One angle of a triangle is twice as large as another. The measure of the third angle is 60° more than that of the smallest angle. Find the measure of each angle.
The measure of the smallest angle is º


Please help :)

Answer:

The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces

Step-by-step explanation:

To find the sample mean, we can find the mean of the confidence interval.

(15.875 + 16.595)/2 = 16.235

To find the margin of error, that is the difference between the mean and one of the edges of the confidence interval. 16.595 - 16.235 = 0.36

The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces

Answer:

C. We are 90% confident that the interval from 15.875 ounces to 16.595 ounces captures the true mean weight of bags of grapes.

Step-by-step explanation:

Answer:

16x4−4x2+4x−116x4−4x2+4x−1

=16x4−(4x2−4x+1)=16x4−(4x2−4x+1)

=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2

=(4x2−2x+1)(4x2+2x−1)∵a2−b2=(a−b)(a+b

Step-by-step explanation:

The tangent to the curve at a point P (x, y) has slope dy/dx at that point. By the chain rule,

dy/dx = (dy/dθ) / (dx/dθ)

We're in polar coordinates, so

y (θ) = r (θ) sin(θ)   ==>   dy/dθ = dr/dθ sin(θ) + r (θ) cos(θ)

x (θ) = r (θ) cos(θ)   ==>   dx/dθ = dr/dθ cos(θ) - r (θ) sin(θ)

We're given r (θ) = 1 - sin(θ), so that

dr/dθ = -cos(θ)

Then the slope of the tangent to the curve at P is

dy/dx = (dr/dθ sin(θ) + r (θ) cos(θ)) / (dr/dθ cos(θ) - r (θ) sin(θ))

dy/dx = (-cos(θ) sin(θ) + (1 - sin(θ)) cos(θ)) / (-cos²(θ) - (1 - sin(θ)) sin(θ))

dy/dx = - (cos(θ) - sin(2θ)) / (sin(θ) + cos(2θ))

The tangent is horizontal if dy/dx = 0 (or when the numerator vanishes):

cos(θ) - sin(2θ) = 0

cos(θ) - 2 sin(θ) cos(θ) = 0

cos(θ) (1 - 2 sin(θ)) = 0

cos(θ) = 0   or   1 - 2 sin(θ) = 0

cos(θ) = 0   or   sin(θ) = 1/2

[θ = π/2 + 2nπ   or   θ = 3π/2 + 2nπ]   or   [θ = π/6 + 2nπ   or   θ = 5π/6 + 2nπ]

where n is any integer.

In the interval 0 ≤ θ ≤ 2π, we get solutions of θ = π/6, θ = 5π/6, and θ = 3π/2. (We omit π/2 because the denominator is zero at that point and makes dy/dx undefined.) So the points where the tangent is horizontal are themselves (√3/4, 1/4), (-√3/4, 1/4), and (0, -2), respectively.

The tangent is vertical if 1/(dy/dx) = 0 (or when the denominator vanishes):

sin(θ) + cos(2θ) = 0

sin(θ) + (1 - 2 sin²(θ)) = 0

2 sin²(θ) - sin(θ) - 1 = 0

(2 sin(θ) + 1) (sin(θ) - 1) = 0

2 sin(θ) + 1 = 0   or   sin(θ) - 1 = 0

sin(θ) = -1/2   or   sin(θ) = 1

[θ = 7π/6 + 2nπ   or   θ = 11π/6 + 2nπ]   or   [θ = π/2 + 2nπ]

Then for 0 ≤ θ ≤ 2π, the tangent will be vertical for θ = 7π/6 and θ = 11π/6, which correspond respectively to the points (-3√3/4, -3/4) and (3√3/4, -3/4). (Again, we omit π/2 because this makes dy/dx non-existent.)

In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:

4x-5

Answer:

Solution given:

B.g(x)=[tex]\frac{x+5}{4}[/tex]

let

g(x)=y

y=[tex]\frac{x+5}{4}[/tex]

Interchanging role of x and y

we get:

x=[tex]\frac{y+5}{4}[/tex]

doing crisscrossed multiplication

4x=y+5

y=4x-5

So

g-¹(x)=4x-5

Given that,

→ g(x) = x+5/4

Then g(x)=y,

→ y = x+5/4

Now we can interchange role of x and y,

→ x = y+5/4

Then use the cross multiplication,

→ 4x = y+5

→ y = 4x-5

Hence, g-¹(x) = 4x-5 is the solution.

Answer:

216

Step-by-step explanation:

y=k÷x

k=xy

k=9×24

k=216

Answer:

Step-by-step explanation:

Answer to question 1:

On average do part-time students spend less than 20 hours per work on academic work and assignments ?

Answer to question 2:

On average do students work greater than 50 hours a week ?

Answer:

It could be a solution

Step-by-step explanation:

This depends on what equation you are solving. It could be a solution for a quadratic or even a transformation problem.

Answer:

Relative minimum: [tex]\left(-\frac{5}{2}, -\frac{33}{4}\right)[/tex], Relative maximum: [tex]DNE[/tex]

Step-by-step explanation:

First, we obtain the First and Second Derivatives of the polynomic function:

First Derivative

[tex]f'(x) = 2\cdot x + 5[/tex] (1)

Second Derivative

[tex]f''(x) = 2[/tex] (2)

Now, we proceed with the First Derivative Test on (1):

[tex]2\cdot x + 5 = 0[/tex]

[tex]x = -\frac{5}{2}[/tex]

The critical point is [tex]-\frac{5}{2}[/tex].

As the second derivative is a constant function, we know that critical point leads to a minimum by Second Derivative Test, since [tex]f\left(-\frac{5}{2}\right) > 0[/tex].

Lastly, we find the remaining component associated with the critical point by direct evaluation of the function:

[tex]f\left(-\frac{5}{2} \right) = \left(-\frac{5}{2} \right)^{2} + 5\cdot \left(-\frac{5}{2} \right) - 2[/tex]

[tex]f\left(-\frac{5}{2} \right) = -\frac{33}{4}[/tex]

There are relative maxima.

Answer: x=4, y=-6

Step-by-step explanation:

Answer:

1.  e. Convenience sampling is used because students are chosen due to convenience of location.

2. a. University students may not be representative of all people in their age group.

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

Questioning students as they leave an academic building, a researcher asks 341 students about their eating habits.

Students sampled as they leave the build, which is convenience, in this case convenience of location, which means that the correct answer to question 1 is given by option e.

2. What potential sources of bias are present if any. Select all that apply.

Only members of one group are asked(university students), and this may not be representative of the rest of the population, which means that the correct answer to question 2 is given by option a.

The probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

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

where,  n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.

"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"

For given question,

a bag contains 12 red, 3 white and 1 blue balls.

Total balls = 12 + 3 + 1

Total = 16

Two balls are drawn from a bag.

The number of possible ways of drawing 2 balls from the bag are:

Using combination formula,

[tex]^{16}C_2\\\\=\frac{16!}{2!(16-2)!}\\\\ =\frac{16!}{2!\times 12!}\\\\ =120[/tex]

So, n(S) = 120

Two balls are drawn with replacement from a bag.

We need to find the probability that both are red.

Let event A: both the balls are red

[tex]\Rightarrow n(A)=^{12}C_2[/tex]

Using combination formula,

[tex]^{12}C_2\\\\=\frac{12!}{2!\times (12-2)!}\\\\= \frac{12!}{2!\times 10!}\\\\ =66[/tex]

Using probability formula,

[tex]\Rightarrow P(A)=\frac{n(A)}{n(S)}\\\\\Rightarrow P(A)=\frac{66}{120}\\\\\Rightarrow P(A)=\frac{11}{20}[/tex]

Therefore, the probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

9514 1404 393

Explanation:

Your question covers a good bit of the material in an algebra course. The short answer is, "the same way you solve a numerical equation." The point of algebra is that literals can stand for numbers, and so be manipulated the same way numbers are.

Expressions are evaluated according to the Order of Operations. For equations involving a single variable, the equation specifies what operations are being performed on that variable. To find the vale of the variable (solve for that literal), you need to "undo" the operations that are performed on it. As with many problems that have layers, you work down through the layers from the outside in. Generally, that means working through the list of operations "backwards," undoing the last one first.

Simple example

  y = mx + b . . . . . . solve for x

In this equation, the operations performed on x are ...

In accordance with the above, the first thing we do is "undo" the addition of b. (Note that this could be a number or literal--or even a complicated expression--and the process would be exactly the same.) To "undo" addition, we add the opposite.

  y -b = mx +b -b   ⇒   y -b = mx

Next, we "undo" the multiplication by m. That is, we divide by m, or multiply by the reciprocal of m. Either is the same as the other.

  (y -b)(1/m) = (mx)(1/m)   ⇒   (y -b)/m = x

Now, we have solved this literal equation for x.

_____

Throughout this process you must adhere strictly to the properties of equality. That is, anything you do to one side of the equation must also be done to the other side.

The reason you study inverses and identity elements is so you understand that addition of an additive inverse produces the additive identity element:

  x + (-x) = 0

Similarly, multiplication by the multiplicative inverse (reciprocal) produces the multiplicative identity element.

  x · (1/x) = 1

When other operations are involved, such as raising to a power, trig functions, roots, logs, exponentiation, each of these has an associated inverse function that produces an identity:

  (x^a)^(1/a) = x^1 = x

  arcsin(sin(x)) = x

  (√x)^2 = x

  10^(log(x)) = x   or   log(10^x) = x

Some of these inverse functions have restricted domains, so care must be used when solving equations involving them.

When a variable of interest appears on both sides of the equal sign, then you must figure a way to rearrange the equation so the terms with the variable can be combined.

Example:

  ax + b = cx +d . . . . . solve for x

  ax -cx = d -b . . . . . . subtract (cx+b). (Of course, this is subtracted from both sides of the equation.)

  x(a -c) = d -b . . . . . combine x-terms

  x = (d -b)/(a -c) . . . . divide by the coefficient of x

Note that we had to divide the entire right-side expression by the x-coefficient, so had to enclose it in parentheses.

More Complicated Example:

A recent Brainly problem asked for the solution to ...

  T = 2π√(L/g) . . . . solve for L

Here, L is divided by g, a root taken, and that multiplied by 2π. Undoing these in reverse order, we first divide by 2π, square both sides to undo the root, then multiply by g to undo the division:

  [tex]T=2\pi\sqrt{\dfrac{L}{g}}\\\\\dfrac{T}{2\pi}=\sqrt{\dfrac{L}{g}}\\\\\left(\dfrac{T}{2\pi}\right)^2=\dfrac{L}{g}\\\\\boxed{L=g\left(\dfrac{T}{2\pi}\right)^2}[/tex]

The problem posted on Brainly had numbers where some of these variables are. That does not affect the solution method, except that sometimes numerical values can be combined where literal values cannot.

_____

Key Points

Answer:

81

Step-by-step explanation:

Given data:

mean μ = 70.

standard deviation σ, 9.6.

P(Z < 1.123) = 0.13

z = 1.13

Use the z-score formula,

x = z×σ +μ

Substitute the values in the above equation.

x = 1.13 9.6 + 70 = 81

The minimum score required for an A grade is = 81

Answer:

283 flowers

Step-by-step explanation:

c=2pi*r

c = 1130.973 =1131

1131/4

282.75 = 283

9514 1404 393

Answer:

Step-by-step explanation:

a) Angle CAE can be found using the tangent relation.

  tan(∠CAE) = CE/AE

  tan(∠CAE) = 6/20

  ∠CAE = arctan(6/20) ≈ 16.7°

__

b. The length of DF can be found using the law of cosines.

  DF² = FA² +DA² -2·FA·DA·cos(A)

  DF² = 14² +10² -2·14·10·cos(16.7°) ≈ 27.8086

  DF ≈ √27.8086

  DF = 5.3

Complete Question

Assisted-Living Facility Rent.Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486 (the Wall Street Journal, October 27, 2012). Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is s = $650. a. Develop a 90% confidence interval estimate of the population mean monthly rent.

Answer:

[tex]CI: 3388.39<X<3583.61[/tex]

Step-by-step explanation:

Sample Size n=120

Mean \=x =3486

Standard Deviation \sigma=650

Confidence interval CI=0.9

Therefore

Level of sig [tex]\alpha=0.1[/tex]

Therfore

The Critical Value from table is

Z_c=1.645

Generally the equation for Standard error is mathematically given by

[tex]S.E=\frac{\sigma}{\sqrt{n}}[/tex]

[tex]S.E=\frac{650}{\sqrt{120}}[/tex]

[tex]S.E=59.3366[/tex]

Generally the equation for Margin error is mathematically given by

[tex]M.E= = Z_c * SE[/tex]

[tex]M.E=1.65 * 59.34[/tex]

[tex]M.E= 97.61[/tex]

Therefore

[tex]CI= \=x \pm M.E[/tex]

[tex]CI= 3486 \pm 97.61[/tex]

Lower limit

[tex]LL= \=x-M.E=3486-97.6087[/tex]

[tex]LL= 3388.39[/tex]

Upper limit:

[tex]UL= \=x+E=3486+97.6087[/tex]

[tex]UL= 3583.61[/tex]

Therefore The  90% confidence interval estimate of the population mean monthly rent.

[tex]CI: 3388.39<X<3583.61[/tex]

I believe your answer is D.) $900

204 + 96 = 300

300 x 3 = 900

I hope this is correct and helps!

Answer:

Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.

We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.

Remember the relation:

Tan(a) = (opposite cathetus)/(adjacent cathetus)

So, if we define H as the height of the cliff

X as the distance between the observer and the cliff

and h as the height of the flagopole

we can write:

tan(40°) = H/X

tan(45°) = (H + h)/X

Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.

But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.

We want to find the value of h.

If we take the quotient between both equations, we get:

Tan(45°)/Tan(40°) = (H + h)/H

1.192 = (H + h)/H

1.192*H = H + h

1.192*H - H = h

0.192*H = h

So the height of the flagpole is 0.192 times the height of the cliff.

Answer:

b. 28[tex]\pi[/tex] in.

Step-by-step explanation:

circumference of a circle = 2 [tex]\pi[/tex] r

whrere r is the radius of rhe circle

= 2 × [tex]\pi[/tex] × 14 in.

= 28 [tex]\pi[/tex] in.

that is option b

We have to find,

The circumference of the given circle in terms of the π.

The formula we use,

→ C = 2πr

Then we can find the circumference,

→ 2 × π × r

→ 2 × π × 14

→ 28π in.

Hence, option (b) is correct answer.

Answer:

y = -2(x + 3)² + 2

y = 2{ -(x + 3)²+ 1}

y = 2{ -(x² + 6x + 9) + 1}

y = 2{ -x² - 6x - 9 + 1}

y = 2{ -x² - 6x - 8 }

y = -2 { x² + 6x + 8}

OR

y = -2{(x + 4)(x + 2)}

Answer:

a

Step-by-step explanation:

square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8

Answer:

Guessing at least one incorrect answer

Step-by-step explanation:

The complement of guessing 5 correct answers on a 5-question true/false exam is-

Guessing at least one incorrect answer because, when 1 or more questions are incorrectly guessed, the event of 5 correct answers can not occur.

Answer:

Take the picture you uploaded.

Click the rotate button twice.

Done

Answers:

Choice 2) Angle ABC is bisected by ray BD.

Choice 3) BC = 1/2 AC

Choice 5) 2*(angle DBC) = angle ABC

================================================

Explanation:

Since B is the midpoint of AC, this means that AC is cut in half to form the smaller equal pieces AB and BC

We can then say

AB+BC = AC

BC+BC = AC

2BC = AC

BC = (1/2)*AC

which shows why choice 3 is one of the answers

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

Angle ABD is shown to be 90 degrees. Let's say we didn't know angle DBC is also 90. Lets call it x

(angle ABD) + (angle DBC) = 180

90 + x = 180

x = 180 - 90

x = 90

So angle DBC is also 90.

We can see that the 180 degree angle (ABC) is cut in half into two smaller 90 degree angles (ABD and DBC). Therefore, angle ABC has been cut in half and that's why choice 2 is another answer.

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

Using the angle addition postulate, we know that,

(angle ABD) + (angle DBC) = angle ABC

(angle DBC) + (angle DBC) = angle ABC

2*(angle DBC) = angle ABC

Showing why choice 5 is the third answer.

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

Choice 1 isn't true since ray BD helps form angle DBC.

Choice 4 isn't true because there isn't a tickmark on segment BD to indicate it's the same length as BC.

Answer:

separate the x from the numbers it will make the equation easier

Answer:

y = -x.

Step-by-step explanation:

The slope of the line (m) = -1.  ( because of the -x in y = -x - 5)

y - y1 = m (x - x1)    where (x1, y1) is a point on the line, so we get;

y - 2 = -1(x - (-2))

y - 2 = -x + -1 * +2

y - 2 = -x - 2

y = -x.

Answer:

[tex]{ \bf{c). \: g(x) = {2}^{x} - 2 }}[/tex]

Answer:

Price per bottle is 1.5 or $1.50

Step-by-step explanation:

To get price per unit, you just divide the amount of money spent by the items purchased. 9/6 = 1.5

Answer:

20.76%

Step-by-step explanation:

[tex]33000=8000(1+\frac{i}{4})^{4*7}\\4.125=(1+\frac{i}{4})^{28}\\\sqrt[28]{4.125}=1+\frac{i}{4} \\i= .207648169[/tex]

which rounds to 20.76%

Answer:

About 0.2076 or 20.76%.

Step-by-step explanation:

Recall that compound interest is given by the formula:

[tex]\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is applied per year, and t is the number of years.

Since Hannah wants to turn an $8,000 investment into $33,000 in seven years compounded quarterly, we want to solve for r given that P = 8000, A = 33000, n = 4, and t = 7. Substitute:

[tex]\displaystyle \left(33000\right)=\left(8000\right)\left(1+\frac{r}{4}\right)^{(4)(7)}[/tex]

Simplify and divide both sides by 8000:

[tex]\displaystyle \frac{33}{8}=\left(1+\frac{r}{4}\right)^{28}[/tex]

Raise both sides to the 1/28th power:

[tex]\displaystyle \left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}= 1+\frac{r}{4}[/tex]

Solve for r. Hence:

[tex]\displaystyle r= 4\left(\left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}-1\right)[/tex]

Use a calculator. Hence:

[tex]r=0.2076...\approx 0.2076[/tex]

So, the quarterly rate of interest must be 0.2076, or about 20.76%.

Answer:

ghthtf

Step-by-step explanation:

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