If A={3,6,9,12 }and B={0,4,8,12}, then find A∩B. *
​

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:

answer is in exaplation

Step-by-step explanation:

cosA

+

cosA

1+sinA

=2secA

Step-by-step explanation:

\begin{lgathered}LHS = \frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=\frac{cos^{2}A+(1+sinA)^{2}}{(1+sinA)cosA}\\=\frac{cos^{2}A+1^{2}+sin^{2}A+2sinA}{(1+sinA)cosA}\\=\frac{(cos^{2}A+sin^{2}A)+1+2sinA}{(1+sinA)cosA}\\=\frac{1+1+2sinA}{(1+sinA)cosA}\end{lgathered}

LHS=

1+sinA

cosA

+

cosA

1+sinA

=

(1+sinA)cosA

cos

2

A+(1+sinA)

2

=

(1+sinA)cosA

cos

2

A+1

2

+sin

2

A+2sinA

=

(1+sinA)cosA

(cos

2

A+sin

2

A)+1+2sinA

=

(1+sinA)cosA

1+1+2sinA

/* By Trigonometric identity:

cos² A+ sin² A = 1 */

\begin{lgathered}=\frac{2+2sinA}{(1+sinA)cosA}\\=\frac{2(1+sinA)}{(1+sinA)cosA}\\\end{lgathered}

=

(1+sinA)cosA

2+2sinA

=

(1+sinA)cosA

2(1+sinA)

After cancellation,we get

\begin{lgathered}= \frac{2}{cosA}\\=2secA\\=RHS\end{lgathered}

=

cosA

2

=2secA

=RHS

Therefore,

\begin{lgathered}\frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=2secA\end{lgathered}

1+sinA

cosA

+

cosA

1+sinA

=2secA

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

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Answer:

0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost

Step-by-step explanation:

Independent events:

If two events, A and B, are independent, then:

[tex]P(A \cap B) = P(A)*P(B)[/tex]

Conditional probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: At least one tag is lost

Event B: Exactly one tag is lost.

Each tag has a 40% = 0.4 probability of being lost.

Probability of at least one tag is lost:

Either no tags are lost, or at least one is. The sum of the probabilities of these events is 1. Then

[tex]p + P(A) = 1[/tex]

p is the probability none are lost. Each one has a 60% = 0.6 probability of not being lost, and they are independent. So

p = 0.6*0.6 = 0.36

Then

[tex]P(A) = 1 - p = 1 - 0.36 = 0.64[/tex]

Intersection:

The intersection between at least one lost(A) and exactly one lost(B) is exactly one lost.

Then

Probability at least one lost:

First lost(0.4 probability) and second not lost(0.6 probability)

Or

First not lost(0.6 probability) and second lost(0.4 probability)

So

[tex]P(A \cap B) = 0.4*0.6 + 0.6*0.4 = 0.48[/tex]

Find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).

[tex]P(B|A) = \frac{0.48}{0.64} = 0.75[/tex]

0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost

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: 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: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:

Scalene triangle

Step-by-step explanation:

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:

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:

t = pn

Step-by-step explanation:

We are to find the relationship between total cost and the number of items.

First we would represent the relationship between total cost and number of items with variables

Let the total cost = t

and the number of items = n

Total cost t is proportional to the number n of items:

t ∝ n

t = kn

where k is constant

Since it is purchased at a constant price p, the constant of proportionality would be p. the k would be replaced with p

t = pn

Answer:

g = 200

Step-by-step explanation:

trust me.

I big brain.

Answer: A

Step-by-step explanation:

Formula for inverse of a matrix is:

[tex]A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\qquad \rightarrow \qquad A^{-1}=\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]

[tex]A=\left[\begin{array}{cc}2&5\\3&8\end{array}\right] \qquad \rightarrow \qquad A^{-1}=\dfrac{1}{2(8)-5(3)}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\dfrac{1}{1}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right][/tex]

We have that  Option A is the correct option as its the correct in verse of the Matrix A

From the question we are told that:

[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]

Inverse of a Matrix

The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is A^{-1}, and A.A^{-1} = I.

Therefore the inverse of the Matrix A is

[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]

Giving

[tex]A^{-1}= \begin{vmatrix}8 & -5 \\-3 & -2\end{vmatrix}[/tex]

In conclusion

The correct Option is Option A as its the correct in verse of the Matrix A

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In conclusion

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:

(1)Equivalence Relation

(2)Not Transitive, (0,3) is missing

(3)Equivalence Relation

(4)Not symmetric and Not Transitive, (2,1) is not in the set

Step-by-step explanation:

A set is said to be an equivalence relation if it satisfies the following conditions:

(1) {(0,0), (1,1), (2,2), (3,3)}

(3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)}

The relations in 1 and 3 are Reflexive, Symmetric and Transitive. Therefore (1) and (3) are equivalence relation.

(2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)}

In (2), (0,2) and (2,3) are in the set but (0,3) is not in the set.

Therefore, It is not transitive.

As a result, the set (2) is not an equivalence relation.

(4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}

(1,2) is in the set but (2,1) is not in the set, therefore it is not symmetric

Also, (2,0) and (0,1) is in the set, but (2,1) is not, rendering the condition for transitivity invalid.

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:

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:

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,

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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:

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:123456

Step-by-step explanation:

Step-by-step explanation:

The temperature outside when Colin went to bed was -4°F. When he woke up the next  morning, it was -11°F outside

To find the change in the temperature , find the difference in temperature

Change in temperature = temperature in morning - temperature at night

change in temperature = [tex]-11 -(-4)= -7[/tex]

temperature changed by -7 °F

So the temperature is dropped by 7°F

Answer:

the temperature is dropped by 7°F

The temperature change when he woke up the next morning given the data was –7 °F.

From the question given above , the following data were obtained:

The temperature change when Colin woke up can be obtained by taking the difference in the temperature at night and morning. This is illustrated as follow:

ΔT = T₂ – T₁

ΔT = –11 – (–4)

ΔT = –11 + 4

ΔT = –7 °F

Thus, from the calculation made above, we can conclude that there was a temperature drop of –7 °F when he woke up the next morning

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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:

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: 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:

(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:

  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)!)