The average age of 15 students is 16 years. If teacher’s age is included the average increases
by 1. Find teacher’s age

Answer:

the answer is 9.75 :)

Step-by-step explanation:

Using the given information, the length of arc EF in circle C is 9.75

From the question, we are to calculate the length of arc EF

First, we will determine the measure of angle BAD

Let angle BAD = θ

From the question,

Length of arc BD = 6.5

Radius of circle A = 4

Using the formua,

[tex]Length \ of \ an \ arc = \frac{\theta}{360 ^\circ}\times 2\pi r[/tex]

Then,

[tex]6.5 = \frac{\theta}{360 ^\circ} \times 2\pi \times 4[/tex]

[tex]\theta = \frac{360 \times 6.5}{2\pi \times 4}[/tex]

[tex]\theta = \frac{2340}{8\pi }[/tex]

[tex]\theta = \frac{292.5}{\pi }^\circ[/tex]

Now, for the measure of arc EF in circle C

Since angle ECF and angle BAD are congruent, then

Angle ECF = [tex]\frac{292.5}{\pi }^\circ[/tex]

Thus,

Length of arc EF = [tex]\frac{\frac{292.5}{\pi}^\circ }{360 ^\circ} \times 2 \pi \times 6\\[/tex]

Length of arc EF = [tex]\frac{292.5^\circ }{\pi \times 360 ^\circ} \times 12 \pi[/tex]

Length of arc EF = [tex]\frac{292.5 \times 12}{360}[/tex]

Length of arc EF = 9.75

Hence, using the given information, the length of arc EF in circle C is 9.75

Learn more on Calculating the length of an arc here: https://brainly.com/question/12152333

#SPJ 2

Answer:

x = 66°

Step-by-step explanation:

Hello,

This question involves use of rules or theorems of angles in a right angled triangle

<DAB + <BAC = 180°

Sum of angles on a straight line = 180°

98° + <BAC = 180°

<BAC = 180° - 98°

<BAC = 82°

Now, we can use <BAC to find x because some of angles in a triangle is equal to 180°

32° + 82° + x = 180°

Sum of angles in a triangle = 180°

114° + x = 180°

x = 180° - 114°

x = 66°

Angle x = 66°

Answer:

18 ft = 6 yds

3 ft = 36 inches

Step-by-step explanation:

We know that 3 ft = 1 yd

Divide 18 ft by 3

18 ft /3 ft = 6 yds

We know that 1 ft = 12 inches

3 ft * 12 inches /ft = 36 inches

Answer:

[tex]\large \boxed{18 feet = 6 yards}[/tex]

[tex]\large \boxed{3 feet = 36 inches}[/tex]

Step-by-step explanation:

1 foot = 1/3 of a yard

Multiply both sides of this equation by 18

[tex]\large \boxed{18 feet = 6 yards}[/tex]

1 foot = 12 inches

Multiply both sides of the equation by 3

[tex]\large \boxed{3 feet = 36 inches}[/tex]

Hope this helps!

Answer:

  0.20, 0.36 seconds

Step-by-step explanation:

We have already seen that the equation for y(t) can be written as ...

  y(t) = √29·sin(4πt +arctan(5/2))

The sine function will have a value of -1/2 for the angles 7π/6 and 11π/6. Then the weight will be halfway from its equilibrium position to the maximum negative position when ...

  4πt +arctan(5/2) = 7π/6 or 11π/6

  t = (7π/6 -arctan(5/2))/(4π) ≈ 0.196946 . . . seconds

and

  t = (11π/6 -arctan(5/2))/(4π) ≈ 0.363613 . . . seconds

The weight will be halfway from equilibrium to the maximum negative position at approximately 0.20 seconds and 0.36 seconds and every half-second thereafter.

Answer:

20

Step-by-step explanation:

Given that:

The study group n = 4

number of participants = 10

the sum of squares for the between-groups source of variation is  60

The objective is to determine the mean square  between groups in this study

The mean square  between groups in this study compares the means of the group with the  sum of squares for the between-groups source (i.e the grand mean)

For this analysis;

the degree of freedom = n-1

the degree of freedom = 4 - 1

the degree of freedom =  3

Thus; the mean square between groups = [tex]\dfrac{60}{3}[/tex]

the mean square between groups = 20

Answer:

Step-by-step explanation:

When we talk about the transformation of functions, we can mention stretching, rotating, dilating, shifting. However, when we want to transform linear functions, there are only two transformations that are worthy in that case, those are vertical stretch or compression and vertical shift.

Now, you may ask, why only vertical transformation? the reason behind that is because horizontal transformation would give the exact same result because it's only a straight line which we are transforming.

Another common question would be, why only two transformations? it's because with these two you can get all the results because it's a straight line.

The image attached shows examples of this.

Answer:

Option (C)

Step-by-step explanation:

If AD is the altitude to BC, both the segments AD and BC will be perpendicular to each other.

By the property of perpendicular lines,

[tex]m_1\times m_2=-1[/tex]

where [tex]m_1[/tex] is the slope of the line AD and [tex]m_2[/tex] is the slope of BC.

[tex]m_2=\frac{y_2-y_1}{x_2-x_1}[/tex]

     [tex]=\frac{8+2}{3-7}[/tex]

     [tex]=-\frac{5}{2}[/tex]

Now from the given property,

[tex]m_1\times (-\frac{2}{5})=-1[/tex]

[tex]m_1=\frac{5}{2}[/tex]

Therefore, slope of altitude BC = [tex]\frac{5}{2}[/tex]

Option (C) will be the answer.

Answer: 135

Step-by-step explanation:

took it on edg2020

Answer:

135

Step-by-step explanation:

Just took the test and got it right

Answer:

-60

Step-by-step explanation:

-3 · 2 = -6 and 10⁴ · 10⁻³ = 10⁽⁴⁺⁽⁻³⁾⁾ = 10¹ = 10 so the answer is -6 · 10 = -60.

Answer: Mullins family eat [tex]\dfrac{9}{20}[/tex] of the pizza the Hernandez family ate.

Step-by-step explanation:

Area of circle = [tex]\pi r^2[/tex] , where r is the radius

Given, Diameter of Hernandez family's pizza = 20 inches

Radius = [tex]\dfrac{20}{2}[/tex] = 10 inches

Area of Hernandez family's pizza  = [tex]\pi (10)^2=100\pi \text{ in.}^2[/tex]

Since, they divide pizza into 15 pieces , area of each slice = [tex]\dfrac{100\pi}{15}=\dfrac{20}{3}\pi\text{ in.}^2[/tex]

They left with 3 slices i.e. they ate 12 slices, area of all 12 slices = 12 x (area of each slice)

= [tex]12\times\dfrac{20}{3}\pi\text{ in.}^2= 80\pi\text{ in.}^2[/tex]

Diameter of Mullins family's pizza = 12 inches

Radius = [tex]\dfrac{12}{2}[/tex] = 6 inches

Area of Mullins family's pizza  = [tex]\pi (12)^2=144\pi \text{ in.}^2[/tex]

Since, they divide pizza into 8 pieces , area of each slice = [tex]\dfrac{144\pi}{8}=18\pi\text{ in.}^2[/tex]

They left with 6 slices i.e. they ate 2 slices, area of all 2 slices = 2 x (area of each slice)

= [tex]2\times18\pi\text{ in.}^2=36\pi\text{ in.}^2[/tex]

Since, [tex]\dfrac{36\pi}{80\pi}=\dfrac{9}{20}[/tex]

Hence, Mullins family eat [tex]\dfrac{9}{20}[/tex] of the pizza the Hernandez family ate.

Answer:

8.86 ( 3 S.F)

Step-by-step explanation:

Using Sine Rule,

AB/ Sin (41) = 13.5/ Sin (90)

AB = 8.856796891

= 8.86 cm (3 s.f.)

Answer:

YES, the number of people who visited the park can be represented as a function of the daily average temperature.

Step-by-step explanation:

From the table of values given which defines the number of visitors to the park as a function of daily temperature, the temperature is the domain values (independent variable), while the number of visitors is the range values (dependent variable).

For any relation to be considered a function, as a principle, any given domain value must have exactly one range value. In other words, there must not be two different range values assign to one domain value.

This means, for the relation between temperature and number of visitors to be considered a function, it must not have a domain value that is mapped to more than one range value.

Examining the table given, if we map each domain value to the range value, we will find out that there are only 1 exact range value for a domain value.

Therefore, we can say: YES, the number of people who visited the park can be represented as a function of the daily average temperature.

Answer:

yes

Step-by-step explanation:

Answer:

I hope it will surely help uh.....

Answer:

sqrt of 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the information given,

Mark: 6,7,8,9,10

frequency:5,4,7,10,4

a) Range = highest mark - lowest mark

Range = 10 - 6 = 4

b) The number of students in the group is the sum of the frequency. Therefore,

Number of students = 5 + 4 + 7 + 10 + 4 = 30 students

c) Mean mark = (mark × frequency)/total frequency

[(6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + 10 × 4)]/ 30

Mean mark = (30 + 28 + 56 + 90 + 40)/30 = 244/30

Mean mark = 8.1

Answer: From the information given, Mark: 6,7,8,9,10 frequency:5,4,7,10,4 a) Range = highest mark - lowest markRange = 10 - 6 = 4b) The number of students in the group is the sum of the frequency. Therefore, Number of students = 5 + 4 + 7 + 10 + 4 = 30 studentsc) Mean mark = (mark × frequency)/total frequency[(6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + 10 × 4)]/ 30Mean mark = (30 + 28 + 56 + 90 + 40)/30 = 244/30Mean mark = 8.1

Step-by-step explanation:

Answer:

y=-5x+16

Explanation:

We already know the slope, and in y=mx+b, m is the slope. So now we have y=-5x+b.

Next, since we do not know the y-intercept, we can substitute the y and x values we are given in the current equation we have, y=-5+b. Now we have 6=-5(2)+b.

Now we can solve for b.

6=-10+b

16=b. We know that b=16.

Therefore, the equation is y=-5x+16

Answer:

4x+4y=1, 6x-y=1

x+y=4, x-y=2

x-y=9, x+y=6

Step-by-step explanation:

Answer:

x equals 27/5

Step-by-step explanation:

just substitute y into the first equation

Answer:

3

Step-by-step explanation:

Answer:

c is the correct answer

Step-by-step explanation:

Answer: Choice A

Yes; Domain = {m, n, p, q}

We have the inputs (think of them as the x values) as m, n, p and q. They make up the domain. The domain is the set of all allowed inputs. We do not have any repeated inputs, which is why we have a function. Any given input leads to exactly one output.

Answer:

(-7/9, -4/9)

Step-by-step explanation:

i used this formula \left(\frac{m\cdot x_{2}+n\cdot x_{1}}{m+n},\frac{m\cdot y_{2}+n\cdot y_{1}}{m+n}\right) in the desmos calculator and this is the answer i got GL

Hope do will on what you are doing :)

If you want you can give me brainliest, it helps me a lot

have a good day :)

Answer:

I got (1,-4) on my Khan

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello,

let's note a and b the two digits, the number is then a*10+b

and the digits in revers mode give b*10 + a so we can write

   (1) a + b = 5

   (2) 10a+ b - 9 =10b + a

From(1) I get b = 5-a

I replace in (2)

10a + 5 - a - 9 = 10(5-a) + a = 50 - 10a = a = 50 - 9a

9a - 4 = 50 - 9a

18a = 50 + 4 = 54 so

a = 54/18 = 3

and then from (1) b = 5 - 3 = 2

So the number is 32

Answer:

A =19.5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin A= opp/ hyp

sin A = 3/9

Take the inverse sin of each side

sin ^-1 sin A = sin ^-1 (3/9)

A =19.47122063

To the nearest  tenth of a degree

A =19.5

Answer:

19

Step-by-step explanation:

inverse sin (1/3) = 19.47122060852

Answer:

The correct answer is:

Poisson (A.)

Step-by-step explanation:

A Poisson distribution is used to model the number of events occurring within a given time interval, when the average number of times that the event occurs within the time interval is given.

Lambda ( λ ) is a rate parameter in Poisson's distribution, and it is used to represent "event/time", and it simply represents the expected number of events in the interval.

Answer:

69 years

Step-by-step explanation:

Data provided in the question

Born date of an Ancient Greek = April 1st 35 BC

Diet date of an Ancient Greek = Aril 1st 35 AD

Based on the above information

We can say that

35 + 35 = 70

We deduct 1 as there is no zero

So, it would be

= 70 - 1 year

= 69 years

Hence, An ancient greek lives 69 years and the same is to be considered

Answer:

0.5645

Step-by-step explanation:

De la pregunta anterior, se nos dan los siguientes valores para el equipo de Ludlow

Probabilidad de jugar de noche = 70% = 0.7

Probabilidad de ganar en la noche = 50% = 0.5

Probabilidad de jugar durante el día = 30% = 0.3

Probabilidad de ganar durante el día = 90% = 0.9

Probabilidad de que cuando ganaron ayer, el juego se jugó por la noche =

(Probabilidad de jugar de noche × Probabilidad de ganar de noche) ÷ [(Probabilidad de jugar de noche × Probabilidad de ganar de noche) + (Probabilidad de jugar de día × Probabilidad de ganar de día)]

Probabilidad de que cuando ganaron ayer, el juego se jugó de noche = (0.5 × 0.7) ÷ (0.5 × 0.7) + (0.9 × 0.3)

= 0.35 ÷ 0.35 + 0.27

= 0.35 ÷ 0.62

= 0.5645

La probabilidad de que el partido se haya jugado de noche = 0.5645

Answer:

trig function is tangent

tan(63)=x/19

multiply each side by 19:

tan(63)19=x

x=37.3

Answer:

156.25

Step-by-step explanation:

[tex]\frac{1}{0.0064}\\\\\frac{10000}{64}\\ then divide \[/tex]

[tex]\frac{10000}{64} = \frac{2500}{16} =\frac{625}{4} = 156.25[/tex]

Answer:

A. [tex]\frac{3}{5}[/tex]

B. [tex]\frac{7}{10}[/tex]

C. B (you already got that right)

Step-by-step explanation:

To find the probability of something, we have to see how many times it happened over the total amount of attempts.

On Tuesday the target was hit 18 times in 30 attempts. So our probability fraction is [tex]\frac{18}{30}[/tex] which simplifies to [tex]\frac{3}{5}[/tex].

Looking at the total results, we can see Ben hit the target 84 times out of 120, so the fraction is [tex]\frac{84}{120}[/tex] which simplifies to [tex]\frac{7}{10}[/tex].

There’s always one rule of statistics/probability - the more data the better. If we want to create a more reliable probability, we’d want more data, and the total data gives us more than just Tuesday’s Data.

Hope this helped!

Answer:  78 units²

Step-by-step explanation:

Use Pythagorean Theorem to find the base of the triangle:

x² + 12² = 15²

x² + 144 = 225

          x² = 81

          x = 9

Now, separate the figure into two shapes --> triangle and rectangle.

[tex]A_{\triangle}=\dfrac{base\times height}{2}=\dfrac{9\times 12}{2}=54\\\\A_{\square}=length \times width = 12 \times 2 =24\\\\A_{trapezoid}=A_{\triangle}+A_{\square}=54+24=\large\boxed{78}[/tex]

You can also use the trapezoid rule:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h\\\\\\.\quad = \dfrac{(9+2)+(2)}{2}\cdot 12\\\\\\.\quad = \dfrac{13}{2}\cdot 12\\\\\\.\quad =13\cdot 6\\\\\\.\quad = \large\boxed{78}[/tex]

Answer:

The answer is 429 = 3×11×13.

Step-by-step explanation:

You have to divide by prime number :

429 ÷ 3 = 143

143 ÷ 11 = 13

13 ÷ 13 = 1

Answer:

3×11×13

Step-by-step explanation: