2. The average score Josie had in 6 subjects is 72 and her average score after 2 additional
subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the
8
th subject correct to the nearest whole number?

2. The integration region,

[tex]\left\{(r,\theta)\mid\dfrac\pi6\le\theta\le\dfrac\pi2\land2\le r\le3\right\}[/tex]

corresponds to what you might call an "annular sector" (i.e. the analog of circular sector for the annulus or ring). In other words, it's the region between the two circles of radii [tex]r=2[/tex] and [tex]r=3[/tex], taken between the rays [tex]\theta=\frac\pi6[/tex] and [tex]\theta=\frac\pi2[/tex]. (The previous question of yours that I just posted an answer to has a similar region with slightly different parameters.)

You can separate the variables to compute the integral:

[tex]\displaystyle\int_{\pi/6}^{\pi/2}\int_2^3r^2\sin^2\theta\,\mathrm dr\,\mathrm d\theta=\left(\int_{\pi/6}^{\pi/2}\sin^2\theta\,\mathrm d\theta\right)\left(\int_2^3r^2\,\mathrm dr\right)[/tex]

which should be doable for you. You would find it has a value of 19/72*(3√3 + 4π).

3. Without knowing the definition of the region D, the best we can do is convert what we can to polar coordinates. Namely,

[tex]r^2=x^2+y^2[/tex]

so that

[tex]\displaystyle\iint_De^{x^2+y^2}\,\mathrm dA=\iint_Dre^{r^2}\,\mathrm dr\,\mathrm d\theta[/tex]

Answer:

Step-by-step explanation:

you just do, everyone in here needs help so i dont think theres people in here just messing arround, you can trust.

Answer:

because we are amazing as always.

Step-by-step explanation:

Please dont do this or i will report u.

bye

Answer:

4

Step-by-step explanation:

A função em questão, f(x), é:

[tex]f(x)=4x-9[/tex]

Primeiramente calcule os valores das funções para x=5 e x=6:

[tex]f(5)=4*5-9\\f(5)=11\\f(6)=4*6-9\\f(6)=15[/tex]

Em seguida, subtraia f(5) de f(6):

[tex]f(6)-f(5) = 15-11\\f(6)-f(5) = 4[/tex]

A resposta para o problema é 4

Answer:

1a) (i) 0.0537

(ii) 0.0250

(iii) 0.6188

1b) The probability that neither Kofi nor Mensah solves the problem correctly = (9/20) = 0.45

Step-by-step explanation:

The complete Question is presented in the attached image to this answer.

1a) This is a normal distribution problem with

Mean lifetime of bulbs = μ = 210 hours

Standard deviation = σ = 56 hours

(i) at least 300 hours, P(x ≥ 300)

We first standardize 300 hours

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (300 - 210)/56 = 1.61

To determine the required probability

P(x ≥ 300) = P(z ≥ 1.61)

We'll use data from the normal probability table for these probabilities

P(x ≥ 300) = P(z ≥ 1.61) = 1 - P(z < 1.61)

= 1 - 0.94630 = 0.0537

(ii) at most 100 hours, P(x ≤ 100)

We first standardize 100 hours

z = (x - μ)/σ = (100 - 210)/56 = -1.96

To determine the required probability

P(x ≤ 100) = P(z ≤ -1.96)

We'll use data from the normal probability table for these probabilities

P(x ≤ 100) = P(z ≤ -1.96) = 0.0250

(iii) between 150 and 250 hours.

P(150 < x < 250)

We first standardize 150 and 250 hours

For 150 hours

z = (x - μ)/σ = (150 - 210)/56 = -1.07

For 250 hours

z = (x - μ)/σ = (250 - 210)/56 = 0.71

To determined the required probability

P(150 < x < 250) = P(-1.07 < z < 0.71)

We'll use data from the normal probability table for these probabilities

P(150 < x < 250) = P(-1.07 < z < 0.71)

= P(z < 0.71) - P(z < -1.07)

= 0.76115 - 0.14231

= 0.61884 = 0.6188 to 4 d.p.

1b) Probability that Kofi solves the problem correctly = P(K) = (1/4)

Probability that Mensah solves the problem correctly = P(M) = (2/5)

Probability that Kofi does NOT solve the problem correctly = P(K') = 1 - P(K) = 1 - (1/4) = (3/4)

Probability that Mensah does NOT solve the problem correctly = P(M') = 1 - P(M) = 1 - (2/5) = (3/5)

To find the probability that neither of them solves the problem correctly, we first make the logical assumption that the probabilities of either of them solving the problem are independent of each other.

Hence, the probability that neither of them solves the problem correctly = P(K' n M')

P(K' n M') = P(K') × P(M') = (3/4) × (3/5) = (9/20) = 0.45

Hope this Helps!!!

Answer:

g = 200

Step-by-step explanation:

trust me.

I big brain.

Answer:On a graph, these values form a curved, U-shaped line called a parabola. All quadratic functions form a parabola on a graph. ... Quadratic functions are used to describe things with smooth symmetrical curves, like the path of a bouncing ball or the arch of a bridge.

Step-by-step explanation:

Answer:

2700000

Step-by-step explanation:

Because it is not at 750000 it gets rounded down

Answer:123456

Step-by-step explanation:

Answer:

Scalene triangle

Step-by-step explanation:

Answer:it’s ZERO

Step-by-step explanation:

The discriminant of the function is zero

A relation is a function if it has only One y-value for each x-value.

The discriminant tells you where the graph of the parabola goes through the x-axis, if at all.

If the discriminant is negative there are no real zeros and the parabola does not cross or touch the x-axis;

if the discriminant is positive the parabola will go through the x axis in 2 places;

if the discriminant is 0 the parabola will touch the x-axis in 1 place.

Our discriminant is 0 since the parabola only touches the x-axis but does not go through.

Hence, the discriminant of the function is zero

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ5

Answer: A = (7ft + x)*(6ft + x)

Step-by-step explanation:

The area of a rectangle is equal to A = L*W

where W is width and L is lenght.

Here we have that the width is 6 feet + x feet and the lenght is 7 feet + x feet

(because we also are counting the area of the sidewalk)

Then the total area is:

A = (7ft + x)*(6ft + x)

Answer: About 14.14 in^3

Step-by-step explanation:

We know that the circumference of a sphere is C=2πr. We are given that the circumference is 9.42 in. We can find the radius to get our volume.

[tex]9.42=2\pi r[/tex]

[tex]4.71=\pi r[/tex]

[tex]r=1.5\\[/tex]

Now that we know radius, we can find our volume.

[tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]

[tex]V=14.14in^3[/tex]

Answer:

$6.03

Step-by-step explanation:

Let's begin by listing out the given variables:

height (h) = 12 cm, diameter (d) = 8 cm, r = d ÷ 2  ⇒ r = 4 cm, cost of coconut oil (c) = $0.01 /cm³

The formula of cylinder is given by:

V = πr²h = π * 4² * 12 = 603.1858 cm³

cost of filling the tin can with coconut oil = cost of coconut oil * Volume of cylinder

Cost = c * V = 0.01 * 603.1858

Cost = $6.03

Answer:

[tex]x=15\sqrt{5}[/tex]

Step-by-step explanation:

[tex]15 \times \sqrt{5} = x[/tex]

[tex]33.54102 \approx x[/tex]

Answer:

first answer is x= -5 second answer is y=7.

Step-by-step explanation:

7-5=2. 2+3=5.

7-1=6.

Add the rooms together to find total square yards:

104.8 + 17.4 + 165.8 = 288 square yards

Add the costs together: 13.95 + 2.75 + 5.75 = $22.45 per square yard

For total cost, multiply total square yards by total cost per square yard

288 x 22.45 = 6,465.60

Total cost: $6,465.60

The total job cost Gracie is $6,465.60.

Step 1:

Add the rooms together to find total square yards

=104.8 + 17.4 + 165.8

= 288 square yards

Step 2:

Add the costs together

= 13.95 + 2.75 + 5.75

= $22.45 per square yard

Step 3:

For total cost, multiply total square yards by total cost per square yard

=288 x 22.45

= 6,465.60

Therefore, the total cost: $6,465.60

To calculate the total cost of work done, refer,

#SPJ2

Answer:

(x-1)^2 + (y-4)^2 = 5^2

Step-by-step explanation:

In order to find the points that lie on the perimeter of the circle, you find the  algebraic equation of the circle.

The general equation for a circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]         (1)

The last is a circle centered at the point (h,k) and with radius r.

In this case you have a circle with a radius of r = 5, and the circle is centered at (1,4). Then, you have:

h = 1

k = 4

r = 5

You replace the values of h, k and r in the equation (1):

[tex](x-1)^2+(y-4)^2=5^2[/tex]

All point that lies on the curve of the last equation, are point that lie on the perimeter of the circle

Answer:

a)

[tex]P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357[/tex]

[tex]P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034[/tex]

[tex]P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377[/tex]

[tex]P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216[/tex]

[tex]P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015[/tex]

[tex]P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004[/tex]

b) 0.154% probability that there are at least 4 defective welders in the sample

Step-by-step explanation:

The welders are chosen without replacement, so the hypergeometric distribution is used.

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

100 welders, so [tex]N = 100[/tex]

Sample of 15, so [tex]n = 15[/tex]

In total, 5 defective, so [tex]k = 5[/tex]

(a) Determine the PMF of the number of defective welders in your sample?

There are 5 defective, so this is P(X = 0) to P(X = 5). Then

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357[/tex]

[tex]P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034[/tex]

[tex]P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377[/tex]

[tex]P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216[/tex]

[tex]P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015[/tex]

[tex]P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004[/tex]

(b) Determine the probability that there are at least 4 defective welders in the sample?

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0015 + 0.00004 = 0.00154[/tex]

0.154% probability that there are at least 4 defective welders in the sample

Answer:

Each mixture has the same amount of salt for every 1 cup of water.

Step-by-step explanation:

It is provided that:

The ratio of the number of teaspoons of salt to the number of cups of water is 1 : 3 in Nia's solution.

On dividing the amount of salt and the amount of water by 3, the ratio will be the same.

[tex]\text{Salt}: 1\div3=\frac{1}{3}\\\\\text{Water}:3\div3=1\\[/tex]

Thus 1 : 3 is equivalent to the ratio [tex]\frac{1}{3}:1[/tex], which means that Nia's solution has [tex]\frac{1}{3}[/tex]teaspoon of salt for every cup of water.

The ratio of the number of teaspoons of salt to the number of cups of water is [tex]\frac{1}{2}:1\frac{1}{2}[/tex] in Trey’s solution.

On dividing the amount of salt and the amount of water by [tex]1\frac{1}{2}[/tex], the ratio will be the same.

[tex]\text{salt}:\frac{1}{2}\div 1\frac{1}{2}=\frac{1}{3}\\\\\text{Water}:1\frac{1}{2}\div1\frac{1}{2}=1[/tex]

So Trey’s ratio is also equal to the ratio [tex]\frac{1}{3}:1[/tex].

Since each mixture has the same amount of salt for every 1 cup of water, they are equally salty and taste the same.

Answer:

a) [tex]r(t)=5t[/tex]

b) [tex]A=\pi\cdot r^2[/tex]

c) [tex]A=\pi\cdot (5t)^2[/tex]

d) [tex]A=25\pi t^2[/tex]

Step-by-step explanation:

We know that the circle is increasing its radio from an initial state of r=0 cm, at a rate of 5 cm/s.

This can be expressed as:

[tex]r(0)=0\\\\dr/dt=5\\\\r(t)=r(0)+dr/dt\cdot t=0+5t\\\\r(t)=5t[/tex]

a) Radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing:

[tex]r(t)=5t[/tex]

b) Area of the circle, A (in square cm), in terms of the circle's radius, r (in cm):

[tex]A=\pi\cdot r^2[/tex]

c) Circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing:

[tex]A=\pi\cdot r^2\\\\A=\pi\cdot (5t)^2[/tex]

d) Expanded form for the area A:

[tex]A=\pi\cdot (5t)^2=25\pi\cdot t^2[/tex]

Answer:

Reject [tex]H_o[/tex] if [tex]t < -2.306[/tex]

Step-by-step explanation:

The decision rule for rejecting the null hypothesis is shown below:-

The machine is thought to be underfilling so that the test is left tailed.

Now the Degrees of freedom is

= 9 - 1

= 8

Critical left tailed value t for meaning level [tex]8 \ df[/tex] and 0.025 = -2.306

Therefore Decision rule will be in the following way:

Reject [tex]H_o[/tex] if [tex]t < -2.306[/tex]

Answer:

20% is the correct answer

Answer:

50%

Step-by-step explanation:

40 is the median.

From median to upper quartile is 25%  & form from upper quartile to maximum is 25%

So, 25 + 25 = 50 %

Answer:

Persia should measure the length of each flower that she used in creating this flower arrangement and add up all the values to get the total height (i.e., the combined height) of the eight flowers used. Make sure to keep the units consistent all throughout the calculation to avoid any errors. For example, if centimetres are used to measure height of one flower, use centimetres all throughout and not switch to using inches at any point.

Hope that answers the question, have a great day!

Answer:

61 1/2

Step-by-step explanation:

math is ez

Answer:

Step-by-step explanation:

Given that,

μ = 25.1

σ = 0.26

a) since standard deviation is ideal measure of dispersion , a combination of control chart for mean x and standard deviation known as

[tex]\bar x \\\text {and}\\\mu[/tex]

Chart is more appropriate than [tex]\bar x[/tex] and R - chart for controlling process average and variability

so we use

[tex]\bar x \\\text {and}\\\mu[/tex]charts

b)

n = 11

we have use 2 σ confidence

so, control unit for [tex]\bar x[/tex] chart are

upper control limit  = [tex]\mu +2\times\frac{ \sigma}{\sqrt{n} }[/tex]

lower control limit = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]

control limit = μ

μ = 25.1

upper control limit  =

[tex]25.1+2\times \frac{0.26}{\sqrt{11} } \\\\=25.2567[/tex]

lower control limit =

[tex]25.1-2\times \frac{0.26}{\sqrt{11} } \\\\=24.9432[/tex]

Upper control limit and lower control limit are in between the specification limits , that is in between 24.9 and 25.6

so, process is in control

c) if we use 3 sigma limit with n = 11

then

upper control limit  = [tex]\mu +3\times\frac{ \sigma}{\sqrt{n} }[/tex]

[tex]25.1+3\times\frac{0.26}{\sqrt{11} } \\\\=25.3351[/tex]

lower control limit  = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]

[tex]25.1-3\times\frac{0.26}{\sqrt{11} } \\\\=24.8648[/tex]

control limit is 25.1

Then, process is in control since upper control limit and lower control limit lies between specification limit

So, process is in control

Answer:

The inequality representing the time taken by the entire cycle is:

[tex]4x+y\leq 3[/tex]

Step-by-step explanation:

The time taken to complete one cycle of a manufacturing machine is no longer than 3 minutes.  

It is provided that the manufacturing machine has two processes.

One of them is repeated 4 times and the second only once.

Assume that the variable x represents the time taken to complete the first process once.

Then the  time taken to complete the first process 4 times would be, 4x.

Also assume that the variable y represents the time taken to complete the second process.

Then the inequality representing the time taken by the entire cycle is:

[tex]4x+y\leq 3[/tex]

Consider the graph below representing the above equation.

Answer: D

Step-by-step explanation:

Answer:

Before A. 32.7247330577, A. 27.8204757722, B. 32.7247330577, C. 15.4868329805, and D. 32.7247330577

Step-by-step explanation:

Used a calculator. Not that Hard.

Answer:

  1707

Step-by-step explanation:

Let's designate the three sets of collinear points, A, B, C, having 4, 6, 7 points, respectively.

Since there are 3 sets of collinear points, exactly two of the vertices must come from the same set.

For two vertices from set A, the remaining two must come from the 13 members of sets B and C. There are a total of (4C2)(13C2) = 468 such quadrilaterals.

For two vertices from set B, we have already counted the quadrilaterals that result when the remaining two are from set A. There are 4·7 = 28 ways to have one each from sets A and C, and 7C2 = 21 ways to have two from set C. Thus, the additional number of quadrilaterals having 2 vertices in set B is ...

  (6C2)(28 +21) = 735

For two vertices from set C, we have already counted the cases where two are from A or two are from B. There are 4·6 = 24 ways to have one each of the remaining vertices from sets A and B. Then the number of additional quadrilaterals having two points from set C is ...

  (7C2)(4)(6) = 504

So, the total number of unique quadrilaterals is ...

  468 +735 +504 = 1707

__

nCk means "the number of ways to choose k from n"

nCk = n!/(k!(n-k)!)