The measures of the angles of the triangle are 32°, 53º,
950. Based on the side lengths, what are the measures
of each angle?
m2A = 95°, mZB = 53º, mZC = 32°
MZA= 32º, mzB = 53º, mZC = 95°
MZA= 43º, mZB = 32°, m2C = 95°
OmZA= 53º, m B = 95°, m2C = 32°

Consult the attached diagram.

In the larger triangle,

tan(16°) = (7250 ft) / (x + y)

and in the smaller triangle,

tan(26°) = (7250 ft) / y

You want to solve for x.

From the first equation (I'm ignoring units from here on, all distances are measured in ft), you have

(x + y) tan(16°) = 7250

x tan(16°) + y tan(16°) = 7250

x tan(16°) = 7250 - y tan(16°)

x = 7250 cot(16°) - y

From the second equation,

y = 7250 cot(26°)

Solving for x gives

x = 7250 cot(16°) - 7250 cot(26°)

x = 7250 (cot(16°) - cot(26°))

x ≈ 10,433 ft

The distance the plane traveled from point A to point B is 10,433 ft.

We have given that,

Carter spots an airplane on the radar that is currently approaching in a straight line, and that will fly directly overhead.

The plane maintains a constant altitude of 7250 feet.

In the larger triangle,tan(16°) = (7250 ft) / (x + y)and in the smaller triangle,

[tex]tan(\ theta)=\frac{\\opposite \side }{hypotenouse}[/tex]tan(26°) = (7250 ft) / y

we have to solve for x.

From the first equation (I'm ignoring units from here on, all distances are measured in ft),

you have

(x + y) tan(16°) = 7250

x tan(16°) + y tan(16°) = 7250

x tan(16°) = 7250 - y tan(16°)

x = 7250 cot(16°) - y

From the second equation,

y = 7250 cot(26°)

Solving for x gives

x = 7250 cot(16°) - 7250 cot(26°)

x = 7250 (cot(16°) - cot(26°))x ≈ 10,433 ft

Therefore the distance the plane traveled from point A to point B is 10,433 ft.

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Answer:

x = 8

y = 6

Step-by-step explanation:

Recall that one of the properties of a parallelogram is that the diagonals bisect each other, which means they divide each other into equal segments.

Therefore,

LP = PN

x = y + 2 (eqn. 1)

PM = KP

2x - 8 = y + 10 (eqn. 2)

Substitute x = y + 2 into eqn. 2 to find y

Thus:

2(y + 2) = y + 10

2y + 4 = y + 10

Take like terms

2y - y = -4 + 10

y = 6

Substitute y = 6 into eqn. 1 to find x:

x = y + 2 (eqn. 1)

x = 6 + 2

x = 8

Answer:

D. [tex]4^{15}[/tex]

Step-by-step explanation:

[tex]=(4^3)^5[/tex]

Multiply the exponent inside the parenthesis with the exponent outside.

[tex]=4^{15}[/tex]

Hope this helps.

Answer:

4^15

Step-by-step explanation:

Ok, so lets replace the base, 4, with x so we don’t get confused by it:

(X^3)^5

When we raise a power to a power, we multiply them , so:

(X^15)

Remember x is 4, so:

4^15 is the answer

Answer:

The future value is: RS 132867.075

Step-by-step explanation:

Given

[tex]PV = 75000[/tex] --- present value

[tex]r = 10\%[/tex] --- annual rate

[tex]n = 6[/tex] --- number of times compounded (3 years/ 6 months)

Required

The future value

This is calculated as:

[tex]FV =PV * (1 + r)^n[/tex]

[tex]FV = 75000 * (1 + 10\%)^6[/tex]

[tex]FV = 75000 * (1 + 0.10)^6[/tex]

[tex]FV = 75000 * (1.10)^6[/tex]

[tex]FV = 132867.075[/tex]

Hence, the future value is: RS 132867.075

Answer:

try the meeting was a good friend of mine for the first person in my family who has been a great friend for any

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 75}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]x - ( - 25) = - 50[/tex]

➺ [tex] \: x + 25 = - 50[/tex]

➺ [tex] \: x = - 50 - 25[/tex]

➺ [tex] \: x = - 75[/tex]

Therefore, the value of [tex]x[/tex] is -75.

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex]x - ( - 25) = - 50[/tex]

➺ [tex] \: - 75 + 25 = 50[/tex]

➺ [tex] \: - 50 = - 50[/tex]

➺ L. H. S. = R. H. S.

Hence verified.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

the scale factor is

-2 and

-4

-11/5 = -11 ÷ 5 = -2.2

Answer:

-2.2

Answer:

[tex]{ \tt{graph \: y \:and \:graph\: z}}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { (5x + 6y)(5x - 6y) }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] ={25x}^{2} - 36 {y}^{2} [/tex]

[tex] = ({5 \times 5)x}^{2} - (6 \times 6){y}^{2} [/tex]

[tex] = ({5x})^{2} -( {6y})^{2} [/tex]

[tex] = (5x + 6y)(5x - 6y)[/tex]

[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]

Answer:

ang sentimeter ay ang tamang yunit ng pagsukat para sa pagsukat sa lugar ng isang panyo

Answer:

[tex]P(Y=0) = 0.1353[/tex]

Step-by-step explanation:

From the question we are told that:

Exponential distribution mean [tex]\=x = 5 miles[/tex]

Distance [tex]d=10miles[/tex]

Generally the equation for Exponential distribution is mathematically given by

 [tex]\lambda=\frac{1}{E(X)}[/tex]

 [tex]\lambda=\frac{1}{5}[/tex]

Therefore

Possion Y

 [tex]10\lambda=10*(1/5)[/tex]

 [tex]10\lambda=2[/tex]

Generally the equation for  The probability that there are no major cracks in a 10 mile stretch of the highway is mathematically given by

 [tex]P(Y=0) = \frac{e-2 (2)0}{0!}[/tex]

 [tex]P(Y=0) = e-2[/tex]

 [tex]P(Y=0) = 0.1353[/tex]

Answer:

Cube with 10 cm

SA = 600 cm V = 1000 cm

Cube with 13 cm

SA = 1014 cm V = 2197

Step-by-step explanation:

SA = 6[tex]s^{2}[/tex]

V = [tex]s^{3}[/tex]

s = side length

Answer:

8

Step-by-step explanation:

i have 6 apples + 2 peers

Answer:

6 plus 2 equals 8

Step-by-step explanation:

If you have 6 apples and your mom gives you 2 more apples then you will have 8 apples.

6,7,8

Answer:

x+120°+20°=180°[ sum of interior angle of triangle]

x+140°=180°

x=40°

then,

x+y= 180°[being straight line]

40°+y= 180°

y=140°

Answer:

YES

Step-by-step explanation:

Yes, because the golden ratio has the value of 1.61803398875

The ratio 8.8:5.5 = 1.6.

They are very close, so yes.

Answer:

43.5 % decrease

Step-by-step explanation:

Take the original price and subtract the new price

850-480

370

Divide by the original price

370/850

.435294118

Change to percent form by multiplying by 100

43.5294118 % decrease

43.5 % decrease

Answer:

65°

Step-by-step explanation:

To obtain Angle A, we use the cosine rule ;

Cos A = (b² + c² - a²) / 2bc

Cos A = (12² + 14² - 14²) / 2(12)(14)

Cos A = 144 / 336

A = Cos^-1(144/336)

A = 64.62°

A = 65°

Answer:

a) z(s)  is in the rejection region for H₀  we reject H₀.

We have enough support to conclude that the two populations are different  

z(s) is in the rejection region so we reject H₀

The two population have a different proportion of non-contaminated food

Step-by-step explanation:

Conditions:

-Independent samples

-Random samples

- Size samples big enough

a) A Brand Chickens Sample:

sample size   n₁  = 80

We will go through a z- test

number of contamination cases  x₁  =  31

Then   p₁  =  31/80     p₁  =  0.3875    and  q₁  =  1 - p₁  ; q₁ = 1 - 0.3875

q₁  =  0.6125

B Brand Chickens Sample:

sample size   n₂  =  80

number of contamination cases  x₂  =  61

Then  p₂ = 61/80   p₂ = 0.7625  and  q₂ =  1  -  p₂ ;   q₂  =  1  -  0.7625

q₂  =  0.2375

Hypothesis Test:

Null Hypothesis                                  H₀     p₂ =  p₁

Alternative Hypothesis                      Hₐ     p₂ ≠ p₁

The alternative hypothesis call for a two-tail test ( ≠ ) we will test if the proportion differs )

A significance level  α =  0.01   then    α/2 = 0.005

From z -Table     α/2  =  0.005  correspond to z(c) =  2.575

To calculate z(s)

z(s)  =   ( p₂  -  p₁ ) / √( p₁*q₁/n₁) + (p₂*q₂)/n₂)

z(s)  = (  0.7625  -  0.3875 ) / √(0,3875*0.6125)/80 + (0.7625*0.2375)/80

z(s)  = ( 0.375 ) / √(0.00296) + (0.00226)

z(s)  = ( 0.375 ) /0.072

z(s)  =  5.21

Comparing    z(s)   and   z(c)    z(s) > z(c)

z(s)  is in the rejection region for H₀  we reject H₀.

We have enough support to conclude that the two populations are different

b) folowing the same procedure now talking about non-contaminated chickens

Tyson  Brand Chickens  p₁ =  0,5   then  q₁ = 0.5

Perdue Brand chickens  p₂ = 0.25 then  q₂ = 0.75

n₁ = n₂ = 80

Hypothesis Test:

Null Hypothesis                        H₀            p₁  = p₂

Alternative Hypothesis            Hₐ            p₁ ≠ p₂

Alternative hypothesis indicates a two-tail test

z(c)  =  2.575

And z(s)  =  (0.5 - 0.25)/ √(0.5*0.5)/80  + (0.25*0.75)/80

z(s) = 0.25 / √( 0.003125 + 0.002343

z(s) = 0.25 / 0.0739

z(s) = 3.38

Comparing z(s)  and z(c)

z(s) >  z(c)  

z(s) is in the rejection region so we reject H₀

The two population have different proportion of non-contaminated food

Answer:

c

Step-by-step explanation:

two plus two

Answer:

2

Step-by-step explanation:

2 is the answer because the circle touches the line only 2 times.

Hope this helps.

Answer:

72.7 is the weighted average score

Step-by-step explanation:

The weighted average score

= score of lab * % share of total grade + score of first major test  * % share of total grade + score of second major test  * % share of total grade + Score of the final exam  * % share of total grade

Substituting the given values, we get -

0.23 * 74 + 0.25 * 69 + 0.25 * 62 + 0.27 * 85

= 72.7

Answer:

12

Step-by-step explanation:

x = 1 and y = 9 so 3x1 + 9 = 12 as 3 x 1 is 3 and adding 9 to it will give 12

Answer:

The c intercept is 42

The t intercepts are: 6, -1 and 7

Step-by-step explanation:

Given

[tex]c(t) = (t - 6)(t +1)(t-7)[/tex]

Solving (a): The c intercept

Simply set t to 0

[tex]c(t) = (t - 6)(t +1)(t-7)[/tex]

[tex]c(0) = (0 - 6)(0 +1)(0-7)[/tex]

[tex]c(0) = (- 6)(1)(-7)[/tex]

[tex]c(0) = 42[/tex]

Solving (b): The t intercept

Simply set c(t) to 0

[tex]c(t) = (t - 6)(t +1)(t-7)[/tex]

[tex](t - 6)(t +1)(t-7) = 0[/tex]

Split

[tex]t - 6= 0,\ \ t +1= 0,\ \ t-7 = 0[/tex]

Solve for t

[tex]t = 6,\ \ t =-1,\ \ t=7[/tex]

Answer:

Step-by-step explanation:

A y = -3.6x + 12.8

The line of best fit is,

⇒ y = - 3.6x + 12.8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, Given that;

⇒ y = ax + b.

And, the best fitting line has values of a = - 3.6 and b = 12.8.

Hence, All you need do is put that into the general equation and try different values for it.

So you have y = - 3.6 x + 12.8

Now Let's run a couple of numbers.

The table shows 1 and 9 for the first entry. This means when x = 1, y should come pretty close to nine.

y = - 3.6(1) + 12.8

y = 9.2

Which is not a bad result for x = 1

You might want to check to see if anything else comes closer in your choices. If it does, then you have to try other points.

C

-0.998 = -3.6(1) + 12.8

This answer cannot work. We've already shown that x =1 will leave us close to 9  not -998

So, C is incorrect.

B

y = 12.8x - 3.6

Let x = 1

y = 12.8(1) - 3.6

y = 9.2 is right by coincidence. We must try another value. The hardest one is going to be 5 and - 5

y= 12.8*5 - 3.6

y = 64 - 3.6 which is no where's near - 5.

So B is wrong.

A

y = -0.998(1) + 12.8 Does this give 9 or anywhere near it? 11.802 You might argue that that is not a bad result. So let's try another pair.

x = 3. y should come to somewhere near 2.

y = -0.998 * 3 + 12.8 which comes to roughly nine. You can check this out.

It is not close enough to 2 to be acceptable.

Thus, The correct option is,

⇒ y = - 3.6x + 12.8

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Answer:

k=7

Step-by-step explanation:

2x+3y=k

2(2)+3(1)=k

4+3=k

k=7

Answer:

7.

Step-by-step explanation:

Substitute x = 2 and y = 1 into the given equation:

2(2) + 3(1) = k

4 + 3 = k

k = 7.

Answer:

Slope = 3

intercept = 2

y = 3x + 2

angle y = 70

angle x = 110

Step-by-step explanation:

Step-by-step explanation:

10075 .+#!!#+#!$!$++$7$+"$($(

Answer:

36, 55 , 35, 16, 20, 71

Step-by-step explanation:

Total number of coffee drinkers, U = 100

Let

n(Cream) = C

n(Sugar) = S

n(cream and sugar) = n(CnS) = 20

Number that like cream = n(C) +  n(CnS) 16 + 20 = 36

Nunber that like sugar = n(S) +  n(CnS) = 35 + 20 = 55

Sugar but not cream = 35 (from. Venn diagram)

Cream but not sugar = 16 (From. Venn diagram)

Cream and sugar =  n(CnS) = 20

Cream or sugar =  n(CuS) = 16 + 20 + 35 = 71