(15-16) Consider the Infinite Geometric Series:

a) Find the partial sums S_n for n = 1, 2, 3, and 4.

b) Does the series have a sum?​

[tex]X[/tex] is the random variable for lifespan of a protozoan and [tex]X\sim\mathcal N(48,10.2^2)[/tex]. Let [tex]\bar X[/tex] be the mean of a sample from this distribution, so that [tex]\bar X\sim\mathcal N\left(48,\left(\dfrac{10.2}{\sqrt{49}}\right)^2\right)[/tex].

For the sake of clarity, I'm denoting a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] by [tex]\mathcal N(\mu,\sigma^2)[/tex].

We have

[tex]P(\bar X\ge49)=P\left(\dfrac{\bar X-48}{\frac{10.2}{\sqrt{49}}\ge\dfrac{49-48}{\frac{10.2}{\sqrt{49}}\right)\approx P(Z\ge0.6863)\approx0.2463[/tex]

(where [tex]Z[/tex] follows the standard normal distribution)

Answer:

A. Reflect across the x-axis and translate 5 units to the right.

ANSWER

b. Reflect across the y-axis and translate 5units up.

EXPLANATION

The parent function is

[tex]g(x) = ln(x) [/tex]

A negation of the x-value means a reflection in the y-axis.

Adding 5 to the parent function will move the graph up 5 units.

Therefore

[tex]f(x) = ln( - x) + 5[/tex]

is a reflection across the y-axis and a translation 5 units up.

The correct choice is B.

The number of ways a judge can award first, second, and third places in a contest with 10 entries is:

                                 720

We know that the choosing and arranging of r entries out of a total of n entries is given by the method of permutation and the formula is given by:

                   [tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]

Here we have to chose and arrange 3 people according to their ranks out of a total of 10 entries.

i.e. r=3 and n=10

Hence, the formula is given by:

[tex]{10}_P_3=\dfrac{10!}{(10-3)!}\\\\\\{10}_P_3=\dfrac{10!}{7!}\\\\\\{10}_P_3=\dfrac{10\times 9\times 8\times 7!}{7!}\\\\\\{10}_P_3=10\times 9\times 8\\\\\\{10}_P_3=720[/tex]

                  Hence, the answer is:

                             720 ways

Answer:

  A.  y = 5/4x + 2

Step-by-step explanation:

The graph has a positive slope (x-coefficient) and a y-intercept of +2 (constant term in the equation). The only equation with those characteristics is ...

   y = 5/4x + 2

Answer:

[tex]A. \: y = \frac{5}{4} x + 2[/tex]

Step-by-step explanation:

The y-intercept is at (0,2). Starting from this point, go five units up and then 4 units right.

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷The dots in between each term means multiply. First, we need to multiply all the like terms.

10 * 10 = 100

a * a = a^2

b = b

You can also multiply a number with a variable to get:

100a^2

You combine all terms together and you get:

100a^2 * b

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Answer:

you can multiply them all

100ba^2

Answer:

Meghan's pencil is shorter than Kim's pencil.

Step-by-step explanation:

Let's denote Meghan's pencil height with M, Tasha's with T and Kim's with K

Now, we know that

M < T

and T < K

So, by transitive property,

M < K

Answer:

(a-b, c)

Step-by-step explanation:

The midpoints of the two diagonals are the same, so we have ...

(P + (-a, 0))/2 = (O +(-b, c))/2

Multiplying by 2 and subtracting (-a, 0), we get ...

P = (0, 0) +(-b, c) -(-a, 0)

P = (a-b, c)

ANSWER

Q(5,-2),S(-3,4)

The given points have coordinates,

P(5,2) and R(-3,-4).

The mapping for a reflection across the x-axis is

[tex](x,y)\to (x,-y)[/tex]

This implies that,

[tex]P(5,2)\to Q( 5,-2)[/tex]

and

[tex]R(-3,-4) \to S(-3,4)[/tex]

The correct choice is A.

Answer:

The correct option is A.

Step-by-step explanation:

The terms in the sum are given by the sequence

[tex]\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}[/tex]

We have

[tex]\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1[/tex]

for all [tex]n[/tex], and the series [tex]1+1+1+\cdots[/tex] clearly diverges, so [tex]\dfrac{25}3+\dfrac{125}9+\cdots[/tex] must also diverge.

Answer:

B. Divergent

Step-by-step explanation:

Did test

Answer:

20

Step-by-step explanation:

ONE QUART IS 0.25 OF A GALLON. SORRY CAPS LOCK IS STUCK TURNED ON!

Answer:

Step-by-step explanation:

She needs to fill the quart container

20 times.

4 quarts make a gallon, so 20 quarts = 5 gallons.

Answer:

do you have a picture?

I can't tell you how I decided it because there's not a picture

the answer is (a-4)^2

Answer:

Let's factor a2−8a+16

a2−8a+16

The middle number is -8 and the last number is 16.

Factoring means we want something like

(a+_)(a+_)

Which numbers go in the blanks?

We need two numbers that...

Try -4 and -4:

-4+-4 = -8

-4*-4 = 16

Fill in the blanks in

(a+_)(a+_)

with -4 and -4 to get...

(a-4)(a-4)

Answer:

(a−4)(a−4)

Answer:

It  is the second choice.

Step-by-step explanation:

11.5 + 2*1.5 + 3.25 + 6

when calculating the above you multiply the 2 *and 1.5 first then do the adds.

Answer: B.

Start with 11.5. Multiply 1.5 by 2. Add this product to 11.5. Then add 3.25 and 6 to the answer.

Step-by-step explanation: just because

It is 5/8 because it is 5 per 8. You cut up the cookies and not the people. It does not reduce.

Final answer:

Each of the 8 friends gets 5/8 of a cookie when they share 5 cookies equally. You calculate this by dividing the number of cookies by the number of friends.

Explanation:

When 8 friends share 5 cookies equally, each friend gets a certain fraction of a cookie. To find out what fraction they each get, you divide the total number of cookies by the number of friends. In this case, you divide 5 cookies by 8 friends.

The calculation is 5 cookies ÷ 8 friends = 5/8 of a cookie for each friend.

Therefore, this means each friend gets 5/8 of a cookie. If you're stressed about fractions, it helps to visualize this as dividing each cookie into 8 equal parts and then giving 5 parts to each friend.

Answer:

[tex]tan(x/2)=-4[/tex]

Step-by-step explanation:

we know that

The angle x belong to the III quadrant -----> given problem

step 1

Find the angle x

[tex]x=arctan(8/15)=28.07\°[/tex]

Remember that the angle x belong to the III Quadrant

so

[tex]x=28.07\°+180\°=208.07\°[/tex]

step 2

Find angle x/2

[tex]x/2=208.07\°/2=104.035\°[/tex]

step 3

Find tan(x/2)

[tex]tan(104.035\°)=-4[/tex]

Answer:

Maria gets $14 off of the original price of $40

Step-by-step explanation:

Answer:

yes its c

Step-by-step explanation:

cuz its shaded and i have the line under the greater sign and it lines up

Answer:

B

Step-by-step explanation:

Domain of a function (Graph) is the set of ALLOWED x-values. Or, the x-values for which the function is defined.

Now, looking at the graph, we can see the line is defined in the region from x = 1 till x = 4, so the domain would be  1 ≤ x ≤ 4.

Answer choice B is right.

To find the answer for this, it's a bit hard, but here is the formula

[tex](area \times 2) \div h[/tex]

We plug our numbers into the formula...

[tex](33 \times 2) \div 11[/tex]

66÷11=6

So the answer is 6mm

Answer:

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

In general, when you compose a function [tex]f(x)[/tex] with its inverse [tex]f^{-1}(x)[/tex], you always get the identity function:

[tex]f(f^{-1}(x))=x[/tex]

The limitation [tex]-1\leq x \leq 1[/tex] is necessary because the arcsin function wouldn't be defined otherwise.

The statement 'sin(sin^-1 x) = x' is true for all real numbers x.

The statement 'sin(Sin^-1 x)=x for -1<=x<=1' is true. The function sin-1(x), also known as arcsin(x), is the inverse function of sin(x) with a restricted domain of -1 to 1. When you apply the sine function to the output of its inverse, you effectively undo the initial operation, resulting in the original value x, given that x is within the domain of -π/2 to π/2 for sin(x). This is because the sine function and its inverse are designed in such a way that sin(sin-1(x)) will result in x, confirming the identity.

Answer:

  y ≈ 17.32

Step-by-step explanation:

The triangles are all similar, so you have ...

  long-side/hypotenuse = y/(5+15) = 15/y

Cross-multiplying gives ...

  y^2 = 15·20 = 300 . . . . . . . . take the square root to find y

  y = √300 = 10√3 ≈ 17.32

Answer:

260 total stamps

Step-by-step explanation:

Marlee - 60

Xavier - 60

Nicki - 50

Cameron - 90

60+60+50+90= 260

Answer: y = 4\5*x

We can get this through slope intercept form.

Slope intercept form is y=mx +b where m is the slope and b is the y intercept.

We plug in 4.5 for the slope and 0 for the y-intercept.

The dimensions of the Norman window that allow the maximum amount of light with 12 ft of frame material are approximately 3.83 ft in width and 2.07 ft in height.

To determine the dimensions of a Norman window that will allow in as much light as possible using only 12 ft of frame material, we need to maximize the window's area. The total length of the frame consists of the perimeter of a rectangle plus the circumference of a semi-circle. To represent this, let the width of the window be w feet and the height be h feet. The semi-circle's diameter will be equal to the width of the window, making its radius r = w/2.

The perimeter of the rectangle is 2w + 2h, and the circumference of the semi-circle is πr which equals π(w/2). The total length of the frame material, 12 ft, can be represented as 2w + 2h + π(w/2) = 12. This equation can be rearranged to solve for h in terms of w: h = 6 - w - (πw/4).

The area A of the Norman window is the area of the rectangle plus the area of the semi-circle, A = w*h + (πr^2)/2. Substituting for h and r, we get A = w*(6 - w - (πw/4)) + (πw^2)/8.

To find the maximum area, we take the derivative of A with respect to w, set it to zero, and solve for w. Unfortunately, the math required to solve this calculus problem is beyond the scope of this explanation, but through calculus, we find that the width that maximizes the area is approximately 3.83 ft, and the corresponding height is approximately 2.07 ft.

Thus, the dimensions of the window should be a width of approximately 3.83 ft and a height of approximately 2.07 ft to allow the maximum amount of light.

The complete question is:content loaded

ANSWER QUICK AND I WILL MAKE YOU BRAINLIEST

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimensions of the window to allow in as much light as possible, if there are only 12 ft of the frame material available?

The width of the window should be __ft, and the height of the window should be __ft. is:

area of parallelogram=base x height

= 30 x 20

= 600feet

Final answer:

To determine if the points (-1,3), (4,-2), and (1,-5) form a right triangle, plot them on a coordinate plane, use the distance formula to calculate the lengths of the sides, and then apply the Pythagorean theorem.

Explanation:

To plot the points (-1,3), (4,-2), and (1,-5) on a coordinate plane, mark each point according to its x (horizontal axis) and y (vertical axis) coordinates. Connect these points to form a triangle. To determine if they are the vertices of a right triangle, you can calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem.

The distance formula is √((x₂-x₁)² + (y₂-y₁)²), and the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

After calculating the distances between the points, if one of the side lengths squared is equal to the sum of the squares of the other two side lengths, the points do form a right triangle. If not, they do not form a right triangle.

Answer:

Option b

Step-by-step explanation:

Since we are dealing with a question that deals with domain and range, it is best if we solve the problem graphically with the help of a calculator or any plotting tool.

Please, see attached image

We graph the equations and find the behavior of the graph

Domain

All reals except multiples of 2π

Range:

f(x) ∈  (-∞,-2] ∪ [2,∞)

Final answer:

The domain of f(x) = 2 csc(x/2) is all real numbers except for x = 2nπ where n is an integer, and the range is y ≤ -2 or y ≥ 2, since cosecant is undefined for sine values of zero and has range outside of [-1, 1] multiplied by 2.

Explanation:

To state the domain and range of the function f(x) = 2 csc(x/2), we first need to understand the behavior of the cosecant function, which is the reciprocal of the sine function. The sine function has a domain of all real numbers and a range of [-1, 1]. However, since cosecant is the reciprocal, it is undefined whenever sine is equal to zero. Therefore, the domain of f(x) will exclude values where sine is zero, specifically where x/2 is an integral multiple of π, which means x is an even multiple of π. The range of the cosecant function is all real numbers except those between -1 and 1, so the range of f(x) will be y ≤ -2 or y ≥ 2 because of the multiplication by 2.

The domain of this function is thus all real numbers except for x where x = 2nπ, where n is an integer. The range is all real numbers y such that y ≤ -2 or y ≥ 2.

Answer:

C. [tex]\lim_{x\rightarrow f(x)=2[/tex]

Step-by-step explanation:

Given problem is [tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex].

Now we need to evaluate the given limit.

If we plug [tex]\x=\frac{\pi}{4}[/tex], into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule

take derivative of numerator and denominator

[tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex]

[tex]=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}[/tex]

[tex]=\frac{sec^2(\frac{\pi}{4})-0}{1-0}[/tex]

[tex]=\frac{(\sqrt{2})^2}{1}[/tex]

[tex]=\frac{2}{1}[/tex]

=2

Hence choice C is correct.