[/tex]

b) By assuming a significance level of α = 0.05 and observing that [tex]p_v[/tex] > α, we can reject the null hypothesis at this level of significance. And in this instance, it makes sense that more than 50% of Americans believe that the Civil War still has an impact on American politics and political life.

c) The confidence interval at 90% would be shown (0.527;0.593).

About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.

a)

1) The presented data and the notation "n=1507" refer to the random sample of Americans, "X" denoting the proportion of those Americans in the sample who believe that the Civil War is still significant to American politics and political life, and "p cap" denoting the estimated number of those Americans.

Since the problem specifies that majority  α=0.05 represents the significance threshold, [tex]p_0[/tex] is the number that we wish to test (no given, but is assumed)

Z would stand for the statistic (interesting variable), and [tex]p_v[/tex] for the p value (variable of interest)

P is the percentage of the public that believes that the Civil War still has an impact on American politics and political life.

2) Useful concepts and formulas

The allegation that more Americans than 50% believe the Civil War is still significant to American politics and political life needs to be tested through a hypothesis (Majority). :

Alternative Hypothesis: p[tex]\geq[/tex] 0.5

Null Hypothesis: p[tex]\leq[/tex] 0.5

The proportion is thought to have a normal distribution.

This test for the percentage of union membership has one tail higher.

Verify whether the sample conforms to the presumptions required for the test to be applied.

a) The random sample must be representative; in this situation, there is no mention of this issue, but it is safe to presume that it exists.

b) The sample size must be sufficient.

[tex]np_0=1507*0.5=753.5 > 10\\n(1-p_0)=1507*(1-0.5)=753.5 > 10[/tex]

3. Determine the statistic.

The formula used to calculate the statistic is as follows:

[tex]z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }= \frac{0.56-0.5}{\sqrt{\frac{0.5(1-0.5)}{1507} } }=4.658[/tex]

P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]

According to the alternative hypothesis, the following would be the p value:

P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]

Using this formula, the confidence interval would be determined.

p ± [tex]z_{\frac{\alpha }{2}}\sqrt{\frac{p(1-p)}{n} }[/tex]

With the value of [tex]\alpha[/tex] and [tex]\alpha _2[/tex], we can get the quantile necessary for the interval in the normal standard distribution for the 90% confidence interval.

[tex]z_{\frac{\alpha }{2} }=2.58[/tex]

adding the following to the formula for the confidence interval:

[tex]0.56-2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.527\\0.56+2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.593[/tex]

Also provided would be the 90% confidence interval (0.527;0.593).

About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.

And because the interval does not contain the value of 0.5, we can conclude that, at a 90% level of confidence, the percentage of Americans who believe that the Civil War is still relevant to American politics and political life is higher than 0.5. This result is consistent with the result of part b.

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The largest positive integer d for which d +10 is a divisor of d³ + 2011 is equal to 1001.

As given,

Divisor= d +10

Dividend= d³ + 2011

(d³ + 2011 ) ÷ ( d+ 10) = [(d² -10d +100) (d +10) +1011] ÷ ( d+ 10)

                                 =(d² -10d +100) + [ 1011 / (d+10)]

Largest positive integer d for which d +10 is a divisor of  d³ + 2011

d + 10 =1011

⇒d=1001

Therefore, the largest positive integer d for which d +10 is a divisor of d³ + 2011 is equal to 1001.

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The length of the hypotenuse AB is approximately 6.53 units.

In a right angled triangle the side opposite the right angle or the largest side is called the hypotenuse of the triangle.

The length of the hypotenuse is calculated using trigonometric ratios. If in a right-angled triangle, the base angle is θ then:

In the given figure we see in ΔABC

AB is the hypotenuse. ∠BAC = 40 ° AC is the base and BC is the perpendicular.

(The side that contains the given angle is the base and the side opposite the given angle is taken as perpendicular)

Now cos ∠BAC = BC ÷ AB

or, cos 40° = 5 ÷ AB

or, AB = 6.527...

or, AB ≈ 6.53

Hence the value of AB is approximately 6.53 units.

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Using the law of sines, it is found that the distance from the farthest soccer player to the goalie is 14.723 yards.

Given,

The distance between the two players = 10yards

The angle from each player to the goalie is 64° and 75°, respectively

We have to find,

the distance from the farthest soccer player to the goalie.

In this problem, considering that the sum of the internal angles of a triangle is of 180º, the angle that the goalie makes with the players is given by:

∠A = 180-(∠B+∠C)

∠A = 41°

Using Sine rule

AC/Sin B = BC / Sin A

AC = 10yrd*Sin75°/Sin41°

AC = 14.723 yards

The farthest distance is of 14.723 yards.

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Answer:

put 244 add 7e8ue

Step-by-step explanation:

i53838 divede 73838

Answer: A.  D.

Step-by-step explanation:

A.

x-b-3<0

x-b-3+3<0+3

x-b<3   (yes)

B.

0>b-x+3

0+x>b-x+3+x

x>b+3

x-b>b+3-b

x-b>3   (no)

C.

x<3-b

x+b<3-b+b

x+b<3   (no)

D.

-3<b-x

-3+3<b-x+3

0<b-x+3

0+x<b-x+3+x

x<b+3

x-b<b+3-b

x-b<3    (yes)

Answer:

A and D

Step-by-step explanation:

Option A

[tex]\begin{aligned}& \textsf{Given inequality}: & x-b-3 & < 0\\& \textsf{Add 3 to both side}: \quad & x-b-3+3 & < 0+3\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]

Option B

[tex]\begin{aligned}& \textsf{Given inequality}: & 0 & > b-x+3\\& \textsf{Add $x$ to both sides}: & 0+x & > b-x+3+x\\& \textsf{Simplify}: & x & > b+3\\& \textsf{Subtract $b$ from both sides}: \quad& x-b & > b+3-b\\& \textsf{Simplify}: & x-b & > 3\end{aligned}[/tex]

Option C

[tex]\begin{aligned}& \textsf{Given inequality}: & x & < 3-b\\& \textsf{Add b to both sides}: \quad & x+b & < 3-b+b\\& \textsf{Simplify}: & x+b & < 3\end{aligned}[/tex]

Option D

[tex]\begin{aligned}& \textsf{Given inequality}: & -3 & < b - x\\& \textsf{Divide both sides by -1}: \quad & \dfrac{-3}{-1} & > \dfrac{b}{-1}-\dfrac{x}{-1}\\& \textsf{Simplify}: & 3 & > -b+x\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]

Note: When multiplying or dividing by a negative number in an inequality, remember to flip the inequality sign.

Answer: 7

Step-by-step explanation:

(fg)(-1/3)=

f(g(-1/3))=

f(3(-1/3) + 1)=

f(-1 + 1)=

f(0)=

0²- 7=7

Expressions in component form for the position vectors having the  polar coordinates are:

a) -12 cos(40)i + 12sin(40) j = -9.19i + 7.71j

b) 3cos(40) i + 3 sin(40) j = 2.29i + 1.92j

c) -24cos(48)i - 24sin(48) j = -16.059i - 17.83j

Use one or more of the following equations: cos=xr, sin=yr, tan=yx, and r=x2+y2 to convert rectangular coordinates to polar coordinates.

The polar coordinate system is indeed a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to determine each point's location on a plane. The polar axis is the ray emanating from the pole inside the reference direction. The pole is the point of reference.

Let the +x and +y represent, respectively, the unit vectors represented by I and j.

(a) 12.6 m, 130° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= m.

    -12 cos(40)i + 12sin(40) j

     = -9.19i + 7.71j

(b) 3.60 cm, 70.0° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= cm.

     3cos(40) i + 3 sin(40) j

      = 2.29i + 1.92j

(c) 24.0 in., 206° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= in.

    -24cos(48)i - 24sin(48) j

    = -16.059i - 17.83j

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I understand that the question you are looking for is:

Obtain expressions in component form for the position vectors having the following polar coordinates.

(a) 12.6 m, 130° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= m

(b) 3.60 cm, 70.0° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= cm

(c) 24.0 in., 206° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= in.

Answer:as a fraction it would be 11 3/5

Step-by-step explanation:

A circle with a circumference of 615.44 units has a radius of 98 units.

A circle is a round closed figure where all its boundary points are equidistant from a fixed point called the center.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant [tex]\pi[/tex] and the diameter of the circle.

C = [tex]\pi[/tex]D

The diameter (D) is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center. On the other hand, the radius (r) of a circle is the distance from the center of a circle to any point on the circumference of the circle. Radius is half of the diameter.

If r = 1/2 D, then

D = 2r

Evaluating the value of Din the formula of the circumference,

C = [tex]\pi[/tex](2r)

C = 2[tex]\pi[/tex]r

Using the value of [tex]\pi[/tex] as 3.14 and the circumference as 615.44 units,

evaluate the equation.

C = 2[tex]\pi[/tex]r

615.44 = 2(3.14)r

r = 615.44/ (2*3.14)

r = 98 units

Therefore, the radius of the circle is 98 units.

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Answer:

-6.34

Step-by-step explanation:

If you used a number line, it'll help! Start at 2.56, and go back (to the left) 8.9, and you will arrive at -6.34

Answer:

Can you only pick one answer?

Answers:

==========================================================

Explanation:

After 1 stage, the depth is -340+60*1 = -280 meters. In other words, it's 280 meters below the surface.

After 2 stages, the depth is now -340+60*2 = -220 meters

After 4 stages, the depth is -340+60*4 = -100 meters

After n stages, the depth is -340+60n. Set this equal to zero and solve for n.

-340+60n = 0

60n = 340

n = 340/60

n = 5.667 approximately

This rounds to n = 6

After n = 5 stages, the depth is -340+60n = -340+60*5 = -40 meters

After n = 6 stages, the depth is -340+60n = -340+60*6 = 20 meters, so the submarine is now at the surface. Of course the sub cannot fly to a height of 20 meters above the ocean's surface, so the highest it can go is 0 meters at the surface itself. This means the 6th stage is a movement of 40 meters (instead of 60 meters).

It might help to draw out a vertical number line to visually keep track of everything.

Answer: q(r(5))= 3

Step-by-step explanation: sub in 5 for x in r(x). Once you do that, you'll get -3 for r(5). Now sub in the value of r(5), -3, for x in q(x). Then you'll end up with -9 once the equation has been evaluated.