Find sin θ if cos θ = 4/7 and θ in quadrant IV.

Answer:  B) 110

Step-by-step explanation:

It is stated that DE and XY are parallel.

Therefore, 110° and x° are Corresponding Angles, which means they are congruent (equal).

110° = x°

110 = x

Answer:

Solution,

Complement of 70°

=90°-70°

=20°

hope this helps...

Good luck on your assignment..

Answer:

20°

Step-by-step explanation:

Complement of 70° is 90°-70°= 20°  

To determine the complement, subtract the given angle from 90.

Answer:

Step-by-step explanation:

Step1 : Verify Sn is valid for n = 1

Answer:

x = -1.796, 7.796

Step-by-step explanation:

3x² - 18x + 5 = 47

3x² - 18x - 42 = 0

use quadratic equation

x = -1.796, 7.796

Answer:

x = 3 +/- √23

Step-by-step explanation:

got it right on edg

Answer:

There is 9 on each pace and 3 on a row

Step-by-step explanation:

54/6=9

if there is 9 on each side and the same on each side, then it has to be 3 in each row and column. Also, this is a Rubix cube

Please give me brainliest, it really helps! :)

Have a good day!

The value of root 10 is between 3 and 3.5

Answer:

correct answer is 456 sq units.

Step-by-step explanation:

Let us have a look at the formula for Surface Area of a prism:

[tex]A =p \times h+2 \times B[/tex]

Where p is the perimeter of base

h is the height of prism

and B is the base area of prism.

Given that:

h = 7.5 units

Hypotenuse of prism's base = 20 units

One of the Other sides = 12  units

Pythagorean theorem can be used to find the 3rd side of right angled base.

Square of hypotenuse = Sum of squares of other two sides

[tex]20^2=12^2+side^2\\\Rightarrow 400=144+side^2\\\Rightarrow side =\sqrt{256}\\\Rightarrow side =16\ units[/tex]

Area of base = area of right angled triangle:

[tex]B = \dfrac{1}{2} \times \text{Base Length} \times \text{Perpendicular Length}\\\Rightarrow B = \dfrac{1}{2} \times 16\times 12 = 96\ sq\ units[/tex]

Perimeter [tex]\times[/tex] height = (12+20+16) [tex]\times[/tex] 7.5 = (48) [tex]\times[/tex] 7.5 = 360 sq units

Now putting the values in formula:

Surface area, A = 360+96 = 456 sq units

So, correct answer is 456 sq units.

Answer:

The probability that 25% or more in the sample speak Spanish is 76%.

Step-by-step explanation:

Sample of 75 Americans

If 25% or more in the sample speak Spanish, it can be deduced that 24% do not speak Spanish.

The proportion of those who do not speak Spanish is 18 (24% of 75)

Therefore, the proportion of those who speak Spanish is 57 (75 - 19)

This implies that 57/75 x 100 = 76% of the sample speak Spanish.

This 76% of the sample who speak Spanish is equal to the 25% or more who do speak Spanish in the sample.

Probability is the chance that an event may occur from many other events that could have occurred.  It is an educated guess or estimate of something or one event happening when all the events in the set are given an equal chance.

Answer:

0.181818

Step-by-step explanation:

There are total 11 candies. The possibility of combinations is 165 which is found by using computation technique 11C3. It is assumed that order does not matter. There are 3 pieces of candy are selected at random. There are 6C2 which is 15 different ways to select cherry and lemon. There are 30 ways to choose 2 cherry and a lemon combination. The probability is [tex]\frac{30}{165}[/tex] = 0.181818

Answer:

x = 5

Step-by-step explanation:

Note: I'm assuming this shape is a trapezoid, so I'm basing a theorem of that fact. Tell me if it's not a trapezoid.

    1. Identify the theorem:

          There is a theorem you can use for this problem that states that the length of the meadian of a trapezoid is equal to the average of the lengths of the bases of the trapezoid.

      So what I mean is:

    (Base 1 Length + Base 2 Length)/2 = length of the median of a trapezoid

     2. Identify:

             Base 1:  FC = 6x-6

             Base 2:  AD = 38

             Median:  EB = 7x-4

      3. Substitute:

  (Base 1 Length + Base 2 Length)/2 = length of the median of a trapezoid

              (FC + AD)/2 = EB    

              (6x-6 + 38)/2 = 7x-4

       4. Solve for x:

                x = 5  

Answer:

4x^3 + 2x^2 +8x -9

Step-by-step explanation:

A third degree polynomial is a  is a polynomial whose highest power of x is to the power of three.  Standard form is

Ax^3 + Bx^2 + Cx + D where A is non zero

An example would be

4x^3 + 2x^2 +8x -9

Answer:

0, 4, -4 and they may want you to mention formally all the kt multiples of [tex]\pi[/tex].

Step-by-step explanation:

Let's do the second derivative of the function: [tex]y(t)=sin(k\,t)[/tex]

[tex]y'(t) =k\,cos(k\,t)\\y"(t)=-k^2\,sin(kt)[/tex]

So now we want:

[tex]y"+16\,y'=0\\-k^2\,sin(kt)+\,16\,sin(kt)=0\\sin(kt)\,(16-k^2)=0\\[/tex]

Then we have to include the zeros of the binomial ([tex]16-k^2[/tex]) which as you say are +4 and -4, and also the zeros of [tex]sin(kt)[/tex], which include all those values of

[tex]kt=0\,,\,\pi\,\,,\,2\pi\, ,\,etc.[/tex]

So an extra one that they may want you to include is k = 0

Answer:

A(s) = 255.8857

Step-by-step explanation:

Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface z = e^-x^2-y^2 that lies above the disk x2 + y2 ≤ 81.

Given that:

[tex]Z = e^{-x^2-y^2}[/tex]

By applying rule; the partial derivatives with respect to x and y

[tex]\dfrac{\partial z }{\partial x}= -2xe^{-x^2-y^2}[/tex]

[tex]\dfrac{\partial z }{\partial y}= -2ye^{-x^2-y^2}[/tex]

The integral over the general region D with respect to x and y is :

[tex]A(s) = \int \int _D \sqrt{1+(\dfrac{\partial z}{\partial x} )^2 +(\dfrac{\partial z}{\partial y} )^2 }\ dA[/tex]

[tex]A(s) = \int \int _D \sqrt{1+(-2xe^{-x^2-y^2})^2 +(-2ye^{-x^2-y^2})^2 } \ dA[/tex]

[tex]A(s) = \int \int _D \sqrt{1+4x^2({e^{-x^2-y^2})^2 +4y^2({e^{-x^2-y^2}})^2 }} \ dA[/tex]

[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)({e^{-x^2-y^2})^2 }} \ dA[/tex]

[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)e^{-2}({{x^2+y^2}) }} \ dA[/tex]

By relating the equation to cylindrical coordinates

[tex]A(s) = \int \int_D \sqrt{1+4r^2 e^{-2r^2} }. rdA[/tex]

The bounds for integration for the circle within the cylinder [tex]x^2+y^2 =81[/tex] is r =9

[tex]A(s) = \int \limits ^{2 \pi}_{0} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }. dr d\theta[/tex]

[tex]A(s) = {2 \pi} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }\ dr[/tex]

Using integral calculator to estimate the  integral,we have:

A(s) = 255.8857

Step-by-step explanation:

6

[tex]6 \sqrt{6} [/tex]

Answer:

6√6is the exact answer

Answer:

1320 ways

Step-by-step explanation:

To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!

12! is the same as 12x11x10x9x8... etc

But in this problem, we are only looking for the top 3.

We can set up a formula

[tex]\frac{n!}{(n-r)!}[/tex]

N is the number of options that are available and r represents the amount we are choosing

In this case, we have 12 teams so n=12

We are looking for the top 3 so r=3

[tex]\frac{12!}{(12-3)!}[/tex]

[tex]\frac{12!}{9!}[/tex]

We expand the equation and cancel out

[tex]\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}[/tex]

Notice how both sides can cancel out every number 9 and below

That leaves us with 12x11x10

1320 ways

The possible ways for the gold, silver, and bronze medals to be awarded is 1320

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Given that, there are 12 teams, each representing a different country, in a women’s Olympic basketball tournament.

We need to find that, in how many ways is it possible for the gold, silver, and bronze medals to be awarded,

Using the concept of permutation, to find the number of ways

ⁿPₓ = n!/(n-x)!

= 12! / (12-3)!

= 12! / 9!

= 1320

Hence, the possible ways for the gold, silver, and bronze medals to be awarded is 1320

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Answer:

47.5%.

Step-by-step explanation:

60 is 2 standard deviations below the mean.

According to the emperical rule, there is approximately 90% of normally distributed  data within 2 standard deviations of the mean. Your interval is half of  that because it is the data between the mean and two standard deviations

below the mean. therefore, the answer is 47.5%.

The percentage of scores that lie between 60 and 80 is 47.75%

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation[/tex]

Given that:

μ = 80, σ = 10

[tex]For\ x=60:\\\\z=\frac{60-80}{10} =-2\\\\For\ x=80:\\\\z=\frac{80-80}{10} =0[/tex]

P(60 < x < 80) = P(-2 < z < 0) = P(z < 0) - P(z < -2) = 0.5 - 0.0228 = 47.75%

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Answer:

Step-by-step explanation:

Everything to know about a and b!

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0, −5)

Focus: (0, [tex]-\frac{19}{4\\}[/tex]−)

Axis of Symmetry: x = 0

Directrix: y = [tex]-\frac{21}{4}[/tex]

For Part b

Table:

x    |     y

______

−2      −1

−1      −4

0       −5

1        −4

2       −1

Answer:

The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].

Step-by-step explanation:

The equation of the curvature is:

[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]

The parametric componentes of the curve are:

[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]

The first and second derivative associated to each component are determined by differentiation rules:

First derivative

[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]

[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]

Second derivative

[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]

[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]

[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]

[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]

Now, each term is replaced in the the curvature equation:

[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]

And the resulting expression is simplified by algebraic and trigonometric means:

[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]

[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]

[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]

[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]

[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]

The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].

Answer:

It will take 5.6 hours to get the given population (3300) of the bacteria.

Step-by-step explanation:

A function that defines the population increase of a bacteria is,

B(h) = [tex]1425e^{0.15h}[/tex]

where h = duration or number of hours for bacterial growth

B(h) = Final population

If the final bacterial population is 3300,

3300 = [tex]1425e^{0.15h}[/tex]

By taking log on both the sides of the equation,

ln(3300) = [tex]ln(1425e^{0.15h})[/tex]

8.10168 = ln(1425) + [tex]ln(e^{0.15h})[/tex]

8.10168 = 7.261927 + 0.15h

h = [tex]\frac{8.10168-7.261927}{0.15}[/tex]

h = 5.5983

h ≈ 5.6 hours

Therefore, it will take 5.6 hours to get the given population (3300) of the bacteria.

Answer:

A) Brown-Brown ,Brown-Blue, Blue-Brown, Blue-Blue  B) 1/4 =0,25   C)3/4=0,75

Step-by-step explanation:

Lets mother's  "BROWN" is  "BROWN-M",  

mother's "BLUE"  is  " BLUE-M"

Lets  father's  "BROWN" is "BROWN-F" and

father's  "BLUE " is  "BLUE-F"

The kid can have the genotype as follows (list of possible outcomes) :

1. BROWN-M>BROWN-F   ( received BROWN as from mother as from father)

2. BROWN-M>BLUE-F  ( Received BROWN from mother and BLUE from father)

3. BLUE-M>BROWN-F ( Received BLUE from mother and Brown from father)

4.  BLUE-M>BLUE-F ( Received BLUE as from mother as from father)

b) As we can see in a) only 1 outcome from 4 is BLUE-BLUE.  So the probability of BLUE-BLUE genotype is

P(BLUE>BLUE)=1/4=0.25  

c) As we know that if the child has at least one brown allele, that color will dominate and the eyes will be brown.

It means that outcomes BROWN-BROWN, BROWN-BLUE and BLUE-BROWN determine brown color of eye. So the number of these outcomes is 3. Total amount of outcomes is 4.

So probability that eyes are brown is P(Brown eyes)=3/4 =0.75

Answer:

21.7 metres (assuming the triangle is a right triangle)

Step-by-step explanation:

Assuming this is a right triangle, we can simply use the Pythagorean Theorem, which states that in a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, a = 20, b = 8.5, and R = c. Plug these in:

a² + b² = c²

20² + 8.5² = R²

400 + 72.25 = R²

472.25 = R²

R = √472.25 ≈ 21.7 m

Thus, R is about 21.7 metres.

~ an aesthetics lover

Answer:

a-The mean age and median age are unchanged.

Step-by-step explanation:

By adding the same you are subtracting, the sum of the ages remains the same. Therefore, the mean remains the same since you are dividing the same total of ages by the same number of people.

The middle number continues to be the middle number, so the median also does not change.

Try an example.

The ages are 30, 40, 50, 60, 70

Mean = (30 + 40 + 50 + 60 + 70)/5 = 250/5 = 50

Median: 50

Now add 10 to the greatest value and subtract 10 from the least value.

The ages now are 20, 40, 50, 60, 80

Mean = (20 + 40 + 50 + 60 + 80)/5 = 250/5 = 50

Median: 50

As you can see, both the mean and the median did not change.

Answer: a-The mean age and median age are unchanged.

Answer:

The mean age and median age are unchanged

Step-by-step explanation:

The median will not change when we alter the lowest and highest values so we can eliminate the answers that say the median changes

The mean is found by adding the values together and dividing by the number of values

If we add 10 and subtract 10, we have not changed the total value before dividing, so the mean does not change

Answer:

10 rows with 6 passengers per row

Step-by-step explanation:

Let x be the number of rows and y the number of passengers per row.

Then we can interpret the story as the following two equations:

xy=60

(x+2)(y-1)=60

Solving these two equations:

y=60/x

(x+2)(60/x-1)=60     (substitute y)

60 - x + 120/x - 2 = 60 (multiply by -x)

x² + 2x - 120 = 0     (factor)

(x-10)(x+12) = 0

x = 10

y = 60/10 = 6

and indeed 10 * 6 = 60 and also 12 * 5 = 60

Answer:

144w[(u - 1)(u + 1)]

Step-by-step explanation:

144w is the highest common factor of the binomial.

144u^2w - 144w = 144w(u^2 - 1) = 144w[(u - 1)(u + 1)]

Answer:

The answer is below

Step-by-step explanation:

What we should do is the following:

First, from the random sample of 852 researchers, it is necessary to obtain the number of adult residents who consumed alcohol in the past year.

After the above, we must calculate the proportion of adult residents who consumed alcohol in the last year by dividing the number of adult residents who consumed alcohol in the last year by 852.

After this, we must compare if the proportion is exactly 70% or different from it.

We have the following hypotheses:

Null Hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is exactly 70%

Alternative hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is not equal to 70%

Answer:

12.566370614359172953850573533118

Step-by-step explanation:

Answer:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X= 38.91[/tex]

And we can find the bias with this formula:

[tex] Bias= \bar X -\mu[/tex]

And replacing we got:

[tex] Bias = 38.91 -40 = -1.09[/tex]

Step-by-step explanation:

For this problem we know that the random variable of interest follows this distribution:

[tex]X \sim N(\mu =40, \sigma= 10)[/tex]

And we have the following random sample given:

39.2, 45.7, 27.4, 25.9, 25.1, 46.3, 42.9, 49.0, 40.6, 47.0

And we can calculate the sample mean with the following formula:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X= 38.91[/tex]

And we can find the bias with this formula:

[tex] Bias= \bar X -\mu[/tex]

And replacing we got:

[tex] Bias = 38.91 -40 = -1.09[/tex]

Answer:

(B) 25%

Step-by-step explanation:

Answer:

I think it's 49 I'm sry if I'm wrong hope you luck

Step-by-step explanation:

Answer: 49

Step-by-step explanation: Apex said so

Answer:

C

Step-by-step explanation:

Given f(x) then f(x + k) represents a horizontal translation of f(x)

• If k > 0 then shift left by k units

• If k < 0 then shift right by k units

Here the shift is 4 units to the left, thus

y = (x + 4)²

Given f(x) then f(x) + k represents a vertical translation of f(x)

• If k > 0 then shift up by k units

• If k < 0 then shift down by k units

Here the shift is 3 units down, thus

y = (x + 4)² - 3 → C

y = (x+4)²-3 is the result of translating y = x² downward by 3 units and to the left by 4 units

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We need to find the function is the result of translating y = x² downward by 3 units and to the left by 4 units

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the axis.

To translate the graph of y = f(x) three units downward, subtract 3 from f(x) which becomes y = x²-3

To translate the graph four units to the left, replace x by x+4

y = (x+4)²-3

Hence,  y = (x+4)²-3 is the result of translating y = x² downward by 3 units and to the left by 4 units

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