What is the solution of 3(x + 4) = -12 ? Group of answer choices 3 0 8 -8

[tex]A\cup B=\{q,s,u,w,y,z\}\\(A\cup B)'=\{r,t,v,x\}\\\boxed{(A\cup B)'\cap C=\{v,x\}}[/tex]

Note that the characteristic solutions to this ODE are [tex]e^{-2x/5}[/tex] and [tex]e^{2x}[/tex], so we can safely assume a particular solution of the form

[tex]y_p=(ax+b)e^{3x}[/tex]

with derivatives

[tex]{y_p}'=ae^{3x}+3(ax+b)e^{3x}=(3ax+a+3b)e^{3x}[/tex]

[tex]{y_p}''=3ae^{3x}+3(3ax+a+3b)e^{3x}=(9ax+6a+9b)e^{3x}[/tex]

Substitute these expressions into the ODE and solve for a and b. Notice that each term on either side contains a factor of [tex]e^{3x}[/tex], which we can cancel.

[tex]-\dfrac54(9ax+6a+9b)+2(3ax+a+3b)+(ax+b)=3x[/tex]

[tex]-\dfrac{17a}4x-\left(\dfrac{11a}2+\dfrac{17b}4\right)=3x[/tex]

[tex]\implies\begin{cases}-\frac{17a}4=3\\\frac{11a}2+\frac{17b}4=0\end{cases}[/tex]

[tex]\implies a=-\dfrac{12}{17}\text{ and }b=\dfrac{264}{289}[/tex]

So the particular solution is

[tex]y_p=\left(-\dfrac{12x}{17}+\dfrac{264}{289}\right)e^{3x}=\boxed{\dfrac{12}{289}(22-17x)e^{3x}}[/tex]

Answer:

The interval    ( 1,8 ; 14,4 ) will contains 99,7 % of all values      

Step-by-step explanation:

For Normal Distribution  N ( μ ; σ ) the Empirical Rule establishes that in the intervals:

( μ  ±  σ )   we find  68,3 % of all values

( μ  ±  2σ ) we find  95,4 % of all values

( μ  ±  3σ ) we find  99,7 % of all values

Then we have a normal distribution  N ( 8,1 ; 2,1 )

3*σ  =  3* 2,1 = 6,3

And   8,1 - 6,3  = 1,8             8,1  + 6,3  = 14,4

Then the interval    ( 1,8 ; 14,4 ) will contains 99,7 % of all values      

[tex]8 {sin}^{2} x + cos \: x - 5 = 0[/tex]

[tex]recall \: that \: {sin}^{2} x + {cos}^{2} x = 1[/tex]

[tex]then \: {sin}^{2} x = 1 - {cos}^{2} x[/tex]

then substitute,

[tex]8( 1 - {cos}^{2} x) + cos \: x - 5 = 0[/tex]

After Further Simplication,

[tex]8 {cos}^{2} x - cos \: x - 3 = 0[/tex]

[tex]let \: y = \cos(x) [/tex]

[tex]8 {y}^{2} - y - 3 = 0[/tex]

use quadratic formulae

[tex]y = 0.375 \: or \: - 0.25[/tex]

therefore

[tex] \cos(x) = 0.375 \: or \: - 0.25[/tex]

[tex] x = 70degrees \: or \: 104.5degrees[/tex]

Answer:

P(t) = {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)

Step-by-step explanation:

The equation of the tangent line to the given path at the specified value of t is expressed as;

P(t) = f(t0) + f'(t0)(t - t0)

f(t0) = (sin(7t), cos(7t), 2t^9/2)

at t0 = 1;

f(t0) = {sin7(1), cos7(1), 2(1)^9/2}

f(t0) = {sin7, cos7, 2}

f'(t0) = (7cos7t, -7sin7t, 9/2{2t^9/2-1}

f'(t0) = (7cos7t, -7sin7t, 9t^7/2}

If t0 = 1

f'(1) = (7cos7(1), -7sin7(1), 9(1)^7/2)

f'(1) =(7cos7, -7sin7, 9)

Substituting the given function into the tangent equation will give:

P(t) = f(t0) + f'(t0)(t - t0)

P(t)= {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)

The final expression gives the equation of the tangent line to the path.

Answer:

Null Hypothesis: H0:μ ≤ 16.8

Alternative Hypothesis: Ha: μ > 16.8

Step-by-step explanation:

We are told that affer testing the hypothesis (at the 5% level of significance), that the average price-earnings ratio increased from the past value of 16.8.

It means that the past value was not more than 16.8.

This follows that the null hypothesis is given as;

H0:μ ≤ 16.8

And since it has been discovered that the ratio increased from the past value of 16.8, the alternative hypothesis is;

Ha: μ > 16.8

Answer:

320

Step-by-step explanation:

Total no of employees = 1600

% of employees attended the training = 80%

no. of employee who attended the training = 80/100* 1600 = 1280

No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training =  1600-1280 = 320

Thus, 320 employees have yet to attend the training

A number that can be divided exactly only by itself and 1.

For Eg:- 7, 10, 13.

Answer:

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic:

Answer:

B. 360 .75

Step-by-step explanation:

The circumference of the circle is represented by π * diameter of the circle. The circumference of the circle is its perimeter. The circumference is arc length of the circle.  The perimeter is curve length around the figure of the circle. The circumference of the circle of 75 inches is represented by 75/360.

Answer: 72/360 multiply by 75

Step-by-step explanation:

i just did this question

===================================================

Work Shown:

a = -27 = first term

r = 1/3 = common ratio, note how this is between -1 and 1

We start with -27 and multiply by 1/3 each time to get the next term

S = infinite sum

S = a/(1-r), which only works because -1 < r < 1 is true

S = -27/(1-1/3)

S = -27/(2/3)

S = (-27/1) divided by (2/3)

S = (-27/1) times (3/2)

S = (-27*3)/(1*2)

S = -81/2

As you generate and add up the terms of the sequence, the infinite sum slowly starts to approach -81/2 = -40.5; we'll never actually achieve this sum exactly. Think of it as approaching an asymptote.

Answer:

x=2

Step-by-step explanation:

2(1+3x)=14​

Divide each side by 2

2/2(1+3x)=14/2

1+3x = 7

Subtract 1 from each side

3x =7-1

3x = 6

Divide by 3

3x/3 = 6/3

x =2​

Answer:

f-4

Step-by-step explanation:

f-4  cannot be simplified

This is the simplest form

Answer:

[tex]\large \boxed{f-4}[/tex]

Step-by-step explanation:

[tex]f-4[/tex]

[tex]\sf f \ is \ a \ nonzero \ number.[/tex]

[tex]\sf The \ expression \ cannot \ be \ simplified \ further.[/tex]

Answer:

Amount of balance maintain = $2,500

Step-by-step explanation:

Given:

Limit of credit card = $5,000

Debt ratio = 50%

Find:

Amount of balance to maintain

Computation:

Amount of balance to maintain = Limit of credit card × Debt ratio

Amount of balance to maintain = $5,000 × 50%

Amount of balance to maintain = $2,500

Answer:

7/36

Step-by-step explanation:

1 die has 6 faces

When two dice are rolled, the total number of outcomes

= 6 × 6 = 36

The Probability of having(5) =

(1 & 4), (2 & 3) , ( 3 & 2), (4 & 1)

= 4

The probability of having (10) =

(5 & 5), (4 & 6) , ( 6 & 4)

= 3

The probability that the score on the dice is either 5 or 10.

P(5) + P(10)

= 4/36 + 3/36

= 7/36

Answer: 7/36

Step-by-step explanation:

36 outcomes

4 chances of getting 5 (1+4, 2+3, 4+1, 3+2)

3 chances of getting 10 (4+6, 5+5, 6+4)

4+3=7

so 7/36 chance

Answer:

federal loans = $29,000

private loans = $14,000

Step-by-step explanation:

x + y = 43000

.045x + .02y = 1585

x = 29,000

y = 14,000

Answer:

Amount of loan from federal : $ 29,000

Amount of loan from private bank : $ 14,000

Step-by-step explanation:

We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.

If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -

x + y = 43,000

At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -

0.045x + 0.02y = 1585

Let's solve the following system for x and y, the amount of each loan,

[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )

[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )

[tex]1935-0.025y=1585[/tex],

[tex]1935000-25y=1585000[/tex],

[tex]-25y=-350000[/tex],

[tex]y=14000[/tex],

[tex]x=29000[/tex]

Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.

Answer: Check out the diagram below for the filled in boxes

14 goes in the first box (inside A, but outside B)

7 goes in the overlapping circle regions

5 goes in the third box (inside B, outside A)

3 goes in the box outside of the circles

==============================================================

Explanation:

[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.

n(A) = 21 means there are 21 items in A

n(B) = 12 means there are 12 items in B

We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]

It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.

--------

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]

So there are 7 items in both regions.

This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.

Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.

Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.

The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.

Again the diagram is posted below with the filled in values.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

The filled Venn diagram is given below.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

n(A) = 21

This is the total of all the items included in Circle A.

n(B) = 12

This is the total of all the items included in Circle A.

n(A') = 8

The items that are not in circle A.

n(A U B ) = 26

The items that are in both circle A and circle B.

Now,

n (A U B) = n(A) + n(B) - n(A ∩ B)

26 = 21 + 12 - n(A ∩ B)

n(A ∩ B) = 33 - 26

n(A ∩ B) = 7

Thus,
The filled Venn diagram is given below.

Learn more about the Venn diagram here:

https://brainly.com/question/1605100

#SPJ2

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:

0 ton

Step-by-step explanation:

The question states that 99,000 acres are harvested. This suggest that there are plenty sellers of almonds.The Sagardia Brothers grew 600 acres of almonds. this is a small percentage of the total output of almonds. This suggests that the market for almonds is perfectly competitive.

In this type of market, if the price of a seller is above equilibrium price, zero units of the commodity would be bought. This is because the goods sold are homogenous and buyers can easily purchase from other buyers that sell at the market price

Answer:

C. Line chart

Step-by-step explanation:

Answer:

B. Histogram

Step-by-step explanation:

Histogram uses time.

Answer:

4.2

Step-by-step explanation:

f varies inversly with L can be translated matimatically as:

● f = k/L

It takes 7 pounds of pressure to break a 3 feet long board.

Replace f by 7 and L by 3.

● 7 = k/3 => k=7×3=21

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's find tge length of a board that takes 5 pounds of pressure to be broken.

● 5 = k/L

● 5 = 21/L

● L = 21/5 = 4.2

So the board is 4.2 feet long

Answer:

42 Dimes, 10 Nickels.

Step-by-step explanation:

Dimes are worth $0.10, nickels are worth $0.05.

If D = number of dimes, and N = number of nickels, then the following equations are true:

0.10D + 0.05N = 4.70

D + N = 52

Next, let's multiply the first equation by 10 so that we can subtract the second one from it.

D + 0.50N = 47

(-) D + N = 52

Subtracting the second equation from the first one gives:

-0.5N = -5

-0.5N/-0.5 = -5/-0.5

N = 10

Finally, substitute N in the original second equation to find D.

D + 10 = 52

D + 10 - 10 = 52 - 10

D = 42

Answer:

The answer is C. SSA ≅ SSA.

Step-by-step explanation:

To check for similar triangles, SSA congruence would not work because the other side can be any length. Also, there is not an SSA postulate because this theorem by itself cannot prove congruence.

The other three properties do work because they show congruence unlike the other congruent factors.

Answer:

40% solution = 20 gallons

80% solution = 60 gallons

Step-by-step explanation:

x = gallons of 40% solution

y = gallons of 80% solution

Total volume is:

x + y = 80

Total amount of fertilizer is:

0.40 x + 0.80 y = 0.70 (80)

Solve by substitution.

0.40 x + 0.80 (80 − x) = 0.70 (80)

0.40 x + 64 − 0.80 x = 56

0.40 x = 8

x = 20

y = 60

Answer:

y+6=-1/2(x-3)

Step-by-step explanation:

Point slope form: y-y1=m(x-x1)

Given that:

m=-1/2 and point (3, -6), you just add these numbers into the equation, and this gives:

y+6=-1/2(x-3)

Hope this helped!

Have a nice day!

Answer:

The probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.

Step-by-step explanation:

The complete question has the data of mean = 80 kg and standard deviation = 8kg

We have to find the probability between 72 kg and 88 kg

Since it is a normal distribution

(x`- u1 / σ/ √n) < Z >( x`- u2 / σ/ √n)

P (72 <x>88) = P ( 72-80/8/√1) <Z > ( 88-80/8/√1)

= P (-1<Z> 1) = 1- P (Z<1) - P (Z<-1)

= 1- 0.8413- (- 0.8413)= 1- 1.6826= 0.6826

So the probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.

[tex]13ab^3+39a^2b^5\\\\\boxed{\boxed{\boxed{13ab^3(1+3ab^2)}}}\\\\[/tex]

Brazil number one.

Answer:

there's no answer for that equation

Answer:

16

Step-by-step explanation:

7x+20+2x-5=159

9x+15=159

9x=159-15

9x=144

x=16

Answer:

b.) 0.30

Step-by-step explanation:

15/50 = 0.3

Answer:

10.125

Step-by-step explanation:

Hello!

To find this we first have to convert the percentage to a decimal

We do this by moving the decimal point two times left

75.0% = 0.75

Now we multiply this by the number

13.5 * 0.75 = 10.125

The answer is 10.125

Hope this helps!

Answer:

90% confidence the Population mean number of texts per day

(42.2561 ,47.1439)

Step-by-step explanation:

Step(i):-  

Given sample size 'n' = 147

mean of the sample size x⁻ = 44.7

standard deviation of the sample 'S' = 17.9

90% confidence the Population mean number of texts per day

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

Step(ii):-

Degrees of freedom

       ν=n-1=147-1=146

t₀.₁₀ =  1.6554

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

[tex](44.7 - 1.6554 \frac{17.9}{\sqrt{147} } ,(44.7 + 1.6554 \frac{17.9}{\sqrt{147} })[/tex]

(44.7 - 2.4439 ,44.7 + 2.4439 )

(42.2561 ,47.1439)

Conclusion:-

90% confidence the Population mean number of texts per day

(42.2561 ,47.1439)