Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x? (

There are 12 cards with a value ≤ 3 (3 between 1, 2, and 3, and multiply by 4 to count each suit). So the probability of drawing one of these cards and thus winning the game is 12/52 = 3/13.

The expected winnings for playing this game once are

3/13 × ($41) + 10/13 × (-$11) = $1

so after playing 877 times, you can expect to win a total of $877.

Answer:

C=25°

a=11

b=12

Step-by-step explanation:

Find angle c,since angles in a triangle add up to 180 and we know angleA andB angle C will be

65+90+C=180

C=180-155

C=25°

To find a

use trig ratios

tanA=opposite/adjacent

tan65=a/5

a=tan65×5

a=10.72 round off to 11

To find b

sinC=opposite/hypotenuse

sin25=5/b

sin25 b=5

b=11.8 or rather 12

Answer:

Step-by-step explanation:

First find  side a and to find this  calculate tan 65

Tan 65 = [tex]\frac{opposite \ side}{adjacent\ side}=\frac{a}{5}\\\\[/tex]

2.144 = a/5

a = 2.144 * 5

b² = a² + c²

   = 121+25

   = 146.

b = √146 = 12.08 = 12

a = 10.72 = 11

Now find Tan C

[tex]Tan \ C = \frac{5}{10.72}\\\\Tan \ C = 0.4664\\[/tex]

C = tan⁻¹ 0.4664

C = 25°

hope it helps.

Answer: look below

Step-by-step explanation:

A straight angle is 180

180-50=130

the opposite is also the same angle which is the same

180-50-50=80 and 80 + 2x =180

x=50

the angles are 50, 50, 50, 50, 80, 130 and 130 degrees respectively

Answer:

The cutoff time be for concert setup should be of 51.4 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Average time it takes their sound tech to set up for a show is 56.1 minutes, with a standard deviation of 6.4 minutes.

This means that [tex]\mu = 56.1, \sigma = 6.4[/tex]

If the band manager decides to include only the fastest 23% of sound techs on the tour, what should the cutoff time be for concert setup?

The cutoff time would be the 23rd percentile of times, which is X when Z has a p-value of 0.23, so X when Z = -0.74.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.74 = \frac{X - 56.1}{6.4}[/tex]

[tex]X - 56.1 = -0.74*6.4[/tex]

[tex]X = 51.4[/tex]

The cutoff time be for concert setup should be of 51.4 minutes.

Answer:

B

Step-by-step explanation:

I'm not really sure tho

Answer:

μ = 170 customers per day

σ = 45 customers per day

n = 31

[tex]\mu_x = 170[/tex]

[tex]\sigma_x = 8[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers.

This means that [tex]\mu = 170, \sigma = 45[/tex]

Suppose she takes a random sample of 31 days.

This means that [tex]n = 31[/tex]

For the sample:

By the Central Limit Theorem, the mean is [tex]\mu_x = 170[/tex] and the standard deviation is [tex]\sigma_x = \frac{45}{\sqrt{31}} = 8[/tex]

Answer:

0.1667

Step-by-step explanation:

We are given;

Arrival rate, λ = 10 requests per hour

Service rate, μ = 12 requests per hour

From queuing theory, we know that;

ρ = λ/μ

Where ρ is the average proportion of time which the server is occupied.

Thus;

ρ = 10/12

ρ = 0.8333

Now, the probability that no requests for assistance are in the system is same as the probability that the system is idle.

This is given by the Formula;

1 - ρ

probability that no requests for assistance are in the system = 1 - 0.8333 = 0.1667

Answer:

40 years old.

Step-by-step explanation:

We can let Elga's age equal [tex]x[/tex]. Alvin's age can be equal to [tex]y[/tex]. We can make several equations from the information we know. We know that Elga's age plus five equal's Alvin's age.

[tex]x+5=y[/tex]

We also know that the sum of their ages is 85.

[tex]x+y=85[/tex]

We can substitute [tex]x+5[/tex] for [tex]y[/tex] in the second equation since [tex]x+5=y[/tex], so we have the following equation:

[tex]x+(x+5)=85[/tex]

We can combine like terms to get

[tex]2x+5=85[/tex]

Subtracting 5 from both sides results in

[tex]2x=80[/tex]

After that, we can divide both sides by 2 to get

[tex]x=40[/tex]

Thus, Elga is 40 years old.

Answer:

e = 40

a=45

Step-by-step explanation:

a + e = 85

a = e+5

e + 5 + e = 85

2e = 80

e = 40

a=45

Given: ????=????−2????+5????

and ????=2????+????+3????

To find: We need to find the value of ????×????

Solution: Here given,

????=????−2????+5????

and ????=2????+????+3????

Therefore, solving these two we have, ????=0

So,????×????=0

Answer:

g(x) =1/4 x²

The choose (1)

first drawing

Answer:

Choosing a card randomly and noting its suit

Step-by-step explanation:

Choosing a card randomly and noting its suit

This is because binomial distributions only work for bernoulli trials (a trail in which there are only two outcomes)

Answer:

y = -6x + 1

Step-by-step explanation:

y = mx + b

b = slope = (-5 - (-17))/(1 - 3) = 12/(-2) = -6

y = -6x + b

-5 = -6(1) + b

b = 1

y = -6x + 1

Answer:

[tex]y=-6x+1[/tex]

Step-by-step explanation:

The linear equation with slope m and intercept c is given as follows:

[tex]y=mx+c[/tex]

The formula for slope of line with points [tex](x_{1} ,y_{2} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] can be expressed as,

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

The line passes the points that are [tex](1,-5)[/tex] and [tex](3,-17)[/tex]

The slope of the line can be obtained as follows:

[tex]m=\frac{-17-(-5)}{(3)-1}[/tex]

[tex]m=\frac{-12}{2}[/tex]

[tex]m=-6[/tex]

The slope of the line is [tex]-6[/tex]

The line passes through the point [tex](3,-17)[/tex]

Substitute 3 for x, - 6 for m and -17 for y in equation [tex]y=mx+c[/tex] to obtain the value of c.

[tex]-17=-6(3)+c[/tex]

[tex]-17=-18+c[/tex]

[tex]-17+18=c[/tex]

[tex]1=c[/tex]

The equation is [tex]y=-6x+1[/tex]

Hence, the equation of the line that passes through the points [tex](1,-5)[/tex] and [tex](3,-17)[/tex] is [tex]y=-6x+1[/tex]

Answer:

1 ans A second phi okay yed

Answer:

Area swept by the blade = 448[tex]in^{2}[/tex]

Step-by-step explanation:

The arc the wiper wipes is for 135 degrees angle.

So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.

Then subtract the area of sector with 14 inches  from area of sector with radius as 24 inches.

So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]

Simplify it,

                                                  =216[tex]\pi[/tex]

Now, let's find area of sector with radius 14 inches

Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]

Simplify it

                                          =73.5[tex]\pi[/tex]

So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]

Simplify it and use pi as 3.14.....

Area of swept =678.584 - 230.907

                               =447.6769

Round to nearest whole number

So, area swept by the blade = 448[tex]in^{2}[/tex]

Answer:

x= -3

Step-by-step explanation:

2x+14= 8

2x= -6

x = -3

Answer:

-3

Step-by-step explanation:

According to the question,

[tex]\longrightarrow[/tex] CE = CD + DE

[tex]\longrightarrow[/tex] 8 = (x + 10) + (x + 4)

[tex]\longrightarrow[/tex] 8 = x + 10 + x + 4

[tex]\longrightarrow[/tex] 8 = 2x + 14

[tex]\longrightarrow[/tex] 8 ― 14 = 2x

[tex]\longrightarrow[/tex] ―6 = 2x

[tex]\longrightarrow[/tex] ―6 ÷ 2 = x

[tex]\longrightarrow[/tex] –3 = x

Therefore, the value of x is ― 3.

Answer:

D Is the correct answer Thats was too easy

Answer:

sec(θ) = hypotenuse / adjacent.

Step-by-step explanation:

sec theta= cos -1  theta

You'll need 2 more lines to complete this two column proof.

---------------------

Line 4

For the "statement" portion, you'll say something like [tex]\angle 2 \cong \angle 3[/tex]

The reason for this statement is "transitive property"

We're basically combining lines 1 and 3 to form this new line.

The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.

---------------------

Line 5

The statement is what you want to prove since this is the last line.

So the statement is [tex]p || q[/tex]

The reason is "converse of corresponding angles theorem"

As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".

Answer: A.

Step-by-step explanation:

Hope this helps!

Work Shown:

Apply the slope formula

m = (y2-y1)/(x2-x1)

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

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

m = -2/4

m = -1/2 is the slope

In decimal form, this converts to -0.5, though usually slopes are in fraction form.

Answer:

[tex]\frac{(2/36)}{(1-(28/36))} = 1/4[/tex]

Step-by-step explanation:

Answer:

A F(x) it is the power function, make sure to take notes as well

MODE IS THE NUMBER THAT IS REPEATED THE HIGHEST TIME..

HERE, IN YOUR QUESTION 5CAME 2 TIMES i.e. it is repeated highest time .so mode=5....

Answer:

11 and 33

Step-by-step explanation:

The the smaller number be [tex]x[/tex]. Since the other number is 3 times as large as the other, we can represent the large number as [tex]3x[/tex]. Because they add up to 44, we have the following equation:

[tex]x+3x=44[/tex]

Combine like terms:

[tex]4x=44[/tex]

Divide both sides by 4:

[tex]x=\frac{44}{4}=\boxed{11}[/tex]

Substitute [tex]x=11[/tex] into [tex]3x[/tex] to find the larger number:

[tex]11\cdot 3=\boxed{33}[/tex]

Therefore, the two numbers are 11 and 33.

9514 1404 393

Answer:

Step-by-step explanation:

The third angle can be found from the sum of angles in a triangle.

  A + B + C = 180°

  C = 180° -62° -97°

  C = 21°

__

The remaining side lengths can be found using the Law of Sines.

  a/sin(A) = b/sin(B)

  a = sin(62°)(15/sin(97°)) ≈ 13.34

Similarly, ...

  c/sin(C) = b/sin(B)

  c = sin(21°)(15/sin(97°)) ≈ 5.42

The remaining side lengths are approximately ...

  a ≈ 13.3

  c ≈ 5.4

Answer:

(1,7), (2,2), (3,5) (4,8)

(2,6), (6,5), (3,2) (5,3)

(4,3), (3,3), (2,3) (1,3)

Step-by-step explanation:

those represent functions b/c the domain of the relation is not written twice

Hope that'll help!

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

Answer:

300%

Step-by-step explanation:

because 9/3×100=900/3=300 so it is 300%

Answer:

300%

Step-by-step explanation:

9/3 * 100%

900%/3 = 300%

Answer: y= -3/7x + 3

Step-by-step explanation:

I used some graph paper for this, mark the two points and use a ruler to connect the lines. y=-3/7x is slope, and 3 is the y intercept.

Answer:

3x + 7y -2=0

Step-by-step explanation:

Two points are given to us and we need to find the Equation of the line passing through the two points . The points are (0,3) and (7,0) . We can use here two point form of the line as ,

[tex]\implies y-y_1 = \dfrac{y_2-y_1 }{x_2-x_1} ( x - x_1) \\\\\implies y - 3 =\dfrac{3-0}{0-7}(x - 0 ) \\\\\implies y - 3 =\dfrac{-3}{7}x \\\\\implies 7y - 2 = -3x \\\\\implies \underline{\underline{3x + 7y -2 = 0 }}[/tex]

Answer:

yes

Step-by-step explanation:

She aims at the center of the target. If she is off by 1.5 in. or less, she hits the target. We need to find what distance from the bull's eye an angle of 0.2° will make at 150 ft distance.

tan A = opp/adj

tan 0.2° = opp/150

opp = 150 * tan 0.2°

opp = 0.52 in.

Since 0.52 in. < 1.5 in. she will hit the target.