Todd Lyle worked Monday through Friday from 8:00 A.M. to 5:00 P,M. with an hour off for lunch. He is paid $10,50 an hour. Find his earnings for the week.

Answer:

1.

In triangle ∆AFD ,∆BGD ,∆CHD

<AFD=<BGD=<CHD

[being corresponding angle]

<DAF=<DBG=<DCH

[being corresponding angle]

<D is common for all.

So

∆AFD ~∆BGD ~∆CHD

[By A .A .A. axiom]

look

again

at picture pasted

By AAA axiom ∆AFD , ∆BGD , ∆CHD are similar with each other.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

a). In ΔAFD, ΔBGD, ΔCHD

∠AFD = ∠BGD = ∠CHD [being corresponding angle]

∠DAF = ∠DBG = ∠DCH  [being corresponding angle]

∠D is common for all.

So ∆AFD ~∆BGD ~∆CHD   [By A .A .A. axiom]

Learn more about similarity of triangle from:

https://brainly.com/question/25882965

#SPJ2

Angle B = 90°

Angle C = 67°

Angle A.

[tex]{\boxed{\mathcal{\red{Angle\: A \:=\: 23° \:}}}}[/tex]✅

We know that,

[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]

➪ ∠ A + ∠ B + ∠ C = 180°

➪ ∠ A + 90° + 67° = 180°

➪ ∠ A + 157° = 180°

➪ ∠ A = 180° - 157°

➪ ∠ A = 23°

[tex]\sf\red{Therefore, \:the\: value \:of \:∠\: A\: is \:23°.}[/tex]

∠ A + ∠ B + ∠ C = 180°

✒ 23° + 90° + 67° = 180°

✒ 180° = 180°

✒ L. H. S. = R. H. S.

[tex]\boxed{Hence\:verified.}[/tex]

Note:-

Please refer to the attached file.

[tex]\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆[/tex]

Answer:

(8, 11π/6)

Step-by-step explanation:

r= √(4√3)²+(-4)² = √48+16=√64=8

0 = tan~¹ -4/(4√3)

= tan~¹ -⅓√3 = 330° = 11π/6

the polar coord. => (8, 11π/6)

9514 1404 393

Answer:

  8∠11π/6

Step-by-step explanation:

To simplify the way we talk of this number, we will refer to it as a vector. We'll assume its head is at the given coordinates, and its tail is at the origin. The magnitude of the vector is the root of the sum of the squares of its components:

  [tex]\displaystyle r=\sqrt{x^2+y^2}=\sqrt{(4\sqrt{3})^2+(-4)^2}=\sqrt{48+16}=\sqrt{64}\\\\r=8[/tex]

The angle of the vector with respect to the +x axis is ...

  [tex]\theta=\arctan{\dfrac{y}{x}}\qquad\text{a 4-quadrant arctangent}\\\\\theta=\arctan{\dfrac{-4}{4\sqrt{3}}}=-\arctan{\dfrac{1}{\sqrt{3}}}\qquad\text{a 4th-quadrant angle}\\\\\theta=\dfrac{11\pi}{6}[/tex]

In magnitude∠angle notation, the polar coordinates are ...

  (4√3, -4)  ⇔  8∠(11π/6) . . . . . θ in radians

_____

Additional comment

Spreadsheets generally have an ATAN2(x, y) function that will return a 4-quadrant version of the angle. The usual ATAN( ) function will give the angle only in quadrants I or IV.

Some graphing calculators may also have the ATAN2 function. Some will simply do the entire conversion for you, without any need to deal separately with magnitude and angle. (You may need to write the number as a complex number, x +iy.)

Answer:

circle

Step-by-step explanation:

Answer:

i think it's 10 because if DE is 10 so BD is the same think it's 10

Answer:

The number of situps is: 16.4405

Step-by-step explanation:

Given

[tex]y = ax + b[/tex]

[tex]a =-1.077[/tex]

[tex]b=30.98[/tex]

[tex]r^2 = 0.74476[/tex]

Required

Predict y when [tex]x = 13.5[/tex]

In the result, we have:

[tex]y = ax + b[/tex]

[tex]a =-1.077[/tex]

[tex]b=30.98[/tex]

This implies that:

[tex]y = -1.077x + 30.98[/tex]

To make prediction when [tex]x = 13.5[/tex]

We have:

[tex]y = -1.077*13.5 + 30.98[/tex]

[tex]y = -14.5395 + 30.98[/tex]

[tex]y = 16.4405[/tex]

Answer:

Number of biscuit needs = 28 packets

Number of Pemmican needs = 18 packets

Number of Butter cocoa needs = 4 packets

Step-by-step explanation:

GIven:

Total calorie required = 5,600 calories

Biscuits 80 (Calorie per packet) 40% of total diet

Pemmican 140 (Calorie per packet) 45% of total diet

Butter cocoa 210 (Calorie per packet) 15% of total diet

Find:

Number of biscuit, Pemmican and butter cocoa need

Computation:

Number of biscuit needs = [5,600(40%)]/80

Number of biscuit needs = [2,240]/80

Number of biscuit needs = 28 packets

Number of Pemmican needs = [5,600(45%)]/140

Number of Pemmican needs = [2,520]/140

Number of Pemmican needs = 18 packets

Number of Butter cocoa needs = [5,600(15%)]/210

Number of Butter cocoa needs = [840]/210

Number of Butter cocoa needs = 4 packets

Answer:

Below in bold.

Step-by-step explanation:

m < C = m < D = 64 degrees

m <A + m < D = 180

m < A + 64 = 180

m<A =  180 - 64 = 116 degrees.

m < B = m< A = 116 degrees.

Step-by-step explanation:

C.P of the marker= Rs. 40

S.P of the marker= Rs. 50

Profit= S.P- C.P

= 50- 40

= Rs. 10

Profit%= {[tex]\frac{Profit}{C.P}[/tex]×100}%

= {[tex]\frac{10}{40}[/tex]×100}%

= 25%

Answer:

49/5 mm

Step-by-step explanation:

7/2×14/5

multiply the numerator and denominator

98/10

simplify

49/5 or

9 4/5 mm

Answer:

16 units

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

The street sign is composed of two rectangles and 1 triangle.

Painted area = area of triangle + area of rectangle 1 + area of square

✔️Area of triangle = ½bh

b = 15 in.

h = 8 in.

Area of triangle = ½*15*8 = 60 in.²

✔️Area of rectangle 1 = L*W

L = 50 in.

W = 6 in.

Area = 50*6 = 300 in.²

✔️Area of Square = s²

s = 15 in.

Area = 15² = 255 in.²

✅Painted area = 60 + 300 + 225 = 585 in.²

Answer:

B. 585 square inches :)

Step-by-step explanation:

Answer:

228.9

Step-by-step explanation:

Answer:

228.6

Step-by-step explanation:

Multiply the inches by 2.54

90 x 2.54 = 228.6

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer: [tex]\$10,\ \$5[/tex]

Step-by-step explanation:

(a) Given

Sam charge $5 for each dog for a thirty minute walk

For an hour which is double the thirty minutes, it must be double of the same charge.

[tex]\Rightarrow 2\times 5=\$10[/tex]

(b)Given

With $20, Christie sells 100 cups of lemonade with a quarter per cup charge

For 100 cup, she generate a revenue of

[tex]\Rightarrow \dfrac{1}{4}\times 100\\\\\Rightarrow \$25[/tex]

So, she earns [tex]25-20=\$5[/tex] that is , her profit is [tex]\$5[/tex]

Complete Question

A manufacturer of banana chips would like to know whether its bag filing machine works correctly at the 445 gram setting is there sufficient evidence at the 0.01 level that the bags are underfilled? Assume the population is normally distributed State the null and alternative hypotheses for the above scenario

Answer:

[tex]H_o=\mu=445g[/tex]

[tex]H_a=\mu<445g[/tex]

Step-by-step explanation:

From the question we are told that:

Mass [tex]M=445g[/tex]

Significance level [tex]\alpha=0.01[/tex]

Generally the Null and Alternative Hypothesis is

[tex]H_o=\mu=445g[/tex]

i.e  The bags are not under filled

[tex]H_a=\mu<445g[/tex]

i.e The bags are under filled

Answer:

He has 2 $5 bills and 10 $10 bills

Answer:

Step-by-step explanation:

Wat lol

Answer:

[tex] = \phi( - 2.50) + \phi(1.50) \\ from \: calc : \\ = 0.4938 + 0.4332 \\ = 0.927[/tex]

Answer:

its nothing 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

3/8 or 1/3 if you round it.

Answer:

2.5, 2 and 1 half stars

Step-by-step explanation:

0.5=1/2, so 5/2= 2.5

Answer:

5

Step-by-step explanation:

it is asking for .5 of the stars, which in percentage is 50%. if the total is 10 because 5 stars in each row and there are 2 rows. you add the numbers of stars per row, then divide it by 2, and you would get 5; so you would circle 5 stars.

Answer:

B. 36 yd

Step-by-step explanation:

I calculated it logically

Answer:

Hey there I think the answer is 0.06 hopefully that helps

Step-by-step explanation:

Answer:

[tex]7n−13[/tex]

Step-by-step explanation:

[tex]4n+3(n−5)+2[/tex]

[tex]4n+3n+3 \times (−5+2)[/tex]

[tex]4n+3n−15+2[/tex]

[tex]7n−15+27n-15+2[/tex]

[tex]7n−13[/tex]

Answer:

can you provide a picture of the question plz

Step-by-step explanation:

Answer:

The expected winnings of the player in one game = 2.55

Step-by-step explanation:

Given - A blue die and a red die are thrown in a game. If the sum of the two numbers is 7 or 11, the player wins $10. If the sum of the two numbers is 12, then the player wins $20. In all other cases, the player loses a dollar.

To find - What are the expected winnings of the player in one game ?

Solution -

Given that,

A blue die and a red die are thrown in a game.

The Sample Space becomes -

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

       (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

       (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

       (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

       (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

       (6, 1), (6, 2), (6, 3), (4, 4), (6, 5), (6, 6) }

So,

n(S) = 36

Now,

Let A be the outcome that, the sum of the two numbers is 7 or 11

A = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2),  (6, 1)

       (6, 5), (5, 6) }

So,

n(A) = 8

So,

P(A) = n(A)/ n(S)

       = 8/ 36

       = 2/9

⇒P(A) = 2/9

Now,

Let B be the outcome that, the sum of the two numbers is 12

B = {(6, 6)}

So,

n(B) = 1

So,

P(B) = n(B)/ n(S)

       = 1/ 36

⇒P(B) = 1/36

Now,

Expected value, E(x) = ∑ x P(x)

                                  = 10 × P(A) + 12 × P(B)

                                  = 10 × 2/9 + 12 × 1/36

                                  = 20/9 + 12/36

                                  = (20×4 + 12)/36

                                  = (80 + 12)/36

                                  = 92/36

                                  = 2.55

⇒Expected value, E(x) = 2.55

∴ we get

The expected winnings of the player in one game = 2.55

Answer:.

Step-by-step explanation:

Answer:

Step-by-step explanation:20/29

Answer:

(x+10)^2

Step-by-step explanation:

x^2+20x+ 100

What 2 numbers multiply to 100 and add to 20

10*10 =100

10+10=20

(x+10) (x+10)

(x+10)^2