Problem is attached in a photo

[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]

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]

Complete Question

I = prt is an example of

• a variable

• an expression

• a constant

• a formula

Answer:

A formula

Step-by-step explanation:

I = prt is an example of a formula called Simple Interest.

Simple Interest can be defined as the formula that is used to calculate the interest that is accumulated on a particular amount of money which was saved in a financial institution or loaned out to a person at a given interest rate for a particular period of time.

The formula for Simple Interest is Expressed as:

I = PRT

Where :

I = Simple Interest

P = Principal = Amount saved, or loaned out

R = Interest rate that is given in percentage form

T = Time that has elapsed in Years.

Answer:

D. A Formula

Step-by-step explanation:

A formula is an equation that uses variables to state a rule.

Hope I was able to help you!

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:

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:

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:

a. the largest number of observations.

Step-by-step explanation:

The mode is the variable in a data that has the highest frequency. Which implies that it occurs more than other variables.

When plotting a histogram, the modal class is one that has the greatest number of observations. Showing that the variables comprised in the class has more occurrence than others. Therefore, the required answer to the question is option a.

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:

A

   The  correct option is B

B

   [tex]t = 0.6093[/tex]

C

 [tex]p-value = 0.27116[/tex]

D

The  correct option is  D

Step-by-step explanation:

From the question we are told that

    The  sample size is  [tex]n = 232[/tex]

    The  number that developed  nausea  is X =  50

    The population proportion is  p  =  0.20  

The  null hypothesis is   [tex]H_o : p = 0.20[/tex]

The  alternative hypothesis is  [tex]H_a : p > 0.20[/tex]

Generally the sample proportion is mathematically represented as

     [tex]\r p = \frac{50}{232}[/tex]

     [tex]\r p = 0.216[/tex]

Generally the test statistics is mathematically represented as

 =>           [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p )}{n} } }[/tex]

=>           [tex]t = \frac{ 0.216 - 0.20 }{ \sqrt{ \frac{ 0.20 (1- 0.20 )}{ 232} } }[/tex]

=>        [tex]t = 0.6093[/tex]

The  p-value obtained from the z-table is

       [tex]p-value = P(Z > 0.6093) = 0.27116[/tex]

  Given that the  [tex]p-value > \alpha[/tex]  then we fail to reject the null hypothesis

Step-by-step explanation:

Here,

[tex]5y = 4x - 12 - 10[/tex]

[tex]y = \frac{4}{5} x - \frac{22}{5} [/tex]

slope is 4÷5

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

5(y+2)=4(x-3)

To find the slope first expand the terms in the equation

That's

5y + 10 = 4x - 12

Write the equation in the form y = mx+ c

That's

5y = 4x - 12 - 10

5y = 4x - 22

Divide both sides by 5 to make y stand alone

y = 4/5x - 22/5

Comparing with the general equation above the slope of the line is

Hope this helps you

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

[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]

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:

work is shown and pictured

Answer:

Hi, there!!!

The answer would be 2(2x-1)/x(x-4).

See explanation in picture.

Hope it helps...

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:

B y = -1/2x + 7/2

Step-by-step explanation:

We know that it has a negative slope since the points go from the top left to the bottom right

We can eliminate A and D

The y intercept is where it crosses the y axis

It should cross somewhere between 2 and 4

C  has a y intercept of 9 which is too big

Lets verify with a point

x = -4

y = -4(-4)+9 = 16+9 = 25  (-4,25)  not even close to being near the points on the graph

checking B

y = -1/2 (-4) +7/2

  = 2 + 7/2 = 11/2 = 5.5  it seems  reasonable

Answer:

[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]

Step-by-step explanation:

Using a graph,

we can see that the line y = -1/2x + 7/2 best fits for the data.

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

The statement is false. A sampling distribution is normal if either n > 30 or the population is normal.

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

Explanation:

If the underlying population is normally distributed, then so is the sample distribution (such as the distribution of sample means, aka xbar distribution).

Even if the population isn't normally distributed, the xbar distribution is approximately normal if n > 30 due to the central limit theorem. Some textbooks may use a higher value than 30, but after some threshold is met is when the xbar distribution is effectively "normal".

Choice A is close, but is missing the part about the population being normal. If we know the population is normal, then n > 30 doesn't have to be required.

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:

16

Step-by-step explanation:

7x+20+2x-5=159

9x+15=159

9x=159-15

9x=144

x=16

Complete Questions:

Create an equation with a solution closest to 0 using digits 1 to 9

_x + _ = _x + _

Answer:

See Explanation

Step-by-step explanation:

Given

_x + _ = _x + _

Required

Fill in the gap using 1 to 9 to give a result close to 0

First, you have to determine what kind of numbers that are close to 0;

In this case, I'll work with -0.4 to 0.4 because the number in this range approximate to 0;

Next, is to fill in the gaps using trial by error method

5x + 2 = 2x + 3

Checking the above expression

Collect Like Terms

[tex]5x - 2x = 3 - 2[/tex]

[tex]3x = 1[/tex]

Divide equation by 2

[tex]x = 0.33[/tex] (Approximated)

Another trial is

6x + 8 = 2x + 7

Checking the above expression

Collect Like Terms

[tex]6x - 2x = 7 - 8[/tex]

[tex]4x = -1[/tex]

Divide equation by 4

[tex]x = -0.25[/tex] (Approximated)

I'll stop here but note that, there are more expressions that can fill in the gaps

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:

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      

Answer: the distance is  3.49 units

Step-by-step explanation:

There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.

When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:

x = R*cos(θ)

y = R*sin(θ)

Then we have:

(7,217pi/180 )

R = 7

θ = (217/180)*pi

x = 7*cos( (217/180)*pi) = -5.59

y = 7*sin( (217/180)*pi) = -4.21

So this point is (-5.59, -4.21) in rectangular coordinates.

And the other point is  (5,-23pi/36 )

R = 5

θ = -(23/36)*pi

x = 5*cos(  -(23/36)*pi ) = -2.11

y = 5*sin(  -(23/36)*pi ) = -4.53

So this point is (-2.11, - 4.53)

Then the point distance between those points is:

D = I (-2.11, -4.53) - (-5.59, -4.21) I

D = I (-2.11 + 5.59, -4.53 + 4.21) I

D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) =  3.49

Answer:

b.) 0.30

Step-by-step explanation:

15/50 = 0.3

Answer:

If a polygon has 3 sides, then the polygon is a triangle.

Step-by-step explanation:

Bold = hypothesis

Italic = conclusion

Statement:

If p, then q.

Converse: If q, then p.

To find the converse, switch the hypothesis and conclusion.

Statement:

If a polygon is a triangle, then it  has 3 sides.

Now we switch the hypothesis and the conclusion to write the converse of the statement.

If it  has 3 sides, then a polygon is a triangle.

We fix a little the wording:

If a polygon has 3 sides, then it is a triangle.

Answer: If a polygon has 3 sides, then the polygon is a triangle.

The converse statement will be;

⇒ If a polygon has 3 sides, then the polygon is a triangle.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The statement is,

''If a polygon is a triangle, then it has 3 sides. ''

Now,

Since, The statement is,

''If a polygon is a triangle, then it has 3 sides. ''

We know that;

The converse of statement for p → q will be q → p.

Thus, The converse statement is find as;

⇒ If a polygon has 3 sides, then the polygon is a triangle.

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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:

150+233-64=319

Jim is 319 ft above sea level.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that:

A simple random sample n = 28

sample standard deviation S = 12.65

standard deviation [tex]\sigma[/tex] = 11.53

Level of significance ∝ = 0.05

The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.

The null hypothesis and the alternative hypothesis can be computed as follows:

Null hypothesis:

[tex]H_0: \sigma^2 = \sigma_0^2[/tex]

Alternative hypothesis:

[tex]H_1: \sigma^2 \neq \sigma_0^2[/tex]

The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.

[tex]X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}[/tex]

[tex]X_0^2 = \dfrac{(28-1)(12.65)^2}{(11.53)^2}[/tex]

[tex]X_0^2 = \dfrac{(27)(160.0225)}{132.9409}[/tex]

[tex]X_0^2 = \dfrac{4320.6075}{132.9409}[/tex]

[tex]X_0^2 = 32.5002125[/tex]

[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}[/tex]

[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}[/tex]

From the chi-square probabilities table at 0.975 and degree of freedom 27;

[tex]X^2_{0.975 , 27}[/tex] = 14.573

[tex]X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}[/tex]

[tex]X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}[/tex]

From the chi-square probabilities table at 0.975 and degree of freedom 27;

[tex]X^2_{0.025 , 27}=[/tex] 43.195

Decision Rule: To reject the null hypothesis if [tex]X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}[/tex] ; otherwise , do not reject the null hypothesis:

The rejection region is [tex]X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573[/tex]

Conclusion:

We fail to reject the null hypothesis since  test statistic value 32.5002125  lies  between 14.573 and 43.195.

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.

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