Find the value of y. -6y+14+4y=32

Answer:

5

Step-by-step explanation:

first you need to simplify this equation and put it in slope intercept form which is y = mx + b

after simplifying you will get y = 5x + 10

since the slope is m , the answer will be 5

Answer:

120

Step-by-step explanation:

3480/29=120

           120

Simplify   ———

            1

final result is  120

Answer:

There are 60 marbles in the bag

Step-by-step explanation:

The total number of marbles  times the probability of red marbles = number of red marbles

total * 7/10 = 42

Multiply each side by 10/7

total * 7/10 * 10/7 = 42*10/7

total

60

There are 60 marbles in the bag

Answer:

So I have never stepped foot into this. But I have experience from this. So for the first one we can use the compound intrest formula - A = P(1+r/n)^nt so if we do that we get.

A = 3000(1+0.05/1)^1*4

So then we get A is equal to 3646.52

The next one we need to calculate

A = P (1 + rt)

So now we do A = 3000(1+0.05*1)

A = 3000*1.05 = 3150. We add them together and we get 6796.52.

So we subtract 6000 from that. He earned

796.52 dollars

Answer:

[tex]\dfrac{1}{16}[/tex]

Step-by-step explanation:

Proportion of Heat Loss Between sundown and midnight[tex]=\dfrac{1}{3}[/tex]

Proportion of Heat Loss between midnight and 4 AM  [tex]=\dfrac{1}{2}[/tex]

Proportion of Total Heat Already Lost [tex]=\dfrac{1}{3}+\dfrac{1}{2} =\dfrac{5}{6}[/tex]

Proportion of Remaining Heat [tex]=1-\dfrac{5}{6}=\dfrac{1}{6}[/tex]

Between 4 AM and 5 AM, five-eighths of the remaining heat is lost.

Proportion of Heat Loss between 4 AM and 5 AM= [tex]\dfrac{5}{8}$ X \dfrac{1}{6} = \dfrac{5}{48}[/tex]

Therefore, Proportion of Remaining Heat Left [tex]=\dfrac{1}{6}- \dfrac{5}{48}=\dfrac{1}{16}[/tex]

We therefore say that:

[tex]\dfrac{1}{16}$ of the total heat loss occurs between 5 AM and sunrise.[/tex]

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

We have,

Given:

Total number of components (n) = 1000

Number of defective components (d) = 350

a.

P(A) is the probability that the first component drawn is defective:

P(A) = d/n = 350/1000 = 0.35

b.

P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:

Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.

P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349

c.

P(A ∩ B) is the probability that both the first and second components drawn are defective:

P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122

d.

P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:

[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:

[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65

Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.

P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228

e.

P(B) is the probability that the second component drawn is defective:

P(B) = Number of defective components / Total number of components

= 350/1000

= 0.35

f.

P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:

P(A|B) = P(A ∩ B) / P(B)

= (0.35 * 0.349) / 0.35

= 0.349

g.

To determine if A and B are independent, we need to compare

P(A) * P(B) with P(A ∩ B).

P(A) * P(B) = 0.35 * 0.35 = 0.1225

P(A ∩ B) = 0.122

Since P(A) * P(B) = P(A ∩ B), A and B are independent events.

It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.

The occurrence or non-occurrence of A does not impact the probability of B.

Thus,

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

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Answer:

How do you figure out if a relation is a function? You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function!

Step-by-step explanation:

Answer:

Null hypothesis:[tex]\mu \leq 6[/tex]      

Alternative hypothesis:[tex]\mu > 6[/tex]      

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing the info we got:

[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]

[tex]p_v =P(t_{25}>1.335)=0.097[/tex]  

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes

Step-by-step explanation:

Information given

[tex]\bar X=370.69/60 =6.178[/tex] represent the sample mean

[tex]s=24.36/36=0.68[/tex] represent the standard deviation for the sample    

[tex]n=26[/tex] sample size      

[tex]\mu_o =6[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is at least 6 minutes, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \leq 6[/tex]      

Alternative hypothesis:[tex]\mu > 6[/tex]      

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing the info we got:

[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]      

The degrees of freedom are:

[tex]df=n-1=26-1=25[/tex]  

The p value would be given by:

[tex]p_v =P(t_{25}>1.335)=0.097[/tex]  

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes.

Answer: 1-20=2  and 60-80=4

Step-by-step explanation:

the first is 2 number of building

and the third one is 4 number of buldings

Hope this helps :)

Answer:

work is shown and pictured

Answer:

a) The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

c)

Step-by-step explanation:

a) Let p be  the probability of winning each ticket be = 0.1

Then q which is the probability of failing each ticket  = 1 - p = 1  - 0.1 = 0.9

Assume X represents the  number of failure preceding the 5th success in x + 5 trials.

The last trial must be success whose probability is p = 0.1 and in the remaining (x + r- 1) ( x+ 4 ) trials we must have have (4) successes whose probability is given by:

[tex]\binom{x+r-1}{r-1}*p^{r-1}*q^{x} = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

Then, the probability distribution of random variable X is

[tex]P(X=x) = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

where;

X represents the  negative binomial random variable.

K= X + 5 = number of ticket buy up to and including fifth winning ticket.

Since K =X+5 this signifies that  X = K-5

as X takes value 0, 1 ,2,...

K takes value 5, 6 ,...

Therefore:

The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

Let p represent the probability of getting a tail on a flip of the coin

Thus p = 0.5 since it is a fair coin

where L = number of flips of the coin including 33rd occurrence of  tails

Thus; the negative binomial distribution of L can be illustrated as:

[tex]P(X=x) = \binom{x-1}{r-1}(1-p)^{x-r}p^r[/tex]

where

X= L

r = 33  &

p = 0.5

Since we are looking at the 33rd success; L is likely to be : L = 33,34,35...

Thus; the PMF of L = [tex]P(L=l) = \binom{l-1}{33-1}(1-0.5)^{l}(0.5)^{33} \\ \\ \\ \mathbf{P(L=l) = \binom{l-1}{33-1}(0.5)^{l} }[/tex]

c)  

Given that:

Let  M be the random variable which represents  the number of tickets need to be bought to get the first success,

also success probability is 0.01.

Therefore, M ~ Geo(0.01).

Thus, the PMF of M is given by:

[tex]P(M = m) = (1-0.01)^{m-1} * 0.01 , \ \ \ since \ \ \ (m = 1,2,3,4,....)[/tex]

[tex]P(M=m) = (0.99)^{m-1} * 0.01 , m = 1,2,3,4,....[/tex]

Completed Question

Outputs to be matched to the functions are:

Answer:

Step-by-step explanation:

Given the vector x: x <- c(2, 43, 27, 96, 18)

Sort

In R, the sort(x)  function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.

Therefore, the output that matches the sort function is:

sort(x): 2, 18, 27, 43, 96

Rank

The rank function returns a vector with the "rank" of each value.

x <- c(2, 43, 27, 96, 18)

Therefore, the output of rank(x)  is: 1, 4, 3, 5, 2

Order

When the function is sorted, the order function gives the previous location of each of the element of the vector.

Using the sort(x) function, we obtain: 2, 18, 27, 43, 96

In the vector: x <- c(2, 43, 27, 96, 18)

Therefore, the output of order(x) is: 1, 5, 3, 2, 4

Answer:

[tex]\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]

Step-by-step explanation:

Volume of water in the tank = 1000 L

Let y(t) denote the amount of salt in the tank at any time t.

Initially, the tank contains 60 kg of salt, therefore:

y(0)=60 kg

Rate In

A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.

[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of solution)

[tex]=(0.03\frac{kg}{liter})( 9\frac{liter}{min})=0.27\frac{kg}{min}[/tex]

Rate Out

The solution is mixed and drains from the tank at the same rate.

Concentration, [tex]C(t)=\dfrac{Amount}{Volume} =\dfrac{y(t)}{1000}[/tex]

[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)

[tex]=\dfrac{y(t)}{1000}* 9\dfrac{liter}{min}=0.009y(t)\dfrac{kg}{min}[/tex]

Therefore, the differential equation for the amount of Salt in the Tank  at any time t:

[tex]\dfrac{dy}{dt}=R_{in}-R_{out}\\\\\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]

Answer:

3.43

Step-by-step explanation:

3 is the whole number and 43 out of 100 is a standard fraction that can simply be stated as 0.43. Hope this helps!

Answer:

3.43

Step-by-step explanation:

Used calculator.

Answer:

D.

Step-by-step explanation:

In the attached file

Answer:

At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.

P-value = 0.003.

Step-by-step explanation:

If we perform a regression analysis relating x and y, we get the best fitting line with equation:

[tex]y=15.82x+92.9[/tex]

and a correlation coefficient r:

[tex]r=0.693[/tex]

We have to test the hypothesis, where the alternative hypothesis claims that there is a relationship between these two variables, and the null hypothesis claiming there is no relationship (meaning that the correlation is not significantly different from 0).

This can be written as:

[tex]H_0: \rho=0\\\\H_a:\rho\neq0[/tex]

where ρ is the population correlation coefficient for x and y.

The significance level is assumed to be 0.05.

The sample size is n=16.

The degrees of freedom are df=14.

[tex]df=n-2=16-2=14[/tex]

The test statistic can be calculated as:

[tex]t=\dfrac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\dfrac{0.693\sqrt{14}}{\sqrt{1-(0.693)^2}}=\dfrac{2.593}{0.721}=3.597[/tex]

For a test statistic t=2.05 and 14 degrees of freedom, the P-value is calculated as:

[tex]\text{P-value}=2\cdot P(t>3.597)=0.003[/tex]

The P-value (0.003) is smaller than the significance level (0.05), so the effect is significant enough.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.

Answer:

The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex]  to [tex]40^o[/tex]

Step-by-step explanation:

The temperature range is the difference between the maximum and the minimum temperature:

[tex]40^o-(-45^o)=40^o+45^o=95^o[/tex]

The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex]  to [tex]40^o[/tex]

Answer:

Dear Laura Ramirez

Answer to your query is provided below

1) option A is correct

2) option B is correct

Step-by-step explanation:

Explanation for the first question attached in image

Also note - The converse of the hinge theorem states that if two triangles have two congruent sides, then the triangle with the longer third side will have a larger angle opposite that third side.

Answer:

1) option A is correct2) option B is correct

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

The answer here is A.

A) A is congruent to D.

A=

Step-by-step explanation:

AP E

Answer:

  AB = 8

Step-by-step explanation:

Since C is the midpoint, ...

  AC = CB

  5x -6 = 2x

  3x = 6 . . . . . . . add 6-2x

  x = 2

Then the length of AB is ...

  AB = 2(CB) = 2(2x) = 4(2)

  AB = 8

Answer:

C.

Step-by-step explanation:

There are 16 ounces in a pint. 8 * 16 = 128

Answer:

15

Step-by-step explanation:

Because the two triangles are similar:

[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]

Hope this helps!

Answer:

270

Step-by-step explanation:

For any arithmetic sequence

nth term is given by

nth term = a + (n-1)d

where a is first term,

d is common difference

d is given by nth term - (n-1)th term

sum of n terms given by

sum = n/2(2a + (n-1)d)

________________________________________________

Given arithmetic sequence

-2,0,2,4,6,8...

first term a = -2

lets take third term as nth term and second term as (n-1)th term to find common difference d.

d = 2 - 0 = 2

using a = -2 , d = 2, n = 18

thus, sum of first 18 terms = n/2(2a + (n-1)d)

                                           =18/2( 2*(-2) + (18-1) 2)

                                           =9 ( -4 + 34)

                                           =9 ( 30) = 270

Thus, sum of first 18 terms is 270.

Answer:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.  

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

[tex]\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}[/tex]

Seperate the differential equation and solve for the constant C.

[tex]\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}[/tex]

You have 100 rodents when:

[tex]100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months[/tex]

You have 1000 rodents when:

[tex]1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months[/tex]

Answer:

the elevation of base camp is 35 ft

Step-by-step explanation:

Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation

Answer:

35 feet

Step-by-step explanation:

65 feet- 30 feet= 35 feet is the elevation of the base

The linear function that describes the table is f(x) = -2x + 3

The linear function of an equation can be found as follows:

y = mx + b

where

Therefore, using the table

b = 3

using (1, 1)

1 = m + 3

m = -2

Therefore, the function that represent the table is as follows:

f(x) = -2x + 3

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Answer:  f(x) = -2x + 3

Step-by-step explanation:

Answer: 207^2 + 9km^2 = 216km^2

Step-by-step explanation:

(my explanation is wrong)

All you want to do is break this figure up into rectangles and triangles.

I see 3 rectangles and 1 triangle.

Three Rectangles:

The bottom one has the dimension of 5 and 20. 5 x 20 = 100 km^2

The middle one has the dimensions of 5+4 and 7. 9 x 7 = 63 km^2

The top one has the dimensions of 4 and 11. 4 x 11 = 44 km^2

Add them all up to get 207km^2

One Triangle:

We can see at the bottom rectangle that the left side is 5 and the right side is 3 + x. X being our missing height of the triangle. The height equals 2.

The triangle now has the dimensions of 2 and 6. 2 x 6 = 12. Then divide by 2 to get 6 km^2

Answer:

216 km²

Step-by-step explanation:

To solve this, you have to divide the figure into different parts.  I divided the parts up into four sections.  I will work on the parts in numerical order.

1.  At the top of the rectangle, it is marked 4 km. On the left side, it is marked 11 km.  This is the length and width.

A = lw

A = 11 × 4

A = 44 km²

2.  On the left side of this rectangle, it is marked 7 km.  At the top it is marked 5 km, but there is a portion that does not have a measurement (the part with a different color than the rest.  Because this line is also part of rectangle 1, we know that the line is 4 km.  Adding up the two numbers gives you 9 km.  

4 + 5 = 9

A = lw

A = 7 × 9

A = 63 km²

3.  On the left side, it is marked 5 km.  On the bottom, it is marked 20 km.

A = lw

A = 20 × 5

A = 100 km²

4.  This is one is a bit more tricky.  This is a triangle, so we have to find the base and the height.  The base is 6 km.  You have to figure the height.  Look at the picture with the red lines.  

The red line on the right side has a length of 17 + 3 + x = 20 + x.  The length is 20 + x because there is a portion of the line that is missing.

The red lines on the left side have a length of 5 + 7 + 11 = 23.  The two side should be equal so

23 = 20 + x

x = 3

Now, you have the height.  Use the equation for area of a triangle to solve.

A = 1/2bh

A = 1/2(3)(6)

A = 1/2(18)

A = 9 km²

Now you have to add up all the areas to find the total area.

44 km² + 63 km² + 100 km² + 9 km² = 216 km²

Answer:

$5,882

Step-by-step explanation:

To calculate the money Lindsay needs today, you can use the following formula to calculate the present value:

PV=FV/(1+i)^n

PV= present value

FV= future value= $8,000

i= interest rate= 8%

n= number of periods= 4

PV= 8,000/(1+0.08)^4

PV=8,000/1.08^4

PV=8,000/1.36

PV= 5,882

According to this, Lindsay will need to have $5,882 in the account today so she will have enough to pay for the repairs in four years.

Answer:

GH¢.37480.36

Step-by-step explanation:

Let the amount invested at 12% per annum =GH¢.x

He  invested 580.00 more than the first at 14%.

Therefore:

The amount invested at 14% =GH¢.(x+580)

For each investment option:

Amount Accrued =Principal + Simple Interest

Amount Accrued at 12%

[tex]=x+x*0.12\\=1.12x[/tex]

Amount Accrued at 14%

[tex]=(x+580)+0.14(x+580)\\=x+580+0.14x+81.2\\=1.14x+661.2[/tex]

Mr. Azu had total accumulated amount of  GH42,358.60

Therefore:

1.12x+1.14x+661.2=42,358.60

2.26x=42,358.60-661.2

2.26x=41697.4

x=GH¢.18450.18

Therefore:

The amount invested at 12% per annum= GH¢.18450.18

The amount invested at 14% per annum= GH¢.18450.18+580

=GH¢.19030.18

Mr Azu's Total Investment = 18450.18 +19030.18

=GH¢.37480.36

Answer:

The table that illustrates this equation is table A:

1   -6   0   up   (0,0)

Step-by-step explanation:

The values of the parameters a, b, and c have to agree with the values for the general quadratic equation in standard form:

[tex]y = a\,x^2+b\,x+c[/tex]

compared to:

[tex]y=x^2-6\,x[/tex]

So the coefficient "a" of the quadratic term in our case is: "1"

the coefficient "b" of the linear term is : "-6"

the coefficient "c" for the constant term s : "0" (zero)

since the coefficient "a" is a positive number, we know that the parabola's branches must be opening "UP".

The y intercept can be found by evaluating the expression for x = 0:

[tex]y=x^2-6x\\y=(0)^2-6\,(0)\\y=0[/tex]

Therefore the y-intercept is at (0, 0)

These results agree with those of Table "A"

Answer:

Table A.)

Step-by-step explanation:

a 1, b -6, c 0, up, (0, 0), Table A.