Find three different numbers such that the
HCF of each pair of these numbers is greater
than 1 but the HCF of all three numbers is 1.


[Hint: For instance, the numbers 6, 10 and
15 satisfy the conditions.]​

Answer:

6 sandwiches to choose from because

3×2 = 6

Answer:

option A

Step-by-step explanation:

Permutation is An arrangement of objects in an ORDER

but combination is the opposite.

Answer:

A) Q(t) = 4e^-(0.0079t)

B) t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Step-by-step explanation:

a)

to write a function of the form Q(t)= Q₀e⁻^kt to model the quantity Q(t) of ²³⁸Pu left after t-years.

so given that; half-life of ²³⁸Pu is 87.7 years,

∴ t =  87.7 years , Q(t) = 0.5Q₀

Now we substitute these value in the form  Q(t)= Q₀e⁻^kt

Q(t)= Q₀e⁻^kt

0.5Q₀ = Q₀e^ -(87.7k)

0.5 = e^ -(87.7k)

now we take the natural logarithm of both sides

In(0.5) = Ine^ -(87.7k)

Now using the property logₙnᵃ = a

-87.7k = In(0.5)

k = - In(0.5) / 87.7

k = 0.0079

ALSO it was given that Q₀ = 4.0 kg

Therefore , model quality Q(t) of ²³⁸pu left after t years is:

Q(t) = 4e^-(0.0079t)

b)

to find the time left after 1.6kg of ²³⁸pu

we simple substitute  Q(t) = 1.6 into Q(t) = 4e^-(0.0079t)

so we have

1.6 = 4e^-(0.0079t)

e^-(0.0079t) = 1.6/4

e^-(0.0079t) = 0.4

again we take the natural logarithm of both sides,

Ine^-(0.0079t) = In(0.4)

again using the property logₙnᵃ = a

-0.0079t = In(0.4)

t = - in(0.4) / 0.0079

t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Answer: 8

Step-by-step explanation:

Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.

Total marbles other than green = 8

Total marbles other than green and yellow = 6

Then the number of sets of seven marbles include at least one yellow one but no green ones:-

[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]

Number of sets of seven marbles include at least one yellow one but no green ones = 8

Answer:

C) 82/2

Step-by-step explanation:

The area of a square is calculated by multiplying a side by itself

so one side of the square is 9 in

the area of a triangle is calculated by multiplying height and base and that divided by 2

since E is the midpoint, if we draw a line show the height from there

the height would be 9

9*9/2 = 82/2

Answer:

C. 10,080

Step-by-step explanation:

We can multiply to find how many minutes there are in 1 day.

24 * 60 = 1,440

Now, we can multiply that value by 7 to find out how many minutes there are in 1 week.

1,440 * 7 = 10,080

Best of Luck!

Answer:

13 units

Step-by-step explanation:

(x₁,y₁) = (-5 , 3)   & (x₂ , y₂) = (7 ,8)

[tex]Distance = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \\[/tex]

              [tex]= \sqrt{(7-[-5])^{2}+(8-3)^{2}} \\\\= \sqrt{(7+5)^{2}+(8-3)^{2}} \\\\= \sqrt{(12)^{2}+(5)^{2}}\\\\=\sqrt{144+25}\\\\=\sqrt{169}\\\\= 13[/tex]

Answer:

i think

x=6.77

y=11.33

Answer:

The probability is 2,010,580/13,378,456

Step-by-step explanation:

Here is a combination problem.

We want to 7 cards from a total of 52.

The number of ways to do this is 52C7 ways.

Also, we know there are 12 face cards in a standard deck of cards.

So we are selecting 3 face cards from this total of 12.

So also the number of cards which are not face cards are 52-12 = 40 cards

Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4

Thus, the required probability will be;

(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560

= 20,105,800/133,784,560 = 2,010,580/13,378,456

9514 1404 393

Answer:

  (d)  4.2×10^15

Step-by-step explanation:

Your calculator will tell you the quotient is about ...

  4.21348...×10^15

The least precise number in the division is 1.5, which has 2 significant digits. Therefore, the result should be rounded to 2 significant digits:

  4.2×10^15

Answer:

Hello,

Step-by-step explanation:

[tex]LUB(E)=0.2=\dfrac{1}{5} \\\\GUB(E)=0.2 34 34 34 ....=0.2+\dfrac{1}{10} *0.343434....\\\\=\dfrac{1}{5} +\dfrac{1}{10} *\dfrac{34}{99} \\\\=\dfrac{198+34}{990} \\\\=\dfrac{116}{495}[/tex]

Step-by-step explanation:

y=mx+c

Answer:

y= 10x +14

Step-by-step explanation:

Distribute parenthesis:

7(x+2) + 3x = 7x +14 +3x

Then combine like terms:

7x + 3x = 10x +14

Answer:

The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Step-by-step explanation:

Given that:

F(x,y) = 8 sin (xy) at (0,9)

The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]

[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]

[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]

We can conclude that the  maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Answer:

the margin of error

= 1.96 x 0.0632

= 0.124

Step-by-step explanation:

this question has the sample size, n = 40

8 people have received help from their parents from this sample.

8/40 = 0.2

which is the sample proportion

z = 1 - 0.2

= 0.8

to calculate standard error

√pz/n

= √0.2 x 0.8/40

= √0.16/40

= 0.0632

at 95% confidence level

z(alpha/2) = 1.96

therefore the margin of error

= 1.96 x 0.0632

= 0.124

Step-by-step explanation:

The inequality shows by line is

i) 1<=x<=6

OR,

x is an positive integer.

Answer:

The dimensions or Area of the rectangle is 1200cm².

Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.

Step-by-step explanation:

[tex]\frac{154}{200} =0.77[/tex]

[tex]1-0.77=0.23[/tex]

[tex]\sqrt{\frac{(0.77)(0.23)}{200} }[/tex]=0.049

0.77±0.049< 0.819, 0.721

Answer:

Step-by-step explanation:

We first examine a simple hidden Markov model (HMM). We observe a sequence of rolls of a four-sided die at an "occasionally dishonest casino", where at time t the observed outcome x_t Element {1, 2, 3, 4}. At each of these times, the casino can be in one of two states z_t Element {1, 2}. When z_t = 1 the casino uses a fair die, while when z_t = 2 the die is biased so that rolling a 1 is more likely. In particular: p (x_t = 1 | z_t = 1) = p (x_t = 2 | z_t = 1) = p (x_t = 3 | z_t = 2) = p (x_t = 4 | z_t = 1) = 0.25, p (X_t = 1 | z_t = 2) = 0.7, p (X_t = 2 | z_t = 2) = p (X_t = 3 | z_t = 2) = p (X_t = 4 | z_t = 2) = 0.1. Assume that the casino has an equal probability of starting in either state at time t = 1, so that p (z1 = 1) = p (z1 = 2) = 0.5. The casino usually uses the same die for multiple iterations, but occasionally switches states according to the following probabilities: p (z_t + 1 = 1 | z_t = 1) = 0.8, p (z_t = 2) = 0.9. The other transition probabilities you will need are the complements of these. a. Under the HMM generative model, what is p (z1 = z2 = z3), the probability that the same die is used for the first three rolls? b. Suppose that we observe the first two rolls. What is p (z1 = 1 | x1 = 2, x2 = 4), the probability that the casino used the fair die in the first roll? c. Using the backward algorithm, compute the probability that we observe the sequence x1 = 2, x2 = 3, x3 = 3, x4 = 3 and x5 = 1. Show your work (i.e., show each of your belief for based on time). Consider the final distribution at time t = 6 for both p (z_t = 1) = p (z_t = 2) = 1.

ANSWER:

Let say we have that the first state of the die is state 1. Therefore the probability of this is p(z1=1)=0.5.

Also the probability that the same die is used(i.e. casino would be in the same state) is p(z2=1|z1=1)=0.8.

Again, suppose the first state of the die is state 2. So, p(z1=2)=0.5 and p(z2=2|z1=2)=0.9.

Other transition probabilities can be written as

p(zt+1=2|zt=1)=1-p(zt+1=1|zt=1)=.2

p(zt+1=1|zt=2)=1-p(zt+1=2|zt=2)=.1

p(z3=1|z1=1) = [p(z3=1|z2=2)*p(z2=2|z1=1)]+[p(z3=1|z2=1)*p(z2=1|z1=1)] = 0.1*0.2+0.8*0.8 = 0.66

p(z3=2|z1=2) = [p(z3=2|z2=2)*p(z2=2|z1=2)]+[p(z3=2|z2=1)*p(z2=1|z1=2)] = 0.9*0.9+0.2*0.1 = 0.83

With this, the total probability that the same die is used for the first three rolls (i.e. casino would be in the same state) is  given thus;

{p(z1=1)*p(z3=1|z1=1)}*{p(z1=2)*p(z3=2|z1=2)}

=  0.5*0.66+0.5*0.83 = 0.745

Prob = 0.745

Answer:

FH = 134

Step-by-step explanation:

From the question given:

G is the midpoint of FH

FG = 14x + 25

GH = 73 - 2x

FH =?

Next, we shall determine the value of x. The value of x can be obtained as follow:

Since G is the midpoint of FH, this implies that FG and GH are equal i.e

FG = GH

With the above formula, we can obtain the value of x as follow:

FG = 14x + 25

GH = 73 - 2x

x =?

FG = GH

14x + 25 = 73 - 2x

Collect like terms

14x + 2x = 73 - 25

16x = 48

Divide both side by 16

x = 48/16

x = 3

Next, we shall determine the value of FG and GH. These can be obtained as shown below:

FG = 14x + 25

x = 3

FG = 14x + 25

FG = 14(3) + 25

FG = 42 + 25

FG = 67

GH = 73 - 2x

x = 3

GH = 73 - 2x

GH = 73 - 2(3)

GH = 73 - 6

GH = 67

Finally, we shall determine FH as follow:

FH = FG + GH

FG = 67

GH = 67

FH = FG + GH

FH = 67 + 67

FH = 134

Therefore, FH is 134

Answer:

Step-by-step explanation:

From the given information;

let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c

SO, using the Pythagoras theorem

a² = c² + 177²

By taking the differentiation of both sides with respect to time t , we have

[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]

[tex]a = \sqrt{ 5041+31329}[/tex]

[tex]a = \sqrt{ 36370}[/tex]

a = 190.71

SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]

Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]

[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]

[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex]  to the nearest hundredth.

Answer:

a). BLUE color

b). 20%

Step-by-step explanation:

a). "Which color was chosen by approximately one fourth of the students?"

  Since one fourth of the students will be represented by one fourth area of the circle given.

That means color of choice represented by the quarter of the circle will be the color liked by one fourth students.

In the figure attached, BLUE color is the choice of one fourth students in the class.

b). Area represented by purple, green and other colors is a quarter of the circle.

If we divide this quarter into five equal sections, then the total of purple and green will be  [tex]4\times \frac{1}{5}[/tex] of the the quarter of the circle.

Measure of the angle defined by purple or green sections = [tex]\frac{4}{5}\times 90[/tex]

                                                                                                     = 72°

Percentage of the students who preferred purple or green = [tex]\frac{72}{360}\times 100[/tex]

                                                                                                     = 20%

Answer:

blue

20%

Step-by-step explanation:

Answer:

x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 3 x + 15 = 0

The left hand side factors into a product with two terms:

(x + 5) (x^2 + 3) = 0

Split into two equations:

x + 5 = 0 or x^2 + 3 = 0

Subtract 5 from both sides:

x = -5 or x^2 + 3 = 0

x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:

x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2

sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):

x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2

sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):

x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2

(2 i sqrt(3))/2 = i sqrt(3):

x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2

(2 (-i sqrt(3)))/2 = -i sqrt(3):

Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Answer:

C. x = −5, 1.7i, −1.7i

Step-by-step explanation:

Quick answer:

C. x = −5, 1.7i, −1.7i

explanation:

C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.

Complete answer:

All odd degree polynomials have at least one real root.

By the real roots theorem, we know that

if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).

Values of [tex]\pm[/tex]p/q are

On trial and error, using the factor theorem, we see that

f(-5) = 0, therefore -5 is a real root.  By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i

The answer is {-5, +/- sqrt(5) i}, or again,

C. x = −5, 1.7i, −1.7i

Answer:

A) Net A (see explanation)

B) AB = 3 in. | BC = 5 in. | CD = 7.2 in.

C) SA = 98.4 in²

Step-by-step explanation:

Part A

Net A is the correct net for the prism. If you look at the way the folds are, the flaps on the top and bottom would fold up to make the side of the prism. On net B, the flaps wouldn’t fit the shape correctly.

Part B

AB = This is the height of the prism.

= 3 in.

BC = This is the slant on the front of the prism.

= 5 in.

CD = This is the length of the prism.

= 7.2 in.

Part C

* First we’ll solve for the two triangles. They are the same shape and size, so we just need to solve one then duplicate it.

One triangle:

A = 1/2bh

= 1/2 (4) (3)

= 6 in²

Back rectangle:

A = bh

= 7.2 (3)

= 21.6 in²

Front rectangle:

A = bh

= 7.2 (5)

= 36 in²

Bottom rectangle:

A = bh

= 7.2 (4)

= 28.8 in²

Total:

A = 6 + 6 + 21.6 + 36 + 28.8

= 98.4 in²

Hello, please consider the following.

[tex]\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }[/tex]

Thank you

Answer:

APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.

When you plug 3 into equation D the entire right side it will become.

y-1=0

y=1, which is true.

When you plug 6 into that equation.

y-1=5

y=6 which is also true.

im sorry but the thing is i cant translate these words but the answer is D

Answer:

(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.

Answer:

Step-by-step explanation:

Because then the value on the other side will be unbounded by the infinity sign while expressing the answers on a number line.

please click thanks and mark brainliest if you like :)

Answer:

the answers are below:

Step-by-step explanation:

a. null hypothesis:

H0: Pw - Pm = 0 (so Pw = Pm)

alternate hypothesis:

H1: Pw - Pm > 0 (so Pw > Pm)

where Pw is the proportion of women

Pm is the proportion of men

b.) proportion of women = o.40

proportion of men =  0.32

sample size of women = 20

sample size of men = 25

[tex]z = 0.4 - 0.32/ \sqrt{((0.4 *0.6)/20) * (0.32 * 0.68)/25)}[/tex]

[tex]z = 0.56[/tex]

c.) p value =

p(z>0.56)

= 0.7123

= 1 - 0.7123

= o.2877 which can be approximated to be 0.288

d. alpha value was set at 0.05

the p value is greater than alpha.

therefore it is not statistically significant.

we conclude that the proportion of roman catholic women is not greater than men.

Answer:

In order for a Normal Probability Distribution to be a Standard Normal Probability Distribution, the mean and standard deviation must have the values of µ = 0 and σ = 1.

Where µ refers to the Mean of the distribution and σ refers to the standard deviation.

µ is pronounced 'mu' and σ is pronounced sigma.

Cheers!