What is the measure of angle HBE?

Answer:  0.0766

Step-by-step explanation:

Let x be the random team scores.

Given: Mean = 76

Standard deviation = 8.4

We assume that x follows normal distribution.

The probability that a random team scores less than 64 points = P(x<60)

[tex]=P(\frac{x-\mu}{\sigma}<\frac{64-76}{8.4})\\\\=P(z<-1.4286) \ \ \ [Z=\frac{x-\mu}{\sigma}]\\\\= 1-P(z<1.4286)\\\\=1-0.9234\\\\=0.0766[/tex]

Hence, the probability that a random team scores less than 64 points =0.0766

If central angle is 360° then Arc length is circumference.

An angle with the circle's center as its vertex is referred to as a central angle. The radius refers to each side of the angle that extends outward from the center to a particular point on the circle.

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.

Since, when considering the circle's central angle we consider 360° which is the central angle of the whole circle.

So, when considering the arc length of a sector, we consider the arc length of the whole circle which is the circumference.

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Given:

The term is [tex]5^x[/tex].

To find:

The differentiation of [tex]5^x[/tex] with respect to x.

Solution:

Formula used:

[tex]\dfrac{d}{dx}a^x=a^x\log(a)[/tex]

Let the given function is:

[tex]f(x)=5^x[/tex]

Here, a=5.

Differentiate the given function with respect to x.

[tex]f'(x)=5^x\log(5)[/tex]

Therefore, the derivative of [tex]5^x[/tex] with respect to x is [tex]5^x\log(5)[/tex].

Answer:

A

Step-by-step explanation:

The others are exterior

9514 1404 393

Answer:

  2.  (b) 6 feet by 18 feet

  3.  -5, -1

Step-by-step explanation:

2. Perhaps the easiest way to answer this is to check to see what the areas are of the offered choices:

  a) 7·19 = 133 . . . . numbers are odd, so the answer is odd, incorrect

  b) 6·18 = 108 . . . . correct choice

  c) 12·24 = 288

  d) 5·17 = 85 . . . . again an odd number

__

If you were to solve this by factoring, you would be looking for factors of 108 that have a difference of 12.

  108 = 1·108 = 2·54 = 3·36 = 4·27 = 6·18 = 9·12

The differences are 107, 52, 33, 23, 12, 3. The dimensions you want are 6 and 18 feet.

_____

3. Completing the square is easier if the quadratic has a leading coefficient of 1. Here, all of the coefficients are divisible by 2, so we can simplify this to ...

  x^2 +6x = -5 . . . . . . divide both sides by 2

Now, we complete the square by adding the square of half the linear term coefficient.

  x^2 +6x +9 = 4 . . . . add (6/2)^2 = 9 to both sides

  (x +3)^2 = 4 . . . . .  write as a square

  x +3 = ±2 . . . . . . . take the square root

  x = -3 ±2 = -5, -1 . . . . add -3 to both sides

The solutions are -5 and -1.

Given:

A figure of right triangle with terminal angle [tex]\theta[/tex], base u, perpendicular v and hypotenuse r.

To find:

The value of [tex]\sin \theta[/tex].

Solution:

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

Substituting Perpendicular = v and hypotenuse = r in the above formula, we get

[tex]\sin \theta=\dfrac{v}{r}[/tex]

The value of [tex]\sin \theta[/tex] is [tex]\dfrac{v}{r}[/tex].

Therefore, the correct option is B.

Answer:

56л

Step-by-step explanation:

area of a pizza of 18 in=  лr²

                                         r=18/2=9

                                          area= л×9²

                                          =81л

area of a pizza of 10in=

                                      r=10/2=5

                                       area=л×5²

                                       =25л

difference=81л-25л

                =56л

Answer:

3/2

Step-by-step explanation:We know that,

Slope of the straight line passing through the points (x1,y1) and (x2,y2) is

m=y2-y1/x2-x1

Here,

Given, x1= 3,x2= 1

    and y1= 2,y2= -4

so, the slope of the straight line is,

m= -4-2/-1-3

   =3/2

Answer:

832.6lbs

Step-by-step explanation:

If s=side, then each side is 12m.

It got cut off but

12mx12m=144m^2 because mxm=m^2.

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9514 1404 393

Answer:

  B. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5

Step-by-step explanation:

Replacing x by x/5 in a function causes its graph to be stretched horizontally by a factor of 5. This is because x must be 5 times as large in order for the function argument to be the same.

Answer:

-4(5)+1(-2*-5+5*3)

Step-by-step explanation:

-20+1(10+15)

-19(25)

-475

Answer:

5

Step-by-step explanation:

Given :- a = -2 , b = 5 , c = -5 & d = 3

Solution :-

The answer is 48 notepads.

Answer:

Answer:

(2x-4()(x-2)

Step-by-step explanation:

this is how it looks when factorised

Answer:

y=-2x^2-8x

you can use a factor form helper and from that it can show you examples on how to solve it

Answer:

option D :

f(-8) = -2 ; f(4) = 3

Step-by-step explanation:

f(-8) = ³√-8 = -2

f(4) = 3 (the constant function)

Answer:

500 -100 = 400

la respuesta es 400

Answer:

Step-by-step explanation:

The key here is to find out how long it will take Justin to triple his money, and then use that number of years in Hailey's equation. If Justin starts with $940, he will triple his money when he has $2820 (940*3). We need to find out how long it takes him to do this using the equation

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]where A(t) is the tripled amount of money, P is the initial investment, r is the interest rate in decimal form, n is the number of compoundings done per year, and t is the time in years. Filling in and solving for t:

[tex]2820=940(1+\frac{.07625}{12})^{12t[/tex] which simplifies a bit to

[tex]2820=940(1+.0063541667)^{12t[/tex] and a bit more to

[tex]2820=940(1.0063541667)^{12t[/tex] Begin to solve for t by dividing both sides by 940 to get:

[tex]3=(1.0063541667)^{12t[/tex] and then take the natural log of both sides to get the t alone eventually. Taking the natural log on the right side enables us to move the 12t down in front. So doing all of that at the same time:

[tex]ln3=12tln1.0063541667[/tex] and divide both sides by ln(1.0063541667):

[tex]173.4450855=12t[/tex] then finally divide both sides by 12 to get

t = 14.5 years. Now we use that number of years to find out how much Hailey will have.

[tex]A(t)=940(1+\frac{.0825}{4})^{(4)(14.5)}[/tex] which simplifies a bit to

[tex]A(t)=940(1+.020625)^{58[/tex] and a bit more to

[tex]A(t)=940(1.020625)^{58[/tex] and

A(t) = 940(3.26768151) so in 14.5 years, Hailey will have

A(t) = $3071.62

Answer:

120 - 4.5t= 75

t = 10 minutes

Step-by-step explanation:

the equation :

120 - 4.5t= 75

the solution:

-4.5 t = 75-120

-4.5t = -45

t = -45/(-4.5) = 10 minutes

The equation to model the given situation is 120 - 4.5t= 75 and the  solution to the equation is 10 minutes.

Given that, a hot air balloon is cruising at an altitude of 120 meters above the ground when it begins its descent.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The balloon will reach an altitude of 75 meters above the ground.

Now, 120-75 =45 meters

Let t be the time to descends 45 meters

So, 120 - 4.5t= 75

⇒ -4.5 t = 75-120

⇒ -4.5t = -45

⇒ t = -45/(-4.5)

⇒ t = 10 minutes

Hence, the equation to model the given situation is 120 - 4.5t= 75 and the  solution to the equation is 10 minutes.

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Answer:

35

All angles of a triangle = 180 degrees subtract 40 from 180 and you get 140

180-40=140 because the other angles are equal with the same equation to get them divide 140 by 2 140/2=70  then you have to get h alone so you divide by the other 2 in the equation 70/2=35  h=35

Answer:

55

Step-by-step explanation:

In triangle ABC (LET'S SAY TRIANGLE IS ABC)

Angle A=40

Angle B = Angle C = x (since 2h is beside B and C both)

40+x+x=180 (Angle sum property)

40+2x=180

2x=140

x=70

2h+70=180 (Angle in a straight line=180)

2h=110

h=55

Answer:

x = 2

Step-by-step explanation:

The denominator of the rational function cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.

5x - 10 = 0 ⇒ 5x = 10 ⇒ x = 2 ← excluded value

Thus x = 2 is the vertical asymptote

I = $ 1,200,000.00

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year,

then, solving our equation

I = 1000000 × 0.03 × 40 = 1200000

I = $ 1,200,000.00

The simple interest accumulated

on a principal of $ 1,000,000.00

at a rate of 3% per year

for 40 years is $ 1,200,000.00.

Step-by-step explanation:

the answer is in the above image

Answer:

d.156.

x+24=180 ( being staright angle)

Answer:

Step-by-step explanation:

8 .) Probability of students has no pets in senior = No. of outcomes favourable / Total no.of outcome

= 15 / 24

9.) Probability of students has pets in junior = No.of outcomes favourable / Total no. of outcomes

= 37/52

Answer:

2 y x

Step-by-step explanation:

Answer:

arc AB = 45°

Step-by-step explanation:

The central angle ABC is equal to the measure of the arc that subtends it, so

AB = ∠ ABC = 45°

Answer:

option A

Step-by-step explanation:

∠WPS +∠OPW  = 180   {straight line}

∠WPS +110 = 180

∠WPS = 180 - 110

∠WPS = 70°

∠RWQ + ∠QWT +∠TWU = 180   {straight line}

∠RWQ + 60 + 50 = 180

∠RWQ + 110 = 180

∠RWQ = 180 - 110

∠RWQ= 70°

∠PWU +  ∠USP + ∠ WPS = 180  {angle sum property of triangle}

∠PWU + 40 + 70 = 180

∠PWU + 110 = 180

∠PWU = 180 - 110  

∠PWU = 70°

Answer:

A

Step-by-step explanation:

∠WPS +∠OPW  = 180 (adj angles on a str line)

       ∠WPS +110 = 180

                ∠WPS = 180 - 110

                            = 70°

∠RWQ + ∠QWT +∠TWU = 180 (adj angles on a str line)

            ∠RWQ + 60 + 50 = 180

                   ∠RWQ + 110 = 180

                             ∠RWQ = 180 - 110

                                         = 70°

∠PWU +  ∠USP + ∠ WPS = 180 (adj angles on a str line)  

            ∠PWU + 40 + 70 = 180

                     ∠PWU + 110 = 180

                              ∠PWU = 180 - 110  

                                          = 70°