The population, p, in thousands of a resort community is given by P(t)=700t/4t[tex]x^{2}[/tex]+9

Answer:  see below

Step-by-step explanation:

1) Foci is plural for Focus.  Since a hyperbola has two focus points, they are referred to as foci.  The foci is where the sum of the distances from any point on the curve to the foci is constant.

2) When determining the equation of a hyperbola you need the following:

    a)  does the hyperbola open up or to the right?

    b)  what is the center (h, k) of the hyperbola?

    c)  What is the slope of the asymptotes of the hyperbola?

3) The equation of a hyperbola is:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]

Answer:

[tex]a^9 + b^ 5 + c^{13}[/tex]

Step-by-step explanation:

[tex](a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)[/tex]

When bases are same and it is multiplication, then add the exponents.

[tex](a^{5+4})+(b^{2+3})+(c^{7+6})[/tex]

[tex](a^9)+(b^ 5) + (c^{13})[/tex]

Apply rule : [tex](a^b)=a^b[/tex]

[tex]a^9 + b^ 5 + c^{13}[/tex]

Answer:

[tex]a^9+b^5-c^{13[/tex]

Step-by-step explanation:

[tex](a^5*a^4) + (b^2*b^3)-(c^7*c^6)[/tex]

When bases are same, powers are to be added.

=> [tex](a^{5+4})+(b^{2+3})-(c^{7+6})[/tex]

=> [tex]a^9+b^5-c^{13[/tex]

Answer:

3x

Step-by-step explanation:

18 x^2 / 6x

Divide the numbers

18/6 =3

Then divide the variables

x^2 /x = x

The result is 3x

Answer:

3x

Step-by-step explanation:

18x^2/6x

x^2 / x is x

18x/6

18/6 is 3

it all simplifies into 3x

Answer:

The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.

Step-by-step explanation:

A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.

Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:

[tex]2\cdot \alpha = 120^{\circ}[/tex]

[tex]\alpha = 60^{\circ}[/tex]

The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])

[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]

[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]

[tex]\beta = 180^{\circ}-\alpha[/tex]

[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]

[tex]\beta = 120^{\circ}[/tex]

The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.

Answer: m= 2

Step-by-step explanation: First Expand the brackets! 5-m+4=2m+3m-3

                                    Then Do the addition and subtraction in both sides!

                                     9-m=5m-3

                                 Then bring m to one side and the constants the other!

                                   6m=12

                                    Then solve for m where m=2

                                     If you want you can check your answer bu substituting m as 2. 5-(2-4)=7 and 2(2) + 3(2-1) which also = 7.

Answer:

Step-by-step explanation:

Given the statement "subtract y from 5", we are to express the statement mathematically. Expressing mathematically is as shown;

5 - y

Since we are removing the value of a variable y from 5, the variable we are subtracting will come last in the expression.  For example say, we want to subtract 5 from 10, since we are taking out 5 from 10, the value of 5 will come last in the expression i.e 10 - 5 not 5 - 10.

According to the statement in question, we can see that we are to subtract y from 5, therefore y will come last in our expression and will be expressed as 5 - y

Answer:

Two possible sets of answers.

5 men, 11 women and 42 children, or

10 men, 2 women and 88 children

Selamat Sadhya!

Step-by-step explanation:

M = number of men

W = number of women

100-M-W = number of children

Total number of pappadas

5M+3W+(100-M-W)/2 = 100

Solve for W

W = (100-9M)/5 .......................(1)

Examine equation (1).

In order to have W as a whole number, M must be multiple of 5

Therefore M = 5 or 10

If M = 5, W = (100-45)/5 = 11 and children = 100-5-11 =  84

If M = 10, W = (100-90)/5 = 2 and children = 100-10-2 = 88

Answer:

√468 = 6√13

Step-by-step explanation:

ABCDEF is a regular hexagon of side length 6.

A'B'C'D'E'F' is the reflection of ABCDEF across BC.

The line FE' is the line from F to E'.  It is also the hypotenuse of the right triangle FEE'.  FE = 6, and EE' = 4a, where a is the apothem of the hexagon.

To find the apothem, draw the 30-60-90 triangle formed by the apothem and the radius (essentially 1/12th of the hexagon).

Using properties of a 30-60-90 triangle:

a = (6/2)√3

a = 3√3

4a = 12√3

Using Pythagorean theorem:

x² = (6)² + (12√3)²

x² = 36 + 432

x = √468

x = 6√13

Answer:

0.0035289

Step-by-step explanation:

From the question;

mean annual salary = $63,500

n = sample size = 31

Standard deviation = $6,200

Firstly, we calculate the z-score of $60,500

Mathematically;

z-score = x-mean/SD/√n = (60500-63500)/6200/√(31) = -2.6941

So we want to find the probability that P(z < -2.6941)

We can get this from the standard normal table

P( z < -2.6941) = 0.0035289

Answer:

The answer is 29 unit.

Step-by-step explanation:

Here,

given that,

DC (l) =4z+1

CD (b)=5z+2

perimeter (p)= 132

now,

perimeter of rectangle (p) is= 2(l+b)

or, 132 = 2×{(4z+1)+(5z+2)}

or, 132= 2×(9z+3)

or, 132= 18z+6

or, 18z=132-6

or, z=126/18

or, z= 7.

therefore, 4z+1=4×7+1=29

5z+2= 5×7+2=37.

As our question is about to find AB,

DC = AB. (as opposite side of rectangle is equal).

so, the valueof AB is 29unit.

Hope it helps...

Answer:  60

Step-by-step explanation:

Formula to calculate sample size (n):

[tex]n=(\dfrac{\sigma\times z^*}{E})^2[/tex]

, where [tex]\sigma[/tex] = population standard deviation, E Margin of error , z* = critical value for the confidence interval.

As per given , we have

E =5

[tex]\sigma=15[/tex]

Critical value for 99% confidence = 2.576

Then,

[tex]n=(\dfrac{15\times2.576}{5})^2\\\\\Rightarrow\ n=59.721984\approx60[/tex]

So, Required sample size = 60 .

Answer:

D. 11.8 cm.

Step-by-step explanation:

This is a 30-60-90 triangle, which means that the hypotenuse is 2x, the short leg is x, and the long leg is x[tex]\sqrt{3}[/tex].

In this case, the hypotenuse is 5.

5 / 2 = 2.5. That is the short leg.

The long leg is 2.5 * [tex]\sqrt{3}[/tex] = 4.330127019.

5 + 2.5 + 4.330127019 = 7.5 + 4.330127019 = 11.83012702, which is about D. 11.8 cm.

Hope this helps!

Answer:

24

Step-by-step explanation:

The computation of the number  of bacteria in the sample after 18 hours is shown below:

We assume the following things

P = 4 = beginning number of bacteria

rate = r = 0.1

Now

We applied the following formula

[tex]A = Pe^{rt}[/tex]

[tex]= 4\times e^{18\times0.1}[/tex]

[tex]=4e^{1.8}[/tex]

[tex]= 4\times6.049647464[/tex]

= 24

We simply applied the above formula to determine the number of bacteria after the 18 hours

Answer:

[tex]\boxed{Cos A = 3/5}[/tex]

Step-by-step explanation:

Cos A = Adjacent/Hypotenuse

Where Adjacent = 30 and Hypotenuse = 50

Cos A = 30/50

Cos A = 3/5

Answer:

[tex]\boxed{\mathrm{cos(A) = \frac{3}{5} }}[/tex]

Step-by-step explanation:

[tex]\displaystyle \mathrm{cos(\theta) = \frac{adjacent}{hypotenuse} }[/tex]

The adjacent side to angle A is 30 units. The length of the hypotenuse of the triangle is 50 units.

[tex]\displaystyle \mathrm{cos(A) = \frac{30}{50} }[/tex]

The fraction can be simplified.

Answer:

D) 53 Degrees.

Step-by-step explanation:

Things we need to establish beforehand: We know that Lines OZ and OX are equal because they are both radii of the circle. We can make an Iscoceles traingle by drawing a line between ZX. We know angle YZO and angle YXO is a right angle because YZ and XY are tangent to the circle. The Arc angle is the same angle as angle ZOX.

1) Find angles OZX and OXZ. these will be 26.5, because 180-127 is 53, which is the sum of the two angles. the two angles are the same, so divide 53 by 2.

2) Find Angles XZY and ZXY. We know that YZO is a right angle, and both XZY and OZX make up this right angle so XZY + OZX = 90. OZX is 26.5, so 90-26.5=XZY. XZY = ZXY, so both angles equal 63.5.

3) Now that we have two angles of triangle XYZ, we can find angle XYZ.     180-(XZY+ZXY)=XYZ, so (180-(63.5+63.5)=53. Angle XYZ=53.

Answer:

We conclude that the true average stopping distance exceeds this maximum value.

Step-by-step explanation:

We are given the following observations that are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.;

X = 32.1, 30.9, 31.6, 30.4, 31.0, 31.9.

Let [tex]\mu[/tex] = true average stopping distance

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 30      {means that the true average stopping distance exceeds this maximum value}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30      {means that the true average stopping distance exceeds this maximum value}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                              T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean stopping distance = [tex]\frac{\sum X}{n}[/tex] = 31.32 ft

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 0.66 ft

            n = sample size = 6

So, the test statistics =  [tex]\frac{31.32-30}{\frac{0.66}{\sqrt{6} } }[/tex]  ~  [tex]t_5[/tex]

                                    =  4.898

The value of t-test statistics is 4.898.

Now, at 0.01 level of significance, the t table gives a critical value of 3.365 at 5 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 4.898 > 3.365, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average stopping distance exceeds this maximum value.

Answer:

(0,0), (-4,0), (0,-5).

Step-by-step explanation:

Note: Matrices are not in proper format.

Consider the given matrix is

[tex]T=\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]

It means vertices are (0,0), (4,0) and (0,5).

Transformation matrix is

[tex]A=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}[/tex]

To find the coordinates of the transformed triangle multiply both matrices and calculate matrix AT.

[tex]AT=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]

[tex]AT=\begin{bmatrix}\left(-1\right)\cdot \:0+0\cdot \:0&\left(-1\right)\cdot \:4+0\cdot \:0&\left(-1\right)\cdot \:0+0\cdot \:5\\ 0\cdot \:0+\left(-1\right)\cdot \:0&0\cdot \:4+\left(-1\right)\cdot \:0&0\cdot \:0+\left(-1\right)\cdot \:5\end{bmatrix}[/tex]

[tex]AT=\begin{bmatrix}0&-4&0\\ 0&0&-5\end{bmatrix}[/tex]

It means coordinates of the transformed triangle are (0,0), (-4,0), (0,-5).

Answer:

A

Step-by-step explanation:

E2020

Answer:

-2             7

-1             -6

Step-by-step explanation:

I used a calculator.

Answer:

[tex]\large \boxed{\sf \ \ 9 \text{ and } 22 \ \ }[/tex]

Step-by-step explanation:

Hello,

We can write that, x being the second number

(4 + 2*x) *x = 198

Let's solve this equation.

[tex](4+2x)x=198\\\\4x+2x^2=198 \\\\\text{*** subtract 198 from both sides ***}\\\\2x^2+4x-198 = 0\\\\\text{*** The product of the zeroes is -198/2=-99=-11*9 and their sum is -4/2=-2 ***}\\\\2x^2+4x-198=2(x-9)(x+11)=0\\\\x=9 \ \ or \ \ x=-11[/tex]

We are looking for positive number so the solution is 9.

And the first number is 4 + 2 * 9 = 4 + 18 = 22

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

22 and 9

Step-by-step explanation:

Let the positive number be x.

Let the other number be y.

x = 2y + 4

xy = 198

Substitute x as 2y + 4 in the second equation.

(2y+4)y = 198

2y² + 4y = 198

2y² + 4y - 198 = 0

2(y-9)(y+11) = 0

y-9=0 or y+11=0

y=9

y=-11

The product is 198, so y is positive.

x(9)=198

x=22

Answer:

y=5x-33

Step-by-step explanation:

We are given a point and a slope. Use the slope-intercept formula.

[tex]y-y_{1} =m(x-x_{1} )[/tex]

where (x1, y1) is a point on the line and m is the slope.

The slope is 5 and the point is (5,-8).

x1=5

y1= -8

m=5

[tex]y--8 =5(x-5 )[/tex]

We want to find the equation of the line, which is y=mx+b (m is the slope and b is the y-intercept). Therefore, we must get y by itself on one side of the equation.

[tex]y+8=5(x-5)[/tex]

First, distribute the 5 on the right side of the equation. Multiply each term inside the parentheses by 5.

[tex]y+8=(5*x)+(5*-5)[/tex]

[tex]y+8=5x-25[/tex]

Next, subtract 8 from both sides since it is being added on to y.

[tex]y+8-8=5x-25-8[/tex]

[tex]y=5x-25-8[/tex]

[tex]y=5x-33[/tex]

The equation of the line is: y=5x-33

Answer:

The answer would be 27π

Step-by-step explanation:

the area is 36pi and the shaded region is 3/4 of the circle, as a 90 degree angle is 1/4 of a 360 degree circle. 3/4 of 36pi is 27pi

Answer:

27π

Step-by-step explanation:

Imagine that this circle was complete. As you can see, only 3 / 4th of the circle remains, with respect to this whole circle. This is not an assumption, though it does appear so. The portion missing forms a right angle with the radii, and thus by definition, that portion is a quarter of a circle.

________

The simplest approach is to assume this circle to be complete, and solve for that area - provided the radii being 6 inches. Afterward we can take 3 / 4th of this area, solving for the area of the shaded region. After all, this circle is 3 / 4ths of our " complete circle. "

Area of an Imaginary " Complete Circle " = π[tex]r^2[/tex] = π[tex](6)^2[/tex] = 36π,

Area of Shaded Region ( 3 / 4th of the " Complete Circle " ) = [tex]\frac{3}{4}[/tex]( 36π ) = 27π

27π is the exact area of the shaded region. If you want an approximated area, take π as 3.14, or a similar quantity to that.

Answer:

For me, ill say there are many ways it can be done.

First, u can pick at random. Or u can decide to do it boys and girls

Step-by-step explanation:

Answer:

192

Step-by-step explanation:

There are a total of 15 marbles . When the lavender is left out 14 remain.

Using combinations we find that each of the four color marbles can be chosen in the following way.

2C1*4C1*4C1*6C1= 2*4*4*6=  192

We select  one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.

Answer:

y=-192

Step-by-step explanation:

¡Hola! ¡Ojalá esto ayude!

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

La fórmula para calcular el área de cualquier triángulo es:

base multiplicada por la altura y dividida por dos.

||

||

||

\/

Bh / 2.

Answer:

Part A: no solution

Part B: Distributive property of multiplication over addition.

Step-by-step explanation:

Part A:

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 6x - 11

6x - 6 = 6x - 11

-6 = -11

Since -6 = -11 is a false statement, there is no solution.

Number of solutions: 0

Part B:

Property used: Distributive property of multiplication over addition.

Part A: Here are the steps I used to solve this equation-

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 6x - 11

6x - 6 = 6x - 11

-6 = -11

Since -6 = -11 is a false statement, there is no solution.

The final number of solutions: 0

Part B: I used the distributive property of multiplication over addition.

Answer:

Vertical angles are congruent.

Step-by-step explanation:

Vertical angles are opposite angles formed by intersecting lines, and are always congruent.