You have one type of nut that sells for $2.80/lb and another type of nut that sells for $9.60/lb. You would like to have 20.4 lbs of a nut mixture that sells for $6.60/lb. How much of each nut will you need to obtain the desired mixture?

Answer:

6:8

Step-by-step explanation:

Answers:

1a) The next four terms are: 513, -728, 1001, -1330

1b) The direct formula is [tex]a_n = (-1)^n*n^3+1[/tex]

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

Explanation:

It helps to start with part B first. The direct formula will help us find the next four terms in a very efficient manner.

Start with the sequence {0, 9, -26, 65, -124, 217, -342}

Subtract 1 from each term to get this new sequence {-1, 8, -27, 64, -125, 216, -343}, which closely resembles the sequence {1, 8, 27, 64, 125, 216, 343}. This is the sequence of perfect cubes. The only difference is that each term alternates from positive to negative and vice versa.

So we will have an n^3 as part of the equation and also a (-1)^n as part of the equation. The (-1)^n portion allows us to alternate in signs. Put together we have (-1)^n*n^3 so far

The last thing we do is add 1 to this so that we undo the operation "subtract 1" we did earlier to the original list.

Therefore the formula is [tex]a_n = (-1)^n*n^3+1[/tex]

--------------------

To help verify we have the right formula, plug in n = 1 and we get

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_1 = (-1)^1*1^3+1[/tex]

[tex]a_1 = 0[/tex]

and plug in n = 2 to get

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_2 = (-1)^2*2^3+1[/tex]

[tex]a_2 = 9[/tex]

and so on. I'll let you check the other terms

--------------------

Let's find the terms a8,a9,a10,a11

This is simply a matter of plugging n = 8, n = 9, n = 10, and n = 11

Plug in n = 8

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_8 = (-1)^8*8^3+1[/tex]

[tex]a_8 = 513[/tex]

Repeat for n = 9

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{9} = (-1)^9*9^3+1[/tex]

[tex]a_{9} = -728[/tex]

Repeat for n = 10

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{10} = (-1)^{10}*10^3+1[/tex]

[tex]a_{10} = 1001[/tex]

Repeat for n = 11

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{11} = (-1)^{11}*11^3+1[/tex]

[tex]a_{11} = -1330[/tex]

Answer:

$792.50

Step-by-step explanation:

As the mortgage rate is 3.75% APR , One has to pay 3.75% of the amount of home in a year as Interest .

Amount of home = $253,600.00

One year interest one has to pay in a year  = [tex]\frac{3.75}{100}[/tex]×253,600

                                                        = $9510.

So, In one month , he has to pay amount $[tex]\frac{9510}{12}[/tex] .

                                                                   = $792.5.

Answer:

Step-by-step explanation:

A) 2x³ +x² -18x -9 = x²(2x +1) -9(2x +1) = (x² -9)(2x +1) = (x -3)(x+3)(2x +1)

__

B) x³ +3x² -x -3 = x²(x +3) -1(x +3) = (x² -1)(x +3) = (x -1)(x +1)(x +3)

__

C) 4x³ -16x² -x +4 = 4x²(x -4) -1(x -4) = (4x² -1)(x -4) = (2x -1)(2x +1)(x -4)

_____

In each case, the third-level factoring mentioned in step 4 is the factoring of the difference of squares: a² -b² = (a -b)(a +b).

_____

The step-by-step is exactly what you need to do. It is simply a matter of following those instructions. You do have to be able to recognize the common factors of a pair of terms. That will be the GCF of the numbers and the least powers of the common variables.

Answer:

56 pentagon.

Step-by-step explanation:

Here is the complete question: Eight point lies on the circle. How many pentagons can you make using five points as vertices?

Given: Five points on vertices.

Using the combination formula to find the number of pentagon.

[tex]_{r}^{n}\textrm{C} = \frac{n!}{r!(n-r)!}[/tex]

⇒ [tex]_{8}^{5}\textrm{C}= \frac{8!}{5!(8-5)!}[/tex]

⇒[tex]_{8}^{5}\textrm{C}= \frac{8!}{5!\times 3!} \\\\_{8}^{5}\textrm{C} = \frac{8\times 7\times 6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times3\times2\times1} = \frac{336}{6}[/tex]

∴ [tex]_{8}^{5}\textrm{C}= 56[/tex]

∴ With eight point lies on circle, we can make 56 pentagons using five points as vertices

Answer:

Step-by-step explanation:

The slope is the ratio of the change in y to the change in x:

  m = ((b+3) -b)/((a +3) -a) = 3/3 = 1

The point-slope form of the equation of a line through point (h, k) with slope m is ...

  y -k = m(x -h)

Here, we have (h, k) = (a, b) and m=1, so the equation in point-slope form is ...

  y -b = x -a

Adding b puts this in slope-intercept form:

  y = x + (b-a)

Answer:

95% confidence Interval would be between $18.775 and $20.225.

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

And margin of error (ME) around the mean calculated as

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

Using the numbers, we get:

ME=[tex]\frac{1.96*5}{\sqrt{64} }[/tex] =1.225

Then 95% confidence Interval would be 20±1.225 or between $18.775 and $20.225

Answer:

The confidence interval is between 18.775 and 21.225.

Step-by-step explanation:

Answer:

75.5 pounds

Step-by-step explanation:

He needs 200

He already has 11.25

He needs:

200 - 11.25 = $188.75 more

1 pound of candy costs 2.50, so x pounds would cost 2.50x

This would need to equal 188.75 (the amount he needs to break even). We can write an equation in x and solve:

[tex]2.50x=188.75\\x=\frac{188.75}{2.50}\\x=75.5[/tex]

James needs 75.5 pounds more to break even

Final answer:

James needs to sell an additional 75.5 pounds of candy to break even, after taking into account the $11.25 he has already earned towards his $200 goal by dividing the remaining amount needed ($188.75) by the price per pound of candy ($2.50).

Explanation:

James is selling candy at a local marketplace and needs to earn at least $200 to break even. He has already earned $11.25. The price of one pound of candy is $2.50. To find out how many more pounds of candy, x, he has to sell to break even, we need to calculate the remaining amount he needs to earn and divide it by the price per pound of candy.

First, subtract the amount already earned from the total needed to break even:

$200 - $11.25 = $188.75

Then, divide this amount by the price per pound of candy to find out how many more pounds he needs to sell:

$188.75 / $2.50 = 75.5

Therefore, James needs to sell an additional 75.5 pounds of candy to break even.

Answer:x+y=58

Step-by-step explanation:

Sum means addition

Answer:

47.72% of students scored between 563 and 637 on the exam .

Step-by-step explanation:

The percentage of the students scored between 563 and 637 on the exam

= The percentage of the students scored lower than 637 on the exam -

the percentage of the students scored lower than 563 on the exam.

Since 563 is the mean score of students on the Statistics course, 50% of students scored lower than 563. that is P(x<563)=0.5

P(x<637)=P(z<z*) where z* is the z-statistic of the score 637.

z score can be calculated using the formula

z*=[tex]\frac{X-M}{s}[/tex] where

Then z*=[tex]\frac{637-563}{37}[/tex] =2

P(z<2)=0.9772, which means that 97.72% of students scored lower than 637 on the exam.

As a Result, 97.72%-50%=47.72% of students scored between 563 and 637 on the exam

Answer:

Option B. 8 mi, 9 mi, 2 mi

Step-by-step explanation:

The option A doesn't have a set of numbers which could be the lengths of the sides of a triangle. The numbers 1,9,10 mean that the longest side is exactly the sum of the others. The only possible way is they lie in the same line, no triangle is formed

Option C gives the numbers 1,9,11. It's impossible to have a side of 11 when you have the sum of the others less than 11. The maximum extension of the other sides (forming a line) won't be enough to reach the length of 11

Option D is also infeasible for the same reason as the option A. The three lines must be aligned to be connected in its extremes

Option B is the only one who can provide a set of possible lengths of a triangle since the sum of the shortest sides is greater than the third. If we open wide enough the angle between the 2 mi side and the 8 mi side, we would eventually connect the 9 mi side and form a triangle

Answer:

B. 22.5m^2

Step-by-step explanation:

To find the area of a trapezoid, you must use the formula:

1/2 × height × (base 1+ base 2)

1. 1/2 × 5m × (8+1)

2. 1/2 x 5m x (9)

3. Switch it around to make it easier to solve

5m × 9× 1/2 (We can do this because of the commutative property.)

4. 45m × 1/2 = 45 ÷ 2 = 22.5m^2

In the context of the problem, this means that the area of the trapezoid is 22.5m^2.

Answer:

66% have graduated within five years.

Step-by-step explanation:

It is given that 70% of freshmen went to public schools. Then the rest 30% i.e.,  [tex]$ \frac{30}{100} = 0.3 $[/tex] should have gone to other schools.

Now, the number the freshmen in public schools is considered as 100% or 1.

60% of the freshmen from public schools have graduated means out of the total freshmen from public schools, 60% of them have graduated. That is why it is denoted as 0.6 and those not graduated as 0.4.

Note that 60% of total students have graduated.

Let us assume there were 100 students initially. Then 70 students went to public school. Number of students graduated = 60%

[tex]$ \implies \frac{60}{100} \times 70  = 42 $[/tex]

That is 42 students have passed from public school.

Now, the ones in other schools:

80% of them have graduated in other schools. That means out of total students 80% of them have graduated.

That means [tex]$ \frac{80}{100} \times 30 = 24 $[/tex]

24 students from other schools have passed.

Therefore, totally 66 students have passed. i.e., 66 percent have passed.

Answer:

The 40% marked up price of refrigerator is  $1260.

Step-by-step explanation:

The cost price of the refrigerator  = $900

Now, the mark up should be 40%

Calculating the markup on the cost price , we get

40 % of $900  =  [tex]\frac{40}{100}  \times 900 = 360[/tex]

or, 40 % mark up = $360

Now, the Marked up cost = Cost Price + Marked up Price

                                          = $900 + $360 = $1260

Hence, the 40% marked up price of refrigerator is $1260.

Answer:

A) 4x - 2y + 3z = - 3

B) 2x - 3y + 2z = 1

C) 6x    + 10z = -2

Multiply A) by -1.5

A) -6x  +3y -4.5z = 4.5  Then adding to B)

B) 2x - 3y + 2z = 1

D) -4x -2.5z = 5.5  then we add this to C)

C) 6x + 10z = -2  Now we multiply D) by 1.5

D) -6x -3.75z = 8.25  Adding C) + D)

6.25z = 6.25

z = 1  Then putting z = 1 into A) and B)

A) 4x - 2y + 3 = - 3  equals A) 4x -2y = -6

B) 2x - 3y + 2 = 1  equals B) 2x -3y = -1 we divide A) by -2

A) -2x + y = 3  then adding to B

B) 2x - 3y  = -1

-2y  = 2

y = -1

FINALLY solving for x we'll use equation A)

A) 4x - 2*-1 + 3*1 = - 3

A) 4x +2 + 3 = -3

A) 4x = -8

x = -2

(Yes, it's just that easy. LOL)

Step-by-step explanation:

Answer:

$6

Step-by-step explanation:

so you add 16 15 and 20 to see how much you earned in total, to get 51 dollars. we subtract 12 because we used it at the movies and get 39 dollars in total. now we subtract this from 45 to see how much more we need to get 6.

equation: 45-(15+16+20-12)........this equals 6 as well

You need to earn more money to buy a $45 video game and it is equal to $6.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

It is given that , you earn some money by doing different works. The earn money from different works is given.

By mowing the lawn money earned = $16

For babysitting money earned = $15

Money earned for the allowance = $20

So , the total money earned is :

= $16 + $15 + $20

= $51

Now , you have spend $12 at the movie theatre. That meant the money now left is :

= $51 - $12

= $39

You need to buy a video game which costs $45. So , you need to earn some more money which is :

= $45 - $39

= $6

Therefore , you need to earn more money to buy a $45 video game and it is equal to $6.

Learn more about algebra here :

https://brainly.com/question/22399890

#SPJ2

Answer:

C) The mean is 22 and the standard deviation is 100.

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

If [tex] X\ sim N(\mu_x =5, \sigma_x =25)[/tex]

And the random variable Y =2+4X.

If we are interested in find the mean and the standard deviation for this new variable we need to apply the concepts of expected value and Variance of random variables.

Using the concept of expected value we have:

[tex]E(Y) =E(2+4X) = E(2) +E(4X)= 2+ 4E(X) =2+4(5) =2+20=22[/tex]

So on this case the [tex]E(Y) =\mu_Y =22[/tex]

Using the concept of variance we have:

[tex]Var(Y)=Var(2+4x)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]

But since 2 is a constant we don't have variance for this and the [tex]Cov(2,4x)=0[/tex] because the covariance of a random variable with a constant is zero. So applying these concepts we have:

[tex]Var(Y)= Var(4x)=4^2 Var (X)= 16 \sigma^2_x =16(25^2)=10000[/tex]

And then if we need the standard deviation we just need to take the square root:

[tex]sd(Y) = \sqrt{10000}=100[/tex]

So the best option for this case would be:

C) The mean is 22 and the standard deviation is 100.

Answer:

Option c) is correct.

Step-by-step explanation:

Given :

[tex]\mu_x = 5[/tex]  and  [tex]\sigma_x = 25[/tex]

Y = 2 + 4X

Calculation:

This problem can be solved by using concept of expected value and variance of random variables.

By expected value concept,

[tex]\rm E(Y) = E(2 + 4X)= E(2) + E(4X)= 2 + 4E(X)=2+4(5)=22[/tex]

Therefore, [tex]\mu_y = 22[/tex]

By variance concept,

[tex]\rm Var(Y)= Var(2+4X)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]

[tex]\rm Cov(2,4X)=0[/tex]

Var(2) = 0

Therefore,

[tex]\rm Var(Y) = Var(4X)= 4^2Var(X)= 16\sigma_x^2=16(25^2)=10000[/tex]

Therefore,

Standard deviation(Y) = [tex]\sqrt{10000}[/tex] = 100

Hence, option c) is correct.

For more information, refer the link given below

https://brainly.com/question/23907081?referrer=searchResults

Answer:

A is the answer

Step-by-step explanation:

If you fail to agree on the actual cash value, amount of loss, or cost of repair or replacement, either can make a written demand for appraisal. ... The two appraisers will then set the amount of loss, stating separately the actual cash value and loss to each item.

When the insured tenant and the insurance company fail to agree on the amount of loss; Choice A is what happens: Either the tenant or the company can request an appraisal, so that an impartial third party determines the amount of loss.

Discussion:

Situations such as in the question may arise when quantifying the amount of loss in an insurance situation.

In such scenarios; the best option is for either the tenant or the company can request an appraisal, so that an impartial third party determines the amount of loss.

The essence of this, is to ensure fairness in quantification of the amount of loss.

Read more on insurance:

https://brainly.com/question/9212174

Answer:

  200 students were in the program

Step-by-step explanation:

The parent should know how to figure ...

  170/85% = total/100%

This is the same as ...

  total = 170/0.85 = 200

200 students were in the program.

_____

Critical Thinking

There are three declarative statements here. There is no question. We have made up a question to answer.

Another possible answer to the non-question could be, "The parent can ask his student how many students were in the program."

Answer:

Step-by-step explanation:

20

cause i said so

Answer:

4 out of 10 or 4/10 is my answer

Answer:

The fraction will be 4/10, or 2/5.

The percentage will be 40%.

Step-by-step explanation:

The fraction and percentage will be the number of black pens divided by the total number of pens.

We can find the total number of pens by adding all the pens in each color together.

2 + 4 + 3 + 1 = 10

The total number of pens is 10. The number of black pens is 4.

The fraction will be 4/10, or 2/5.

The percentage will be 40%.

I hope this helps. Happy studying. :)

Answer: No, the percentage of the fleet out of compliance is not different from their initial thought.

Step-by-step explanation:

Since we have given that

n = 22

x = 5

So, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{5}{22}=0.23[/tex]

he company initially believed that 20% of the fleet was out of compliance. Is this strong evidence the percentage of the fleet out of compliance is different from their initial thought.

so, p = 0.2

Hypothesis would be

[tex]H_0:p=\hat{p}\\\\H_a:p\neq \hat{p}[/tex]

So, the t test statistic value would be

[tex]t=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\t=\dfrac{0.23-0.20}{\sqrt{\dfrac{0.2\times 0.8}{22}}}\\\\\\t=\dfrac{0.03}{0.085}\\\\t=0.353[/tex]

Degree of freedom = df = n-1 = 22-1 =23

So, t{critical value} = 2.080

So, 2.080>0.353

so, we will accept the null hypothesis.

Hence, No, the percentage of the fleet out of compliance is not different from their initial thought.

Final answer:

A hypothesis test can be conducted to determine whether the percentage of the fleet out of compliance is different from the initial belief of 20% by using a null hypothesis of p = 0.20 and an alternative hypothesis of p ≠ 0.20, followed by a Z-test for proportions.

Explanation:

To determine whether there is strong evidence that the percentage of the fleet out of compliance is different from the company's initial belief of 20%, we should set up a hypothesis test. The null hypothesis (H₀) is that the true proportion of cars that are out of compliance is equal to 20% (H₀: p = 0.20). The alternative hypothesis (Ha) is that the true proportion of cars that are out of compliance is different from 20% (Ha: p ≠ 0.20).

Using the sample data of 5 failures out of 22 tested, a statistical test such as the Z-test for proportions can be conducted to determine if we should reject the null hypothesis. This would involve calculating the test statistic comparing the sample proportion to 0.20 and then finding the p-value to make a decision based on the chosen significance level, usually 0.05. If the p-value is below the significance level, we would reject the null hypothesis, indicating that there is evidence that the percentage of the fleet out of compliance is different from 20%.

Answer:

Factory made 4 batches of granola bars yesterday.

Step-by-step explanation:

Given:

1 batch of granola bar is made of 1/8 barrel of raisins.

1/8 barrels can be rewritten as 0.125 barrels.

Hence we can say 1 batch of granola bar is made of 0.125 barrels.

Also Given:

Yesterday Factory used 1/2 barrel of raisins.

1/2 barrels can be rewritten as 0.5 barrels.

Hence we need to find how much batches of granola bars were made using 0.5 barrels of raisins.

Now,

For 0.125 barrels raisins = 1 batch of granola bar

for 0.5 barrels of raisins = Batches of granola bar for 0.5 barrels of raisins

By Using Unitary method we get;

Batches of granola bar for 0.5 barrels of raisins = [tex]\frac{1\times 0.5}{0.125}=4[/tex]

Hence Factory made 4 batches of granola bars yesterday.

Answer:

Step-by-step explanation:

The triangle given is aright angle triangle. This is because one if its angles is 90 degrees. The other two angles add up to give 180 degrees. Looking at the right angle triangle, taking the 8 degree angle as the reference angle, the length of the adjacent side is 82, the length of the opposite side is t. Applying trigonometric ratio,

Tan # = opposite side / adjacent side.

# = 8 degrees

Tan 8 = t/82

t = 82 tan8

t = 82 × 0.1405

t = 11.521

Answer: tangent of A = 2.4

Cotangent of B = 0.4167

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{5}{12} = cot∠B \\ 2\frac{2}{5} = cot∠A[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ \\ \\ \frac{10}{24} = cot∠B → \frac{5}{12} = cot∠B \\ \\ \frac{24}{10} = cot∠A → 2\frac{2}{5} = cot∠A[/tex]

I am joyous to assist you anytime.

For this case we must write a quadratic equation of the form:

[tex]x ^ 2 + bx + c = 0[/tex]

We have two roots:

[tex]x_ {1} = - 7\\x_ {2} = 1[/tex]

Thus, we can rewrite the equation in a factored form as:

[tex](x + 7) (x-1) = 0[/tex]

If we apply distributive property we have:

[tex]x ^ 2-x + 7x-7 = 0[/tex]

Different signs are subtracted and the major sign is placed.

[tex]x ^ 2 + 6x-7 = 0[/tex]

Answer:

The quadratic equation is:

[tex]x ^ 2 + 6x-7 = 0[/tex]

Answer:

Tan33=x/y

y= x/Tan33

Tan40=(10+x)/y

y= (10+x)/Tan40

Therefore

x/Tan33 = (10+x)/Tan40

xTan40-xTan33 =10Tan33

x= 10Tan33/(Tan40-Tan33)

x=34.2m

Step-by-step explanation:

Answer: Our required probability is 0.48.

Step-by-step explanation:

Since we have given that

Probability that days are cloudy in January = 51%

Probability that days are cloudy and foggy = 25%

So, we need to find the probability that a randomly selected day in January will be foggy if it is cloudy.

So,P( Foggy|cloudy) is given by

[tex]\dfrac{P(Foggy\cap cloudy)}{P(cloudy)}\\\\=\dfrac{25}{51}\\\\=0.48[/tex]

Hence, our required probability is 0.48.

Answer: it will take him 4.5 hours to cover same distance

Step-by-step explanation:

Marathon runner covered the whole distance in 4 hours running at a constant speed of 8.1 km per hour.

Speed = distance / time

Distance = speed×time

Therefore, distance covered by the marathon runner in in 4 hours, running at a speed of 8.1 km per hour is

8.1 × 4 = 32.4 kilometers

if he decreased the speed to 7.2 km per hour, the distance remains 32.4 kilometers. Therefore,

At 7.2 km per hour, the time it would take him to cover the same distance would be

Distance/ speed = 32.4/7.2 = 4.5 hours

Answer:

Step-by-step explanation:

Rejection of aspirin argument is more dangerous because the incorrect dosage of aspirin may cause more severe adverse reactions than the incorrect dosage of vitamin C. It would be prudent to use a lower level of significance to test the aspirin argument.