AAP4C
Applications of Trigonometry
1. A ladder that is 10 feet long is leaning against a wall at a 71° angle.
a. How far from the wall is the foot of the ladder?
b. How high up the wall does the ladder reach?​

Answer:

D - 33.75

Step-by-step explanation:

If the rectangles are similar, then you can use this cheat:

Width:

9/4 = 2.25

2.25 is the scale factor between the two rectangles.

Using the new-found scale factor, you can do this:

15 x 2.25 = 33.75

This means the length on the second rectangle is 33.75 inches long.

Hoping this helps you! :)

Answer:

neither

gfhhhufkufjkg

Answer:

40

Step-by-step explanation:

26 is 65% of 40

Answer:

700,000

Step-by-step explanation:

Answer:

The given equation has TWO positive integer valued solutions, {6, 7}

Step-by-step explanation:

Here we are given two trinomial factors, each of which needs to be set equal to zero and in each case the resulting quadratic equation solved.

(x^2 - 7x + 11) has the coefficients {1, -7, 11}, and so the discriminant of this quadratic is b^2 - 4(a)(c), or 49 - 4(11), or 5.

Because this discriminant is positive, we know immediately that this quadratic has two real, unequal roots involving √5 (NO integer roots).

Next we focus on (x^2 - 13x + 42).  The discriminant is b^2 - 4(a)(c), or

169 - 168, or 1.  Again we see that there are two real, unequal roots:

      +13 ± √1                  +13 ± 1

x = ---------------  or  x = -------------

             2                            2

OR x = 14/2 = 7 (integer) or x = 12/2 = 6 (integer).

The given equation has TWO positive integer valued solutions, {6, 7}

Answer:

Option A is correct answer..

Pls sandhya se baat karado yaar ,

nhi to mai mar jaunga .

Pls sandhya baat karlo na yaar .

ʜᴀᴠᴇ ᴀ ɢᴏᴏᴅ ᴅᴀʏ

❥︎ ʏᴜɢᴀʟᵇᵒˢˢ!

Answer:

its A

Step-by-step explanation:

Answer:

5a - 8b

Step-by-step explanation:

Mr Davis buys 5 package of a glue stick

= 5a

Mr. Wilson buys 8 packages of b glue sticks

= 8b

Therefore the difference in the total is

5a-8b

Answer:

12

Step-by-step explanation:

hope u find this helpfull

Answer:

Step-by-step explanation:

x = 12

the triangle was made smaller (i forget what the term is)

it was made smaller by  [tex]1\frac{1}{3}[/tex]

to find that you divide 24 by its equivalent side on the other triangle which would be 18

24 / 18 =  [tex]1\frac{1}{3}[/tex]

to find what x is equal to you have to find the equivalent side on the other triangle. this would be 16. since the triangle with 16 is bigger the equation is:

16 / [tex]1\frac{1}{3}[/tex] = 12

so x = 12

Answer:

What is the difference between linear and exponential functions? Linear functions change at a constant rate per unit interval. An exponential function changes by a common ratio over equal intervals.

Answer:

150:30

Step-by-step explanation:

It's essentially saying 5:1, 5 girls to one boy.

so with this in mind.

150:x

150/5

30

therefore

150:30

Answer:

30 boys attended the mixer. ( Wow 5 girls for a boy thats alot )

Step-by-step explanation:

1. Divide 150 girls by 5 ( 5 for every boy ) = 30 boys.

Thats it lol.

Btw can I have brainliest if I got it correct please?

Answer:

x = 4cos(t) – 1 and y = 4sin(t) + 3

Step-by-step explanation:

Equation of a circle:

The equation of a circle has the following format:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In which:

The centre is is [tex](x_0,y_0)[/tex] and r is the radius. The parametric equations are given by:

[tex]x(t) = r\cos{(t)} + x_0[/tex]

[tex]y(t) = r\sin{(t)} + y_0[/tex]

In this question:

[tex](x + 1)^2 + (y - 3)^2 = 4^2[/tex]

This means that the centre is [tex](-1,3)[/tex] and the radius is 4. So, the answer is:

x = 4cos(t) – 1 and y = 4sin(t) + 3

Answer:

Amount = Initial value × (1 + rate of interest)^years and 374

Step-by-step explanation:

The formula to determine the student population and the estimated student population is given below:

As we know that

Amount = Initial value × (1 + rate of interest)^years

= 284 × (1 + 0.04)^7

= 284 × 1.04^7

= 373.72

= 374

Answer:

a) V = 35.1 in.^3

b) V = 288 pi in.^3

c) h = 2.7 in.

Step-by-step explanation:

a)

radius of base = 2 in.

height = 8 in.

volume of cone = (1/3)(pi)(r^2)h

V = (1/3)(pi)(2 in.)^2(8 in.)

V = 35.1 in.^3

You are correct.

b)

You must leave the answer in terms of pi, so do not use 3.14 or another approximation for pi.

radius of base = 6 in.

height = 24 in.

volume of cylinder = (pi)(r^2)h

V = (1/3)(pi)(6 in.)^2(24 in.)

V = 288 pi in.^3

c)

volume = 288 pi in.^3

radius = 18 in.

288 pi in.^3 = (1/3)(pi)(18 in)^2 h

288 in. = (1/3)(324)h

288 in. = 108h

h = 2.666 in.

h = 2.7 in.

Answer:

-3

Step-by-step explanation:

Slopes of a perpendicular line are the opposite reciprocal.

So, the opposite of 1/3 is -1/3.

Then the reciprocal of -1/3 is -3 (since -3 is -3/1).

Answer:

$365

Step-by-step explanation:

did the math

Answer:

X=-2

Y=0

Step-by-step explanation:

X+y=-2 = x=-2-y

3x+4y=-6

3(-2-y)+4y=-6

-6-3y+4y=-6

y=0

x+3(0)=-2

x=-2

Answer:

[tex]\boxed {\boxed {\sf (-2,0)}}[/tex]

Step-by-step explanation:

To solve by substitution we must first isolate 1 variable in an equation.

Let's use the first equation.

[tex]x+3y= -2[/tex]

Subtract 3y from both sides to isolate the variable x.

[tex]x+3y-3y= -2 -3y[/tex]

[tex]x= -2 -3y[/tex]

Now we can substitute the expression (-2-3y) in for x in the second equation.

[tex]3x+4y= -6[/tex]

[tex]3(-2-3y)+4y= -6[/tex]

Distribute the 3. Multiply each term inside the parentheses by 3.

[tex](3*-2)+ (3*-3y)+4y=-6\\-6-9y+4y=-6[/tex]

Combine the like terms on the left side.

[tex]-6-5y= -6[/tex]

Add 6 to both sides to isolate the variable.

[tex]-6+6-5y=-6+6\\-5y=0[/tex]

Divide both sides by -5.

[tex]-5y/-5=0/-5 \\y=0[/tex]

Now we know that y is equal to 0 and can substitute it into the first equation and find x.

[tex]x+3(0)=-2[/tex]

[tex]x+0=-2 \\x= -2[/tex]

x is equal to -2 and y is equal to 0.

Answer:

X^7

Step-by-step explanation:

3+4=7

Answer:

Step-by-step explanation:

Answer:

60% of 60 is 36. The answer should be 36

Step-by-step explanation:

60 / 100 * 60

0.6 * 60

36

Just divide the number by 100 and multiply it by the percentage.

Mark me as brainliest if you want to.

Answer:

D

Step-by-step explanation:

I just did it :)

Answer:

y + 3= -7(x + 2)

Step-by-step explanation:

...........

Answer:

a) 0.587 = 58.7% probability that the company uses flexible work arrangements or gives time off for volunteerism.

b) 0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.

c) 0.3317 = 33.17% probability that the company uses flexible work arrangements.

d) 0.4634 = 46.34% probability that the company does not use flexible work arrangements given that the company does give time off for volunteerism.

e) 0.795 = 79.5% probability that the company does not use flexible work arrangements or the company does not give time off for volunteerism.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a. The company uses flexible work arrangements or gives time off for volunteerism.

41% use flexible work arrangements.

Of the 100-41 = 59% that do not use flexible work arrangments, 30% give time off for volunteerism. So

[tex]p = 0.41 + 0.59*0.3 = 0.587[/tex]

0.587 = 58.7% probability that the company uses flexible work arrangements or gives time off for volunteerism.

b. The company uses flexible work arrangements and does not give time off for volunteerism.

41% use flexible work arrangements. Of those, 100 - 50 = 50% do not give time off for volunteerism. So

[tex]p = 0.41*0.5 = 0.205[/tex]

0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.

c. Given that the company does not give time off for volunteerism, the company uses flexible work arrangements.

Here, we use conditional probability.

Event A: Does not give time off for volunteerism

Event B: Uses flexible work arrangments.

0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.

This means that [tex]P(A \cap B) = 0.205[/tex]

Probability that the company does not give time off for volunteerism:

0.205(uses flexible work arrangments).

100 - 30 = 70% of 59%. So

[tex]P(A) = 0.205 + 0.7*0.59 = 0.618[/tex]

The desired probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.205}{0.618} = 0.3317[/tex]

0.3317 = 33.17% probability that the company uses flexible work arrangements.

d. The company does not use flexible work arrangements given that the company does give time off for volunteerism.

Again conditional probability.

Event A: Gives time off for volunteerism

Event B: Does not use flexible work arrangements.

Probability of giving time off for volunteerism:

50% of 41%(have flexible work arrangements).

30% of 59%(don't have flexible work arrangements).

So

[tex]P(A) = 0.5*0.41 + 0.3*0.59 = 0.382[/tex]

Gives time off for volunteerism and does not use flexible work arrangements.

30% of 59%. So

[tex]P(A \cap B) = 0.3*0.59 = 0.177[/tex]

The desired probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.177}{0.382} = 0.4634[/tex]

0.4634 = 46.34% probability that the company does not use flexible work arrangements given that the company does give time off for volunteerism.

e. The company does not use flexible work arrangements or the company does not give time off for volunteerism.

Does not use flexible work arrangments: 59%

Dont give time off for volunteerism(70% already in the 59%, so we dont add) and 50% of 41%.

[tex]p = 0.59 + 0.5*0.41 = 0.795[/tex]

0.795 = 79.5% probability that the company does not use flexible work arrangements or the company does not give time off for volunteerism.

Answer:

(4 + y)(4 - y)

Step-by-step explanation:

[tex]16 - {y}^{2} \\ \\ = {4}^{2} - {y}^{2} \\ \\ = (4 + y)(4 - y)[/tex]

Answer:

3

Step-by-step explanation:

the y axis

Step-by-step explanation:

6 customers per hour [tex]=1[tex] customer per 10 minutes

[tex]X \sim \operatorname{Exp}(\beta=10) \quad[/tex] (given mean)

Pdf is given by: [tex]f(x)=\frac{1}{\beta} e^{-x / \beta}, 0<x[/tex]

Pdf: [tex]f(x)=\frac{1}{10} e^{-x / 10}, \quad 0<x,[tex] and zero otherwise.

Cdf: [tex]P(X \leq x)=1-e^{-x / \beta}[/tex]

[tex]P(X \leq x)=1-e^{(-x / 10)} \quad[/tex] for [tex]x>0 \Longrightarrow P(X>x)=e^{-x / 10}[/tex]

a)[tex] \begin{array}{c}

P(X<12)=1-\exp (-12 / \beta)=1-e^{-1.2}=1-0.301194=0.698806 \approx 0.699 \\

P(X<12)=0.699 \end{array}[/tex]

[tex]\begin{aligned}

&\begin{array}{c}

P(X>20)=\exp (-20 / \beta)=e^{-2} \approx 0.135335 \approx 0.1353 \\

P(X>20)=0.1353

\end{array}\\[/tex]

&\text { c) }\\

&P(8<X<15)\\

&\begin{array}{l}

=P(X<15)-P(X<8) \\

=(1-\exp (-15 / \beta))-(1-\exp (-8 / \beta)) \\

=\exp (-8 / \beta)-\exp (-15 / \beta) \\

=e^{-0.8}-e^{-1.5} \\

=0.449329-0.22313 \approx 0.226199 \approx 0.2262 \\

\quad P(8<X<15)=0.2262

\end{array}

\end{aligned}

\begin{aligned}

&\text { d) }\\

&\begin{array}{l}

P(14<X<22) \\

=P(X<22)-P(X<14) \\

=(1-\exp (-22 / \beta))-(1-\exp (-14 / \beta)) \\

=\exp (-14 / \beta)-\exp (-22 / \beta) \\

=e^{-1.4}-e^{-2.2} \\

=0.246597-0.110803 \approx 0.135794 \approx 0.1358 \\

P(X<14 \cup X>22)=1-P(14<X<22)=1-0.1358=0.8642 \\

P(X<14 \cup X>22)=0.8642

\end{array}

\end{aligned}

Answer:

B. 12 in.

Step-by-step explanation:

Diameter = 5 in.

Diagonal = 13 in.

Apply Pythagorean theorem to find the height of the cylinder.

Thus:

13² - 5² = height²

144 = height²

√144 = height

12 in. = height

Answer:

B. 12 in.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Even I need help with that

Answer:

87.5

Edited: Yea should be 56, misread it LOL.

Appoligise to that silly mistake

Step-by-step explanation:

Answer:3kg of small bag costs £10.20 while 3kg of the medium bag costs £11.40. Hence, the bag with better value which is the cheapest is a 3kg of the big bag which costs £3.9

Step-by-step explanation: