The mean age of 10 women in an office is 31 years old. The mean age of 3 men in an office is 20 years old. What is the mean age (nearest year) of all the people in the office?

Answer:

slope = difference in y / difference in x

slope = 6/3 = 2 <===

Answer:

[tex]m(\widehat{EH})[/tex] = 130°

Step-by-step explanation:

Angles subtended at the center by the arcs [tex](\widehat{HG})[/tex] and [tex](\widehat{EF})[/tex] are ∠HPG and  ∠EPF.

Since these angles are the vertical angles both will be equal.

m∠HPG ≅ m∠EPF

3x - 10 = 2x + 10

3x - 2x = 10 + 10

x = 20

Therefore, [tex]m(\widehat{HG})=(3\times 20) - 10[/tex]

                               = 50°

Similarly [tex]m(\widehat{EF})[/tex] = 50°

In the same way angles subtended at the center will be equal.

m∠EPH ≅ m∠FPG

and [tex]m(\widehat{EH})=m(\widehat{FG})[/tex]

Since [tex]m(\widehat{EH})+m(\widehat{FG})+m(\widehat{EF})+m(\widehat{HG})=360[/tex]°

[tex]m(\widehat{EH})+m(\widehat{EH})+50+50=360[/tex]

[tex]2m(\widehat{EH})=360-100[/tex]

[tex]m(\widehat{EH})=130[/tex]

Therefore, measure of arc EH = 130°

Answer: The length of the hypotenuse is √(10)*a

Step-by-step explanation:

Remember the Pythagorean theorem.

If b is the larger base, and a the shorter base, and H is the hypotenuse:

a^2 + b^2 = H^2

now, we know that b = 3*a.

(3*a)^2 + a^2 = H^2

10*a^2 = H^2

√(10)*a = H

Then we have the length of the hypotenuse in terms of the shorter base, B.

Answer:

Answer:

3x + 3y = 0

7x - y = 8

Step-by-step explanation:

Answer:

y = -2x + 9

Step-by-step explanation:

(1-3)/(-2--3) = -2/1 = -2 = m

y = mx + b

1 = -2(4) + b

9 = b

y = -2x + 9

Answer:

8x + 20 ≥ 25

Step-by-step explanation:

Well 8 times the sum of a number "x" plus 20,

So we can write the following,

8x + 20

and that should be greater than or equal to 25

8x + 20 ≥ 25

Thus,

as an inequality it is 8x + 20 ≥ 25.

Hope this helps :)

Answer:

20xπ units

Step-by-step explanation:

Use the formula for the length of an arc.

θ/360 × 2πr

The length of the arc and the central angle is already given.

18/360 × 2πr = xπ

Solve for r.

r = (xπ)/(18/360)/(2π)

r = 10x

The radius is 10x.

The circumference is 2πr.

2π(10x)

20xπ

The circumference of the circle is 20xπ units.

Answer:

2(5+9)_6

=10+18_6

=22

is it wht u require

Answer:

Expected value 550,000

Step-by-step explanation:

Calculation of the expected value of the chosen number

We should know that each of the digit of the number may likely be thought of what we called a random variable, in which the first digits and the last digits comes uniformly from [1,2,3,4,5,6,7,8,9] while the last digit can't be 0 because of what we called the palindrome condition).

Therefore each of these two digits will have an expected value of 5 while the other four digits will come uniformly from this digits which are [0,1,2,3,4,5,6,7,8,9] in which each of the digits will have an expected value of 4.5.

Thus Expected value is additive, which means we have to also take place the value into account.

Now let find the EXPECTED VALUE

The expected value will be :

(100,000+1)⋅(5)+(10,000+1,000+100+10)⋅(4.5)

Expected value=550,000

Therefore the Expected value will be 550,000

Answer:

The answer is option D.

Step-by-step explanation:

(4a - b)(2a - 3b)

Expand the terms

We have

8a² - 12ab - 2ab + 3b²

Which is

8a² - 14ab + 3b²

That's option D.

Hope this helps you

Answer:

A, B and D

Step-by-step explanation:

Following are steps in practical problem solving:

=> Assign an identifying variable to the quantity to be found.

=> Write a sentence stating conditions placed on the quantity.

=> Solve the sentence for the variable.

Answer:

Assign an identifying variable to the quantity to be found.

.Write a sentence stating conditions placed on the quantity.

Solve the sentence for the variable.

Answer:

Step-by-step explanation:

C 32 units

Answer:

2.5 cm

Step-by-step explanation:

The volume of a triangular prism is cross section × length.

The cross section area is the triangle area. The triangle length is 4 cm, the height is not given. The length of the triangular prism is 7cm.

4 × h × 1/2 × 7 = 35

14h = 35

h = 35/14

h = 5/2

The height of the triangular cross section is 2.5 cm.

Answer:

< 3 and < 7

Step-by-step:

Corresponding angles mean that two angles are on the same side of the line. In this situation, the line is "t". Angles 3 and 7 are the only angles on the same side as each other.

Hope this helps!

Answer:

<3 and <7

Step-by-step explanation:

look at pic

Answer:

∠APD and ∠CPB are Vertical Angles

Equation: 6x - 10 = 4x + 8

Step-by-step explanation:

We use the Vertical Angles Theorem to solve for x:

Step 1: Set up equation

6x - 10 = 4x + 8

Step 2: Subtract 4x on both sides

2x - 10 = 8

Step 3: Add 10 to both sides

2x = 18

Step 4: Find x by dividing 2 on both sides

x = 9

Step 5: Plug in x for 9 to find degree measure

m∠CPB = 4(9) + 8

m∠CPB = 36 + 8

m∠CPB = 44°

m∠CPB = m∠APD (Vertical Angles)

m∠APD = 44°

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

∠APD and ∠CPB are vertically opposite angles

The equation is 6x-10=4x+8

[tex]6x-10=4x+8\\6x-4x=8+10\\2x=18\\x=9[/tex]

Plug x as 9 for the angle.

[tex]4(9)+8\\36+8\\44[/tex]

∠APD and ∠CPB = 44 degrees

Answer:

ABC. def, m is a brain training site. off work at abc .bac. cab .equal abcdef

Answer:

[tex]a_{7}[/tex] = [tex]\frac{3}{32}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a. [tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 6 and r = [tex]\frac{1}{2}[/tex] , thus

a₇ = 6 × [tex](\frac{1}{2}) ^{6}[/tex] = 6 × [tex]\frac{1}{64}[/tex] = [tex]\frac{6}{64}[/tex] = [tex]\frac{3}{32}[/tex]

Answer:

[tex](B) a=\dfrac{T-b-c-d}{4}[/tex]

Step-by-step explanation:

Let the points for the three local matches be b, c, and d.

Let a be the number of points at the district match.

Since district match points count for four times the number of points than local matches do.

Total Points, T=4a+b+c+d

Next, we make 'a' the subject of the formula.

[tex]T=4a+b+c+d\\4a=T-b-c-d\\$Divide both sides by 4$\\a=\dfrac{T-b-c-d}{4}[/tex]

The correct option is B.

Answer:

B.  a equals T minus b minus c minus d all over 4

Step-by-step explanation:

Good luck! Hope this helped :)

Answer:

Here you go mate!

Step-by-step explanation:

Not sure if it's right though

Answer:

  B.  False

Step-by-step explanation:

In order for segments to form a triangle, the sum of the lengths of the shorter two must be at least as much as the length of the longest one.

The sum of the shorter two is 6 + 5 = 11. This is not as great as 12, the length of the longest one, so no triangle can be formed.

Answer:

[tex] \hat p-ME = 0.67-0.04= 0.63[/tex]

[tex] \hat p+ME = 0.67+0.04= 0.71[/tex]

And we can conclude that the etimated unfavorable rating is between 63 and 71%

Step-by-step explanation:

For this case we know that the estimated unfavorable rating is given by:

[tex]\hat p=0.67[/tex]

And the margin of error for this estimate is given by:

[tex]ME= 0.04[/tex]

If we want to find the confidence interval we just need to do the following:

[tex] \hat p-ME = 0.67-0.04= 0.63[/tex]

[tex] \hat p+ME = 0.67+0.04= 0.71[/tex]

And we can conclude that the etimated unfavorable rating is between 63 and 71%

Answer: A) 4.8 inches

              B) 3.125 miles

Step-by-Step Explanation:

[tex]\dfrac{2\ inches}{25\ miles}=\dfrac{x}{60\ miles}\\\\\\\dfrac{2(60)}{25}=x\\\\\\x=\large\boxed{4.8}[/tex]

[tex]\dfrac{2\ inches}{25\ miles}=\dfrac{\frac{1}{4}\ inch}{y}\\\\\\2y=25\bigg(\dfrac{1}{4}\bigg)\\\\\\y=\dfrac{25}{8}\\\\\\y=\large\boxed{3.125}[/tex]

Answer:

The answer is below

Step-by-step explanation:

A store carries four brands of DVD​ players, J,​ G, P and S. From past​ records, the manager found that the relative frequency of brand choice among customers varied. Using the given probability values for each of the four​ brands, find the probability that a random customer will choose brand J or brand P.

P(J)=0.22​, ​P(G)=0.18​, ​P(P)=0.35​, ​P(S)=0.25

Answer: Probability is the ration of possible outcomes to the total number of possible outcomes. The probability of mutually exclusive events i.e. events that cannot occur at the same time is the sum of their individual probabilities. If two events A and B are mutually exclusive events, then:

P(A or B) = P(A) + P(B)

Given that P(J)=0.22​, ​P(G)=0.18​, ​P(P)=0.35​, ​P(S)=0.25, the probability that a random customer will choose brand J or brand P is given by:

P(J or P) = P(J) + P(P) = 0.22 + 0.35 = 0.57

Answer:

F(2b-1) = 4b² - 6b + 4

Step-by-step explanation:

Replace all the x with 2b-1

F(x) = x² - 2x + 4

F(2b-1) = (2b-1)² - 2(b) + 4

= 4b² - 4b + 1 - 2b + 4

= 4b² - 6b + 4

Answer:

D. 0.85

Step-by-step explanation:

Given

Probability of S = 0.8

Probability of R = 0.7

Probability of S and R = 0.65

Required

Probability of S or R

Using probability notations;

P(S) = 0.8

P(R) = 0.7

P(S n R) = 0.65

The question requires that we solve for P(S or R)

For overlapping events S and R; the following formula is applicable.

P(S or R) = P(S) + P(R) - P(S n R)

Substitute the values of P(S), P(R) and P(S n R)

P(S or R) = 0.8 + 0.7 - 0.65

P(S or R) = 0.85

Hence, the probability that either a rec team or a school team has a game is 0.85

Answer:

a = 1

Step-by-step explanation:

The factor in front of x must be the same in both equations.

So (a+2) in the first must be 3 (like it is in the second).

That is the case when a=1.

So the +7 and the -4 are not relevant!

Answer:

D. 0.366

Step-by-step explanation:

Hello!

A stemplot is a way of arranging a data set.

In the stem you'll find the integer and first two decimal digits of the batting average, because these values are repeated several times.

In the leafs you'll find the third decimal digit.

So for the first value of the stem "0.32" there is only one observation:

0.329 ⇒  0.32 | 9

For the second value "0.33" correspond 14 observations: 0.330, 0.331, 0.331,0.333, 0.333, 0.333, 0.334, 0.334, 0.334, 0.336,  0.337, 0.338, 0.338, 0.338

0.33 | 0, 1, 1, 3, 3, 3, 4, 4, 4, 6, 7, 8, 8, 8

For the third value "0.34" correspond 12 observations: 0.340, 0.340, 0.341, 0.341, 0.342, 0.342, 0.342,  0.344, 0.344, 0.345, 0.346, 0.349

0.34 | 0, 0, 1, 1, 2, 2, 2, 4, 4, 5, 6, 9

For the fifth value "0.35" and the sixth value "0.36" there is only one observation, so, as happened with the first one, these values of the stem will only have one "leaf"

0.358 ⇒ 0.35 | 8

0.366 ⇒ 0.36 | 6

So the whole stem plot for this 30 observations is:

Stem | Leafs

0.32  | 9

0.33  | 0, 1, 1, 3, 3, 3, 4, 4, 4, 6, 7, 8, 8, 8

0.34  | 0, 0, 1, 1, 2, 2, 2, 4, 4, 5, 6, 9

0.35  | 8

0.36  | 6

Considering this, the correct option is D

I hope this helps!

Answer:

Option (D)

Step-by-step explanation:

If the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are lying of the line.

Slope of the line represented by the function 'f' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Two points are lying on the line are (-2, 4) and (0, -2).

Slope of the line passing through these points 'm' = [tex]\frac{4+2}{-2-0}[/tex]

m = -3

Y-intercept of the line 'b' = -2 [From the graph]

Therefore, equation of the function will be,

f(x)  = (-3)x - 2

f(x) = -3x - 2

Similarly, for other function represented by the line in red,

Slope of the line passing through (-6, 0) and (0, 6) = [tex]\frac{6-0}{0+6}[/tex]

m' = 1

Y-intercept of g(x) = 5 [From the graph]

Equation that represents the function g(x) = 1.x + 5

g(x) = x + 5

For g(x) = f(x)

-3x - 2 = x + 6

-3x - x = 2 + 6

-4x = 8

x = -2

Therefore, for x = -2 both the functions will have the value.

f(-2) = g(-2)

Option (D) will be the answer.

Answer:

Rectangle Y has a length of 6 and width of 4

Step-by-step explanation:

Just did it

Answer:

Not too sure, but I think it's D.

Step-by-step explanation:

Hope you understand :)