Find the measure of f.

Answer:

Step-by-step explanation:

[tex]Mean=\frac{all.ages.added.together.of.all.kids}{total.number.of.kids}[/tex] Hopefully, that makes sense! To get the numerator of that problem, we take the number of kids and multiply it by the corresponding age and add them all together. To get the denominator, we add the total number of kids together. That will look like this mathematically, setting the mean equal to 14.44, as stated:

[tex]14.44=\frac{13(15)+14(42)+15X+16(10)+17(3)}{15+42+X+10+3}[/tex] and simplify that a bit to

[tex]14.44=\frac{195+588+15X+160+51}{70+X}[/tex] and a bit more to

[tex]14.44=\frac{994+15X}{70+X}[/tex] and cross multiply

14.44(70 + X) = 994 + 15X and

1010.8 + 14.44X = 994 + 15X and

16.8 = .56X so

X = 30

30 kids are 15 years old for the mean age to be 14.44

d.30

Answer:

Solution given:

x. [tex] \:\:\:[/tex] f. [tex] \:\:\:[/tex] fx

13. [tex] \:\:\:[/tex] 15. [tex] \:\:\:[/tex] 195

14.[tex] \:\:\:[/tex] 42 [tex] \:\:\:[/tex] 588

15. [tex] \:\:\:[/tex] x. [tex] \:\:\:[/tex] 15x

16. [tex] \:\:\:[/tex] 10. [tex] \:\:\:[/tex] 160

17. [tex] \:\:\:[/tex] 3. [tex] \:\:\:[/tex] 51

. n=70+x. [tex]\sum[/tex]=994+15x

we have

mean=sum/n

14.44=[tex]\bold{\frac{\sum}{n}}[/tex]

14.44=[tex]\bold{\frac{994+15x}{70+x}}[/tex]

doing crisscrossed multiplication

(70+x)*14.44=994+15x

1010.8+14.44x=994+15x

15x-14.44x=1010.8-994

0.56x=16.8

x=16.8/0.56

x=30

Lets do

[tex] \\ \sf \longmapsto \: 3(x + 5) - 7 = 2(x +2) \\ \\ \sf \longmapsto \: 3x + 15 - 7 = 2x + 4 \\ \\ \sf \longmapsto \: 3x + 8 = 2x + 4 \\ \\ \sf \longmapsto \: 3x - 2x = 4 - 8 \\ \\ \sf \longmapsto \: x = - 4[/tex]

Answer: x=1 and y=0

Step-by-step explanation:

y+2x=2x

y=2x-2x

y=0

2x=2. X = 2/2

X=1

Answer:

x=1   y=0

Step-by-step explanation:

y + 2 = 2x               y = 2x - 2

y + 2x = 2

(2x - 2) + 2x = 2

4x = 4

x = 1

y + 2 = 2(1)

y + 2 = 2

y = 0

Answer:

tan x = c/b

cos x = b/a

sin x = c/a

Step-by-step explanation:

an easy way to memorize it would be SOH CAH TOA

SOH = sin, opposite, hypotunese

-- you find the angle and you divide it's opposite and hypotunese when it asks for sin

CAH = cos, adjacent, hypotunese

-- you find the angle's adjacent side and hypotunese, then divide

TOA = tan, opposite, adjacent

-- you find the angle's opposite side and divide it by the adjacent side

Answer:

m<EFG = 72°

m<GFH = 108°

Step-by-step explanation:

m<EFG = 2n + 16

m<GFH = 3n + 24

Linear pairs are supplementary, therefore,

m<EFG + m<GFH = 180°

Substitute

2n + 16 + 3n + 24 = 180

Add like terms

5n + 40 = 180

5n + 40 - 40 = 180 - 40 (subtraction property of equality)

5n = 140

5n/5 = 140/5 (division property of equality)

n = 28

✔️m<EFG = 2n + 16

Plug in the value of n

m<EFG = 2(28) + 16 = 72°

✔️m<GFH = 3n + 24

Plug in the value of n

m<GFH = 3(28) + 24 = 108°

Answer:

DE ║ BC

BC = 2(DE)

Step-by-step explanation:

From the picture attached,

AD = DB [Given]

AE = EC [Given]

Therefore, points D and E will be the midpoints of the sides AB and AC.

By midsegment theorem,

Segment joining midpoints of the two sides of a triangle is parallel and measures the half of the third side of the triangle.

DE ║ BC

DE = [tex]\frac{1}{2}(BC)[/tex]

BC = 2(DE)

The value of m for the complex number to be purely real are 3 and -5.

The value of m for the complex number to be purely imaginary are -2 and 3.

For the complex number to be located in the second quadrant, the value of m must be less than -3 and 5.

Given the complex number:

[tex]z=\frac{m^2-m-6}{m+3}+(m^2-2m-15)i[/tex]

a) For the complex number to be purely real, then the imaginary part of the complex number must be zero that is:

[tex](m^2-2m-15)i = 0\\m^2-2m-15=0[/tex]

Factorize

[tex]m^2+5m-3m-15=0\\m(m+5)-3(m+5)=0\\(m-3)(m+5)=0\\m-3=0 \ and \ m+5=0\\m=3 \ and \ m=-5[/tex]

Hence the value of m for the complex number to be purely real are 3 and -5.

b) For the complex number to be purely imaginary, then the real part of the complex number must be zero. Hence;

[tex]\frac{m^2-m-6}{m+3}=0 \\m^2-m-6=0[/tex]

Factorize

[tex]m^2-m-6\\m^2-3m+2m-6=0\\m(m-3)+2(m-3)=0\\(m+2)(m-3)=0\\m+2=0 \ and \ m-3=0\\m=-2 \ and \ m = 3[/tex]

Hence the value of m for the complex number to be purely imaginary are -2 and 3.

c) For the complex number to be in the second quadrant, then the ratio of y to x must be negative i.e less than zero as shown:

[tex]\frac{m^2-2m-15}{\frac{m^2-m-6}{m+3} } < 0\\ \frac{m^2-2m-15(m+3)}{{m^2-m-6} }\\ \frac{(m+3)(m-5)(m+3)}{{(m-3)(m+2)} } <0\\(m+3)(m-5)(m+3) <0\\m+3<0, m-5<0 \ and \ m+3<0\\m<-3 \ and \ m<5[/tex]

Hence for the complex number to be located in the second quadrant, the value of m must be less than -3 and 5.

Answer:

Step-by-step explanation:

Small cone:

r = 4 mm

h = 8 mm

Volume of small cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]

                                    [tex]=\frac{1}{3}*\pi *4*4*8\\\\=\frac{128}{3}*\pi \ mm^{3}[/tex]

Bigger cone :

r = 8 mm

h = 16 mm

Volume of bigger cone = [tex]\frac{1}{3}*\pi *8*8*16[/tex]

                                       [tex]= \frac{1024}{3}\pi \ mm^{3}[/tex]

Volume of the space = Volume of bigger cone - volume of small cone

                                   [tex]= \frac{1024}{3}\pi-\frac{128}{3} \pi \\\\=\frac{896}{3}*\pi \\\\= \frac{896}{3}*3.14\\\\= 937.81 \ cm^{3}[/tex]

Answer:

Square

Step-by-step explanation:

In a square,

All the four angles are equal. Each angle = 90.

All the four sides are equal.

Answer:

c = 21

Step-by-step explanation:

**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**

If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.

PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.

With that in mind, we can apply this ratio to find WX.

We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.

c = 21

Hope this helps (●'◡'●)

Answer:

1.11

Step-by-step explanation:

Slope of a line = (y2 - y1)/(x2-x1) = (100 - 0)/(90-0) = 100/90 = 10/9 = 1.11

The graph above or below should answer the question.

Answer:

The midpoint is (1.5, -5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

( -3+6) /2 = 3/2 = 1.5

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

( -5+-5) /2 = -10/2 =-5

The midpoint is (1.5, -5)

Hi!

[tex]A=(-3,-5) \ and \ B=(6,-5)\\\\Medium \ point=(\frac{-3+6}{2};\frac{-5+(-5)}{2})=\boxed{(\frac{3}{2};-5)}[/tex]

Answer:

i guess Bis the answer bcuz, A sample space is a collection or a set of possible outcomes of a random experiment

Statement B is correct, which best defines the sample space that is " a sample space is the set of all possible outcomes for the a given situation".

A sample space is a collection or a set of possible outcomes of a random experiment. It is represented by using the symbol "s".

For example,

When we flip or toss a coin, two outcomes are possible such as head and tail. Therefore the sample space for this experiment is given as

Sample space, S = {H, T} = {Head, Tail}

According to the given option

Option B is correct. That is a sample space is the set of all possible outcomes for a given situation.

Learn more about sample space here:

https://brainly.com/question/17144524

#SPJ2

Answer:

30 degrees.

Step-by-step explanation:

Let the acute angle be x.

Then as the 2 acute angles in a right triangle sum to 90 degrees,

x = 90 - 60

= 30.

We used the information we know to give us this equation.

90°+60°+x=180°

We add 90° and 60° to give 150°

150°+x=180°

Answer:

the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

Step-by-step explanation:

if there is no mistake in the problem description, I read the following function :

C(x) = y = 0.3x² - 1.2x + 2

I don't know if you learned this already, but to find the extreme values of a function you need to build the first derivative of the function y' and find its solutions for y'=0.

the first derivative of C(x) is

0.6x - 1.2 = y'

0.6x - 1.2 = 0

0.6x = 1.2

x = 2

C(2) = 0.3×2² - 1.2×2 + 2 = 0.3×4 - 2.4 + 2 = 1.2-2.4+2 = 0.8

so, the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

Answer:

[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Answer:

option A is write answer

I hope you help

Answer:

none of these

Step-by-step explanation:

it's 96000 so none

Step-by-step explanation:

7 × 6 = 42 Answer

hope it helps

Answer:

78

Step-by-step explanation:

For every 1 bout Lina makes, Harry makes two boats.

1 + 2 is 3.

117 divided by 3 = 39, which is how many boats Lina made.

39 x 2 = 78, which is how many boats Harry made.

To check our answer, 39 + 78 = 117, which is how many boats they made altogether, so the answer is correct.

Answer:

78

Step-by-step explanation:

My knowledge!!

Hope it helps!

Answer:

72√2

Step-by-step explanation:

3√2 × 2√8 × √3 × √6

The above can be simplified as follow:

3√2 × 2√8 × √3 × √6

Recall

a√c × b√d = (a×b)√(c×d)

3√2 × 2√8 × √3 × √6 = (3×2)√(2×8×3×6)

= 6√288

Recall

288 = 144 × 2

6√288 = 6√(144 × 2)

Recall

√(a×b) = √a × √b

6√(144 × 2) = 6 × √144 × √2

= 6 × 12 × √2

= 72√2

Therefore,

3√2 × 2√8 × √3 × √6 = 72√2

Answer:

Solution given:

radius [r]=3ft

height[h]=5ft

Volume of cone=⅓*πr²h

$ubstitute value

Volume of cone =⅓*3.14*3²*5=47.1ft²

Volume of cone is 47.1ft²

Answer:

a. 129 meters

Step-by-step explanation:

The given parameters of the tree and the point B are;

The horizontal distance between the tree and point B, x = 125 meters

The angle of depression from the top of the tree to the point B, θ = 46°

Let h represent the height of the tree

The horizontal line at the top of the tree that forms the angle of depression with the line of sight from the top of the tree to the point B is parallel to the horizontal distance from the point B to the tree, therefore;

The angle of depression = The angle of elevation = 46°

By trigonometry, we have;

tan(θ) = h/x

∴ h = x × tan(θ)

Plugging in the values of the variables gives;

h = 125 × tan(46°) ≈ 129.44

The height of the tree, h ≈ 129 meters

Answer:

e s r

Step-by-step explanation:

Total gasoline = 10 gallons

Gasoline left after 100 miles = 5 gallons

Gasoline used in 100 miles

= Total gasoline - Gasoline left after 100 miles

= 10 gallons - 5 gallons

= 5 gallons

Gasoline used in 1 mile

= Gasoline used in 100 miles/100

= 5 gallons/100

= 0.05 gallons

Answer:

A

Step-by-step explanation:

A compressed by a factor of 1/4 in the y or vertical direction