There were 25 teachers in a school whose mean age was 30 years. A teacher retired at the age of 60 years and a new teacher was appointed in his place. The mean age of teachers in the school was reduced by one year. Find the age of new teacher?

Answer:

[tex]x=5, \\x=-1[/tex]

Step-by-step explanation:

Given [tex](x-2)^2=9[/tex], to solve for [tex]x[/tex], our goal is to isolate [tex]x[/tex].

Take the square root of both sides:

[tex]x-2=\pm\sqrt{9},\\x-2=\pm 3[/tex](recall that [tex]3^2=(-3)^2=9[/tex]).

Therefore, we have two cases:

[tex]\begin{cases}x-2=3,x=\boxed{5} \\x-2=-3, x=\boxed{-1}\end{cases}[/tex]

Answer:

m1 = 107°

m2 = 73°

m3 = 107°

m1+m2+m3+m4 = 360°

107+73+107+73=360°

Answer:

1 hr 55 mins

Step-by-step explanation:

50 mins between 12:10 and 1:00 p.m.

Add 5 mins to change 2:05 to 2:00.

55 mins and 1 hr

Answer:

Step-by-step explanation:

First fill in the missing angles of each triangle:

angle IJK = 180-47-51 = 82°

angle KJL = 180 - 63 - 57 = 60°

Within EACH triangle, the side length is proportional to the opposite angle.

Therefore for triangle IJK,

JK < JL < IK

and for triangle JKL

JL < KL <JK

so combining (chaining) the two inequalities,

JL < LK <JK < JL < IK

Answer:

Step-by-step explanation:

first lets find angle J in triangle IJK

for angle J

47 + 51 + angle J =180 degree (sum of interior angle of a triangle )

98 + angle J =180

angle J =180 - 98

angle J =82 degree

Now lets find angle J in triangle JKL

for angle J

57 + 63 + angle J =180 degree (being sum of interior angle of the triangle)

120 + angle J =180

angle J = 180 - 120

angle J =60 degree

now lets place the angle from samllest to largest

angle I = 41 degree

angle K = 51 degree

angle K of JKL triangle = 57 degree

angle J of JKL triangle = 60 degree

angle L =63 degree

angle J of IJK triangle = 80 degree

Side opposite to the smallest angle is smallest in sides and side opposite to the longest angle is largest in side.So,

side opposite to angle I is JK

side opposite to angle K is IJ

side opposite to angle K of JKL triangle is JL.

side opposite to angle J of JKL triangle is LK.

side opposite to angle L is JK.

side opposite to angle J of IJK triangle is IK.

therefore required answer is

JK , IJ , JL , LK , JK , IK

Answer:

Chisquare goodness of fit test

Step-by-step explanation:

Given the data:

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec 25 28 24 18 17 27 9 18 22 14 12 26

The Chisquare goodness of fit test is used to test the relationship between the observed and theoretical or expected model data. Here, we make and assumption about the population using the sample distribution. For the goodness of fit test, there is only one observed variable, here it is the number of factory accident. The null hypothesis is of the claim that the number of factory accidents per month is the same for each month ;

Null hypothesis : Number of factory accident each month is the same ; while the alternative hypothesis is tests that some month gave greater number of accidents, that is ; the number of factory accidents is not the same for each month.

Answer:

133 - x = 180

x= 47

142 - y = 180

y = 38

x + y = n

47 + 38 = 85

Answer:

$1200

Step-by-step explanation:

S + C = 1200

S = C + 900

C + 900 + C = 1200

2C + 900 = 1200

2C = 300

C = 150

The chair costs $150. The sofa is $1050.

Together they cost $1200.

Answer:

75 km.

Step-by-step explanation:

Fractions of a number

To get the fraction of a number, we multiply that number by the given fraction.

For example two-thirds of 60 is 2/3 × 60 = 2 × 20 = 40 and one-fifth of 100 is 1/5 × 100 = 100/5 = 20

Now, we are supposed to find a fraction of 100 km. Assume its three-quarters.

So, three-quarters of 100 km is 3/4 × 100 km = 3 × 100 km/4 = 3 × 25 km = 75 km

So, three-quarters of 100 km is 75 km.

Answer:

Pr(B) = 0.69

Pr(J/B) = 0.35

Pr(J∩B) = 0.14

Pr(G/J') = 0.66

Pr(G) = 0.31

Step-by-step explanation:

Applying,

Pr = possible outcome (a)/Total outcome(t)

(1) Pr(B) = a/t............ Equation 1

From the diagram

Given: a = 220+65+35 = 320, t = 220+65+35+145 = 465

Substitute these values into equation 1

Pr(B) = 320/465

Pr(B) = 0.69

(2) Pr(J/B) = (35+65)/(220+65)

Pr(J/B) = 100/285

Pr(J/B) = 0.35

(3) Pr(J∩B) = 65/465

Pr(J∩B) = 0.14

(4) Pr(G/J') = 145/220

Pr(G/J') = 0.66

(5) Pr(G) = 145/465

Pr(G) = 0.31

Answer:

E. p - 7 + 7 = 22 + 7

Step-by-step explanation:

p - 7 + 7 = 22 + 7 ( -7 + 7 = 0)

p = 22 + 7

p - 7 = 22//

Answer:

Step-by-step explanation:

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

 =-21

Answer:

7**6

Step-by-step explanation:

The expression 7^6 ; can be interpreted as 7 raised to the power of 6 ; which is (7 * 7 * 7 * 7 * 7 * 7). To execute this expression using a computer or basic mathematical operation on a computer we use the power symbol which the computer understand this the double multiplication symbol (**)

Hence, 7^6 = (7**6)

Answer:

28.26 cm

Step-by-step explanation:

circumference of a circle = πd

=3.14 * 9 cm

=28.26 cm

Given:

Angle IHG formed by two rays.

To find:

The rays that form the sides of ∠IHG.

Solution:

From the given diagram it is clear that the initial point of both rays is point H.

First ray passes through the point I with initial point H, so the name of first ray is [tex]\overrightarrow{HI}[/tex].

Second ray passes through the point G with initial point H, so the name of second ray is [tex]\overrightarrow{HG}[/tex].

The rays [tex]\overrightarrow{HI}[/tex] and [tex]\overrightarrow{HG}[/tex] form the sides of ∠IHG.

Therefore, the correct options are E and F.

Step-by-step explanation:

diameter (d) = 7cm

radius (r)= d/2 .... formula

= 7/2 .....put the value

= 3.5cm

the measure of radius is 3.5cm.

Answer:

$41.75

Step-by-step explanation:

$251-84=167

167 divided by 4 is $41.75

Hope this helps! :)

Answer:

B

Step-by-step explanation:

the larger triangle is 4 times bigger.....so the measurements for the sides are multiplied by 4.

the shape however is the same ....so the internal angle will still be 83 degrees

Answer:

[tex]127.3 - 1.578 \approx 125.7[/tex]

Step-by-step explanation:

Given

[tex]127.3 - 1.578 = 125.722[/tex]

Required

Round to the precision of the 1.578

The number in the subtraction column is 1.578; so, the question implies that we round up 125.722 to the precision of 1.578

The precision of 1.578 is 4 (i.e. it has 4 digits). Hence, 125.722 will be approximated to 4 significant digits.

So, we have:

[tex]125.722 \approx = 125.7[/tex]

or

[tex]127.3 - 1.578 \approx 125.7[/tex]

Answer:

The total amount is 384

Step-by-step explanation:

Let m = the amount of money

5/8 of the money is 240

5/8 * m = 240

Multiply each side by 8/5

8/5 * 5/8 * m = 8/5 * 240

m =384

The total amount is 384

Answer:

85%

Step-by-step explanation:

To get the percentage of the number of questions Jamie answered, divide 68 by 80 to get 0.85, which is 85% in decimal form.

Answer:

14+x

Step-by-step explanation:

Answer:

Jayden earns $ 9.25 per hour.

Step-by-step explanation:

Time                 Earnings

  8                      74

  1                       x

[tex]\frac{8}{1} = \frac{74}{x}\\\\8 \times x = 74 \times 1\\\\x = \frac{74}{8} = \$ 9.25[/tex]

Answer:

9.25

Step-by-step explanation:

He earned 9.25 money per hour because you divide 74/8 and it will give you 9.25. If you wanna double-check you can multiply 9.25 times 8 and you'll get 74.

Answer: raw data

Step-by-step explanation:

Raw data, is also referred to as the primary data, and it refers to the data that's collected from a source. It is a day that is yet to be processed. e.g the raw scores during examination can be considered to be raw data since it hasn't been processed yet to get further information.

Therefore, if the numbers collected from a survey are measurements, then the measurements before any calculation is performed is called raw data.

question isn't loading

Step-by-step explanation:

Answer:

i think it is b but don't take my word

Step-by-step explanation:

Answer:

49500

Step-by-step explanation:

According to the Question,

We have, District geons = 20 , District Size = 5

Now, We choose 2 geons From 100 Geons and arrange them in 10 district relations.

= [tex]\left[\begin{array}{ccc}100\\2\end{array}\right] * 10[/tex]

= (100 × 99)/2 × 10

= 49.5×100×10   ⇒ 49500

Answer:

18

Step-by-step explanation

Answer:

there 24 possible outcomes.

each color/letter on the spinner could coincide with each side of the dice, so there 4*6 possible outcomes

{A, 1},{A,2},{A,3},{A,4},{A,5},{A,6},{B,1},{B,2}, ...

Sample Space=S={A,B,C,D}

Hence

|S|=4

Sample Space=S={1,2,3,4,5,6}

Hence

|S|=6