Tomas Briggs and Sons reviewed their first year operations. Gross sales were $204,000 Customer returns and allowances were $18,000 The cost of the merchandise they sold was $90,000 First-year expenses were $84,000 The overall profit before taxes was $12,000 Represent the following in percentages: Total net sales in dollars were The cost of the merchandise sold was First-year expenses were Overall profit was Don't forget how to calculate net sales!

Answer:

P= -0.05q+22

Step-by-step explanation:

To find the linear equation that relates price with quantity demanded, first we must find the slope. Because the independent variable is the quantity demanded and the dependent variable is the price, the slope represents how the price changes when there is an extra unit of quantity demanded. The problem gives this information: "for every additional card (extra unit) they need to drop the price by $0.05". The slope (m) in this case is negative because an extra unit, reduces the price: -0.05

The second step is to use this formula:

Y-y1= m*(X-x1)

y1 and x1 is a point of the demand curve, in this case it is y1= $7 and x1=300

Y-$7= -$0.05*(X-300)

Y-7=-0.05X+15

Y= -0.05X+15+7

Y= -0.05X-22

Price= -0.05 quantity demanded +22

Answer:

Ans. Joe will have $720,862.28 and Jill will have $819,348.90 after 30 years.

Step-by-step explanation:

Hi, since the interest is compounded with each payment, the effective rate of Joe is exactly equal to its compounded rate, that is 9.3%, but in the case of Jill, this rate is compounded weekly, this means that we have to divide 9.3% by 52 (which are the weeks in a year) in order to obtain an effective rate, in our case, effective weekly.

On the other hand, the time for Joe is pretty straight forward, he saves for 30 years at an effective annual interest rate of 9.3%, but Jill saves for 30*52=1560 weeks, at a rate of 0.1788% effective weekly.

They both have to use the following formula in order to find how much money will they have after 30 years of savings.

[tex]FutureValue=\frac{A((1+r)^{n}-1) }{r}[/tex]

In the case of Joe, this should look like this

[tex]FutureValue=\frac{5,000((1+0.093)^{30}-1) }{0.093} =720,862.28[/tex]

In the case of Jill, this is how this should look like.

[tex]FutureValue=\frac{96.15((1+0.001788)^{1560}-1) }{0.001788} =819,348.90[/tex]

Best of luck.

Step-by-step explanation:

Perfect number is the positive integer which is equal to sum of proper divisors of the number.

Aliquot part is also called as proper divisor which means any divisor of the number which isn't equal to number itself.

Number : 6

Perfect divisors / Aliquot part = 1, 2, 3

Sum of the divisors = 1 + 2 + 3 = 6

Thus, 6 is a perfect number.

Number : 28

Perfect divisors / Aliquot part = 1, 2, 4, 7, 14

Sum of the divisors = 1 + 2 + 4 + 7 + 14 = 28

Thus, 28 is a perfect number.

Answer:

24.39mL of the solution would be given per hour.

Step-by-step explanation:

This problem can be solved by direct rule of three, in which there are a direct relationship between the measures, which means that the rule of three is a cross multiplication.

The first step to solve this problem is to see how many mg of the solution is administered per hour.

Each minute, 200 ug are administered. 1mg has 1000ug, so

1mg - 1000 ug

xmg - 200 ug

[tex]1000x = 200[/tex]

[tex]x = \frac{200}{1000}[/tex]

[tex]x = 0.2mg[/tex]

In each minute, 0.2 mg are administered. Each hour has 60 minutes. How many mg are administered in 60 minutes?

1 minute - 0.2 mg

60 minutes - x mg

[tex]x = 60*0.2[/tex]

[tex]x = 12mg[/tex]

In an hour, 12 mg of the drug is administered. In 250 mL, there is 123 mg of the drug. How many ml are there in 12 mg of the drug.

123mg - 250mL

12 mg - xmL

[tex]123x = 250*12[/tex]

[tex]x = \frac{250*12}{123}[/tex]

[tex]x = 24.39[/tex]mL

24.39mL of the solution would be given per hour.

Final answer:

Approximately 24.39 milliliters of the intravenous solution would be administered per hour to deliver an hourly drug rate of 12 milligrams based on the given concentration.

Explanation:

To calculate how many milliliters of the intravenous solution would be given per hour, first convert the rate of drug administered from micrograms to milligrams: 200 \5g is equal to 0.2 mg. Since the drug administration rate is 0.2 mg per minute, we need to multiply this by 60 minutes to get the hourly rate:

0.2 mg/minute x 60 minutes/hour = 12 mg/hour.

Next, we need to find out how many milliliters of the solution contain 12 mg of the drug. Since we have 123 mg in 250 mL, we can set up a proportion to solve for the volume needed:

(123 mg/250 mL) = (12 mg/V mL)

V = (12 mg x 250 mL) / 123 mg = 24.39 mL.

Therefore, approximately 24.39 mL of the solution would be administered per hour.

Answer:

The resultant velocity of the airplane is 213.41 m/s.

Step-by-step explanation:

Given that,

Velocity of an airplane in east direction, [tex]v_1=210\ mph[/tex]

Velocity of wind from the north, [tex]v_2=38\ mph[/tex]

Let east lies in the direction of the positive x-axis and north in the direction of the positive y-axis.

We need to find the resultant velocity of the airplane. Let v is the resultant velocity. It can be calculated as :

[tex]v=\sqrt{v_1^2+v_2^2}[/tex]

[tex]v=\sqrt{(210)^2+(38)^2}[/tex]

v = 213.41 m/s

So, the resultant velocity of the airplane is 213.41 m/s. Hence, this is the required solution.

Final answer:

The resultant velocity of the airplane, combining its eastward direction and the northward wind, is approximately 213.4 miles per hour at an angle of 10.3 degrees north of east.

Explanation:

The student's question relates to the concept of resultant velocity, which is a fundamental topic in Physics. When two velocities are combined, such as an airplane's velocity and wind velocity, the outcome is a vector known as the resultant velocity. To calculate this, one must use vector addition.

The airplane has a velocity of 210 miles per hour due east, which can be represented as a vector pointing along the positive x-axis. The wind has a velocity of 38 miles per hour from the north, represented as a vector along the positive y-axis. To find the resultant velocity, these two vectors must be combined using vector addition.

Mathematically, the resultant vector [tex]\\(R)[/tex] can be found using the Pythagorean theorem if the vectors are perpendicular, as in this case:
[tex]\[ R = \sqrt{V_{plane}^2 + V_{wind}^2} \][/tex]

Where \\(V_{plane}\\) is the velocity of the airplane and [tex]\(V_{wind}\)[/tex] is the velocity of the wind.

The direction of the resultant vector can be determined by calculating the angle [tex]\(\theta\)[/tex] it makes with the positive x-axis using trigonometry, specifically the tangent function:
[tex]\[ \theta = \arctan\left(\frac{V_{wind}}{V_{plane}}\right) \][/tex]

By substituting the given values:

The resultant velocity (magnitude) is then calculated by:

[tex]\[ R = \sqrt{(210)^2 + (38)^2} = \sqrt{44100 + 1444} = \sqrt{45544} \][/tex]

This yields a resultant speed of approximately 213.4 miles per hour.

The direction \\(\theta\\) will be:

[tex]\[ \theta = \arctan\left(\frac{38}{210}\right) \][/tex]

Using a calculator, one finds that [tex]\(\theta\)[/tex] is approximately 10.3 degrees north of east.

Answer:

(B) 0.0588

Step-by-step explanation:

The probability is calculated as a division between the number of possibilities that satisfy a condition and the number of total possibilities. Then, the probability that the first card is diamonds is:

[tex]P_1=\frac{13}{52}[/tex]

Because the deck has 52 cards and 13 of them are diamonds.

Then, if the first card was diamonds, the probability that the second card is also diamond is:

[tex]P_2=\frac{12}{51}[/tex]

Because now, we just have 51 cards and 12 of them are diamonds.

Therefore, the probability that both cards are diamonds is calculated as a multiplication between [tex]P_1[/tex] and [tex]P_2[/tex]. This is:

[tex]P=\frac{13}{52}*\frac{12}{51}=\frac{1}{17}=0.0588[/tex]

Answer:

For a monthly cost of at least $7 and at most $8, you can have between 100 and 110 calling minutes.

Step-by-step explanation:

The problem states that the monthly cost of a celular plan is modeled by the following function:

[tex]C(x) = 4 + 0.10(x-70)[/tex]

In which C(x) is the monthly cost and x is the number of calling minutes.

How many calling minutes are needed for a monthly cost of at least $7?

This can be solved by the following inequality:

[tex]C(x) \geq 7[/tex]

[tex]4 + 0.10(x - 70) \geq 7[/tex]

[tex]4 + 0.10x - 7 \geq 7[/tex]

[tex]0.10x \geq 10[/tex]

[tex]x \geq \frac{10}{0.1}[/tex]

[tex]x \geq 100[/tex]

For a monthly cost of at least $7, you need to have at least 100 calling minutes.

How many calling minutes are needed for a monthly cost of at most 8:

[tex]C(x) \leq 8[/tex]

[tex]4 + 0.10(x - 70) \leq 8[/tex]

[tex]4 + 0.10x - 7 \leq 8[/tex]

[tex]0.10x \leq 11[/tex]

[tex]x \leq \frac{11}{0.1}[/tex]

[tex]x \leq 110[/tex]

For a monthly cost of at most $8, you need to have at most 110 calling minutes.

For a monthly cost of at least $7 and at most $8, you can have between 100 and 110 calling minutes.

Answer:

PROPORTION.

Step-by-step explanation:

The relative frequency in a relative frequency histogram refers to                                  PROPORTION.

A relative frequency histogram uses the same information as a frequency histogram but compares each class interval with the number of items. The difference between frequency and relative frequency histogram is that the vertical axes uses the relative or proportional frequency rather than simple frequency

Answer:

You inject 60.9628 milliliters of dosage

Step-by-step explanation:

1 pound = 0.453592kg,

Patient's weight in pounds = 168

Patient's weight in kg = [tex]76.2035  kg[/tex]

Now we are given that The dosage is 0.4 mg per kilogram of bod

So, dosage = [tex]0.4 \times 76.2035 mg = 30.4814 mg[/tex]

1 microgram = 0.001 mg

Concentration of drug = [tex]500 micrograms/ml = 500 * 0.001 mg/ml = 0.5 mg/ml[/tex]

Now we are supposed to find How many milliliters (= cc) are you to inject?

So,milliliters of dosage required to inject = [tex]\frac{30.4814}{0.5} = 60.9628[/tex]

Hence you inject 60.9628 milliliters of dosage

Answer:

0.681

Step-by-step explanation:

Let's define the following events:

S: a Carter office worker is rated satisfactory

U : a Carter office worker is rated unsatisfactory

ND: a Carter office worker is placed by Nancy Dwyer

DN: a Carter office worker is placed by Darla Newberg

We have from the original text that

P(S | ND) = 0.8, this implies that P(U | ND) = 0.2.

P(S | DN) = 0.65, this implies that P(U | DN) = 0.35. Besides

P(DN) =  0.55 and P(ND) = 0.45, then we are looking for

P(DN | U), using the Bayes' formula we have

P(DN | U) = [tex]\frac{P(U | DN)P(DN)}{P(U | DN)P(DN) + P(U | ND)P(ND)}[/tex] = [tex]\frac{(0.35)(0.55)}{(0.35)(0.55)+(0.2)(0.45)}[/tex]=0.681

Final answer:

The probability that a Carter office worker rated unsatisfactory was placed by Darla is approximately 0.346.

Explanation:

To find the probability that a Carter office worker rated unsatisfactory was placed by Darla, we can use Bayes' theorem. Let's denote the event that the worker is placed by Darla as D and the event that the worker is rated unsatisfactory as U. We are given the following probabilities:

P(Darla places) = 55% = 0.55

P(Nancy places) = 45% = 0.45

P(Satisfactory | Nancy places) = 80% = 0.80

P(Satisfactory | Darla places) = 65% = 0.65

We want to find P(D | Unsatisfactory), which is the probability that the worker was placed by Darla given that they are rated unsatisfactory. Using Bayes' theorem, we have:

P(D | U) = (P(D) * P(U | D)) / (P(D) * P(U | D) + P(N) * P(U | N))

Substituting the given probabilities, we get:

P(D | U) = (0.55 * (1 - 0.65)) / (0.55 * (1 - 0.65) + 0.45 * (1 - 0.80))

P(D | U) ≈ 0.346

Therefore, the probability that a Carter office worker rated unsatisfactory was placed by Darla is approximately 0.346.

Answer:

the length PQ is 9 units,the length QR is 9 units,the length PR is 9.48 units,the triangle is not a right triangle,this is a isosceles triangle

Step-by-step explanation:

Hello, I think I can help you with this

If  you know two points, the distance between then its given by:

[tex]P1(x_{1},y_{1},z_{1} ) \\P2(x_{2},y_{2},z_{2})\\\\d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1}  )^{2}+(z_{2}-z_{1} )^{2} }[/tex]

Step 1

use the formula to find the length PQ

Let

P1=P=P(2, −3, −4)

P2=Q=Q(8, 0, 2)

[tex]d=\sqrt{(8-2)^{2} +(0-(-3))^{2}+(2-(-4))^{2}} \\ d=\sqrt{(6)^{2} +(3)^{2}+(6 )^{2}}} \\d=\sqrt{36+9+36}\\d=\sqrt{81} \\d=9\\[/tex]

the length PQ is 9 units

Step 2

use the formula to find the length QR

Let

P1=Q=Q(8, 0, 2)

P2=R= R(11, −6, −4)

[tex]d=\sqrt{(11-8)^{2} +(6-0))^{2}+(-4-2 )^{2}}  \\\\\\d=\sqrt{(3)^{2} +(6)^{2}+(-6 )^{2}}} \\d=\sqrt{9+36+36}\\d=\sqrt{81} \\d=9\\[/tex]

the length QR is 9 units

Step 3

use the formula to find the length PR

Let

P1=P(2, −3, −4)

P2=R= R(11, −6, −4)

[tex]d=\sqrt{(11-2)^{2} +(-6-(-3)))^{2}+(-4-4 )^{2}}  \\\\\\d=\sqrt{(9)^{2} +(-6+3)^{2}+(-4-(-4) )^{2}}} \\d=\sqrt{81+9+0}\\d=\sqrt{90} \\d=9.48\\[/tex]

the length PR is 9.48 units

Step 4

is it a right triangle?

you can check this by using:

[tex]side^{2} +side^{2}=hypotenuse ^{2}[/tex]

Let

side 1=side 2= 9

hypotenuse = 9.48

Put the values into the equation

[tex]9^{2} +9^{2} =9.48^{2}\\ 81+81=90\\162=90,false[/tex]

Hence, the triangle is not a right triangle

Step 5

is it an isosceles triangle?

In geometry, an isosceles triangle is a type of triangle that has two sides of equal length.

Now side PQ=QR, so this is a isosceles triangle

Have a great day

Answer:

P(cell has at least one of the positive nickel-charged options) = 0.83.

P(a cell is not composed of a positive nickel charge greater than +3) = 0.85.

Step-by-step explanation:

It is given that the Nickel Charge Proportions found  in the battery are:

0 ==> 0.17

.

+2 ==> 0.35

.

+3 ==> 0.33

.

+4 ==> 0.15.

The numbers associated to the charge are actually the probabilities of the charges because nickel is an element that has multiple oxidation states that is usually found in the above mentioned states.

a) P(cell has at least one of the positive nickel-charged options) = P(a cell has +2 nickel-charged options) + P(a cell has +3 nickel-charged options) + P(a cell has +4 nickel-charged options) = 0.35 + 0.33 + 0.15 = 0.83.

Or:

P(a cell has at least one of the positive nickel-charged options) = 1 - P(a cell has 0 nickel-charged options) = 1 - 0.17 = 0.83.

b) P(a cell is not composed of a positive nickel charge greater than +3) = 1 - P(a cell is composed of a positive nickel charge greater than +3)

= 1 -  P(a cell has +4 nickel-charged options)  '.' because +4 is only positive nickel charge greater than +3      

= 1 - 0.15

=  0.85

To summarize:

P(cell has at least one of the positive nickel-charged options) = 0.83!!!

P(a cell is not composed of a positive nickel charge greater than +3) = 0.85!!!

The probability of a cell having at least one positive nickel-charge is 0.83 and the probability that a cell is not composed of a positive nickel charge greater than +3 is 0.85; This was calculated based on probabilities of Nickel in different charge states.

For this problem, you're basically being asked to interpret a probability distribution of Nickel charge proportions, which involves summing probabilities.

(a) The probability that a cell has at least one of the positive nickel-charged options is the sum of the probabilities of Nickel in the +2, +3, and +4 states. From the given data, we simply add: 0.35 (for +2), 0.33 (for +3), and 0.15 (for +4). So, the total probability is 0.83.

(b) The probability that a cell is not composed of a positive nickel charge greater than +3 means we're looking for the probability of Nickel in the 0, +2, and +3 states. Here, we add: 0.17 (for 0 state), 0.35 (for +2 state), and 0.33 (for +3 state) to get a total probability of 0.85.

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Answer:

you need 100ml of 5X TAE and 400ml of water.

Step-by-step explanation:

You need to use a rule of three:

[tex]C_1V_1=C_2V_2[/tex]

where:

[tex]\left \{ {{C_1= 5X} \atop {C_2=1X}} \right.[/tex]

and

[tex]\left \{ {{V_1 = V_{TAE}} \atop {V_2=500ml}} \right.[/tex]

Therefore:

[tex]V_{TAE} = \frac{V_2*C_2}{C_1}[/tex]

[tex]V_{TAE} = 100ml[/tex]

Then just rest the TAE volume to the final Volume and you get the amount of water that you need to reduce the concentration.

Answer:

Step-by-step explanation:

It shall be 100xl times the number of 1x tae

a. As described in the problem you will be paying in the bill $0.15 per minute which means you have a linear relationship where both the total cost of the bill and the minutes will grow at the same rate (the price of the minute times the minutes) like this

[tex]C(t)=0.15t[/tex]

where C(t) is the total cost of the cell phone bill and t will be the time in minutes

b. The domain of the function will be the values that we can enter to the function. It is defined in the problem that this cost of the minutes its only up to 600 minutes so there is our limitation for the values that will enter the function. The domain will be between 0 and 600 both included because if he calls 0 minutes the bill will be 0 and if he calls 600 he would pay 0.15 for this last minute as well.

[tex][0,600][/tex]

Answer:

The value of q are 0.781,-1.281.

Step-by-step explanation:

Given : Two vectors [tex]A=i+j+kq[/tex] and [tex]B=iq-2j+2kq[/tex] are perpendicular to each other.

To find : The value of q ?

Solution :

When two vectors are perpendicular to each other then their dot product is zero.

i.e. [tex]\vec{A}\cdot \vec{B}=0[/tex]

Two vectors [tex]A=i+j+kq[/tex] and [tex]B=iq-2j+2kq[/tex]

[tex](i+j+kq)\cdot (iq-2j+2kq)=0[/tex]

[tex](1)(q)+(1)(-2)+(q)(2q)=0[/tex]

[tex]q-2+2q^2=0[/tex]

[tex]2q^2+q-2=0[/tex]

[tex]2q^2+q-2=0[/tex]

Using quadratic formula,

[tex]q=\frac{-1\pm\sqrt{1^2-4(2)(-2)}}{2(2)}[/tex]

[tex]q=\frac{-1\pm\sqrt{17}}{4}[/tex]

[tex]q=\frac{-1+\sqrt{17}}{4},\frac{-1-\sqrt{17}}{4}[/tex]

[tex]q=0.781,-1.281[/tex]

Therefore, The value of q are 0.781,-1.281.

Answer:

(A) No solutions regardless of values of a and b.

Step-by-step explanation:

Asumming that the system of equations is [tex]x+2y-3z=a\\ 2x+4y-6z=2a+2[/tex], the corresponding augmented matrix of the system is [tex]\left[\begin{array}{cccc}1&2&-3&a\\2&4&-6&2a+2\end{array}\right][/tex].

If two time the row 1 is subtracted to row 1, we get the following matrix

[tex]\left[\begin{array}{cccc}1&2&-3&a\\0&0&0&2a+2-2a\end{array}\right][/tex].

Then the system has no solutions regardless of values of a and b.

Answer:

a) The set of solutions is [tex]\{(0,-3x_3,x_3): x_3\; \text{es un real}\}[/tex] y b) the set of solutions is [tex]\{(-6,\frac{-41}{17}-\frac{30}{17}x_4 , \frac{37}{17}+\frac{8}{17} x_4 ,x_4): x_4\;\text{es un real}\}[/tex].

Step-by-step explanation:

a) Let's first find the echelon form of the matrix [tex]\left[\begin{array}{ccc}5&2&6\\-2&1&3\end{array}\right][/tex].

The system has a free variable (x3).

       x1+[tex]\frac{2}{5}[/tex](-3x3)+[tex]\frac{6}{5}[/tex]x3=

      x1-[tex]\frac{6}{5}[/tex]x3+[tex]\frac{6}{5}[/tex]x3

     then x1=0.

The system has infinite solutions of the form (x1,x2,x3)=(0,-3x3,x3), where x3 is a real number.

b) Let's first find the echelon form of the aumented matrix [tex]\left[\begin{array}{ccccc}1&-2&1&-4&1\\1&3&7&2&2\\0&-12&-11&-16&5\end{array}\right][/tex].

The system has a free variable (x4).

      x2=[tex]\frac{-41}{17}-\frac{30}{17}[/tex]x4.

The system has infinite solutions of the form (x1,x2,x3,x4)=(-6,[tex]\frac{-41}{17}-\frac{30}{17}[/tex]x4,[tex]\frac{37}{17}[/tex]+ [tex]\frac{8}{17}[/tex]x4,x4), where x4 is a real number.

Answer:

$64

Step-by-step explanation:

We have been given that a local food mart donates 20% of it's Friday's sales to charity. This Friday the food mart had sales totaling 320.00 dollars.

To find the the amount donated to the charity, we will find 20% of $320.

[tex]\text{The amount donated to the charity}=\$320\times\frac{20}{100}[/tex]

[tex]\text{The amount donated to the charity}=\$320\times0.20[/tex]

[tex]\text{The amount donated to the charity}=\$64[/tex]

Therefore, $64 were donated to the charity.

Answer: The data are quantitative because they consist of counts or measurements.

Step-by-step explanation:

The definition of quantitative data says that if we can count or measure some thing in our data such as number of apples on each bag , length, width, etc then the data is said to be quantitative.

On the other hand  in qualitative data we can obverse characteristics and features but can't be counted or measured such as honesty , color, tastes etc.

Given : In studying different societies, an archaeologist measures head circumferences of skulls.

Since here we are measuring circumferences of skulls, therefor it comes under  quantitative data.

Hence, the correct answer is : The data are quantitative because they consist of counts or measurements.

The correct answer is D. The data are quantitative because they consist of counts or measurements. Quantitative data is numerical and can be measured and analyzed statistically.

Step by Step Solution:

When an archaeologist measures head circumferences of skulls, they are collecting quantitative data. Quantitative data consists of counts or measurements that are numerical in nature and can be subjected to statistical analysis. Examples of quantitative data in archaeology include measuring the length of projectile points, counting pollen grains, or recording quantities of animal bones at a site.

Therefore, the correct answer is:

D. The data are quantitative because they consist of counts or measurements.

Answer:

2/6 or 1/3 so color 2 out of the six squares

Step-by-step explanation:

1/2 - 1/6 is equal to 3/6 - 1/6 so 2/6

Answer:

R = { (2,2), (2, 4), (2, 6), (2,8), (4, 2), (4, 6), (6, 2), (6, 8) }

Step-by-step explanation:

Given,

A = { 0, 1, 2, 3, 4, 5, 6 }

B = { 0,1, 2, 3, 4, 5, 6, 7, 8 }

Also, R is the relation from A to B as follows,

R = { (a, b) : HCF ( a, b ) = 2 ∀ a ∈ A, b ∈ B }

Since,

HCF ( 2, 2 ) = HCF ( 2, 4 ) = HCF ( 2, 6 ) = HCF ( 2, 8 ) = HCF ( 4, 2 ) = HCF ( 4, 6) = HCF ( 6, 4) = HCF ( 6, 2 ) =HCF ( 6, 8 ) = 2

Where, 2, 4, and 6 belong to A,

And, 2, 4, 6 and 8 belong to B,

Hence,

R = { (2,2), (2, 4), (2, 6), (2,8), (4, 2), (4, 6), (6, 2), (6, 4), (6, 8) }

Answer:

840

Step-by-step explanation:

Total number of gifts (teddy bears)= 4

Total number of nieces = 7

We need to find the number of ways to give the 4 teddy bears to 4 of the 7 nieces, where no niece gets more than one teddy bear.

Number of possible ways to give first teddy = 7

It is given that no niece gets more than one teddy bear.

The remaining nieces are = 7 - 1 = 6

Number of possible ways to give second teddy = 6

Now, the remaining nieces are = 6 - 1 = 5

Similarly,

Number of possible ways to give third teddy = 5

Number of possible ways to give fourth teddy = 4

Total number of possible ways to distribute 4 teddy bears is

[tex]Total=7\times 6\times 5\times 4=840[/tex]

Therefore total possible ways to distribute 4 teddy bears are 840.

Final answer:

There are 35 different ways to give 4 identical teddy bears to 4 of the 7 nieces where no niece receives more than one teddy bear. The calculation is done using combinations formula C(7, 4).

Explanation:

To determine the number of different ways the 4 teddy bears can be given to 4 out of 7 nieces where each niece gets only one teddy bear, we use combinations. Combinations are a way of selecting items from a group, where the order does not matter. In mathematics, this is denoted as C(n, k), which represents the number of combinations of n items taken k at a time.

In this case, we want to find C(7, 4), because we have 7 nieces (n=7) and we are choosing 4 of them (k=4) to each receive one teddy bear. This is calculated by:

C(7, 4) = 7! / (4! * (7-4)!) => C(7, 4) = (7 * 6 * 5 * 4!) / (4! * 3!). Since 4! in the numerator and denominator cancel each other out, it simplifies to:

C(7, 4) = 7 * 6 * 5 / (3 * 2 * 1) = 35

Therefore, there are 35 different ways to give the 4 identical teddy bears to 4 of the 7 nieces when no niece gets more than one teddy bear.

Let [tex]m,n[/tex] be any two integers, and assume [tex]m-n[/tex] is even. (This would mean either both [tex]m,n[/tex] are even or odd, but that's not important.)

We have

[tex]m^3-n^3=(m-n)(m^2+mn+n^2)[/tex]

and the parity of [tex]m-n[/tex] tells us [tex]m^3-n^3[/tex] must also be even. QED

Answer:

Standard Deviation = 9.75        

Step-by-step explanation:

We are given the following data:

n = 25

Ages: 60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92

Formula:

For sample,

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

Mean = [tex]\frac{1851}{25} = 74.04[/tex]

Sum of square of differences = 2278.96

S.D = [tex]\sqrt{\diplaystyle\frac{2278.96}{24} } = 9.74[/tex]

To calculate the standard deviation of the given ages, we find the mean, subtract it from each age to find deviations, square these, find their mean, and take the square root to get the standard deviation, which is 6.96.

The question is asking to calculate the standard deviation of the ages of 25 senior citizens. To find the standard deviation, we need to follow these steps:

Calculate the mean (average) age of the senior citizens.

Subtract the mean from each age to find the deviation of each value.

Square each deviation.

Calculate the mean of these squared deviations.

Take the square root of the mean of the squared deviations to get the standard deviation.

Performing these calculations, we find that the mean (average) age is 73.24. The sum of the squared deviations is 1210. After dividing this sum by the number of values (25), we get the variance, which is 48.4. Finally, taking the square root of the variance gives us the standard deviation, which to two decimal places is 6.96.

This measure of standard deviation is crucial in understanding the spread of ages among senior citizens in the sociologist's survey.

Answer: The required value would be 0.000013.

Step-by-step explanation:

Since we have given that

0.001 % of [tex]\dfrac{4}{3}[/tex]

As we know that

To remove the % sign we should divide it by 100.

Mathematically, it would be expressed as

[tex]\dfrac{0.001}{100}\times \dfrac{4}{3}\\\\=\dfrac{0.004}{300}\\\\=0.000013[/tex]

Hence, the required value would be 0.000013.

Answer:

The angle that the ramp makes with the ground is 11.54°

Step-by-step explanation:

From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.

We can use the fact that the sin(θ) = [tex]\frac{Opposite}{Hypotenuse}[/tex] to find the angle that the ramp makes with the ground.

[tex]sin(\theta)=\frac{3.5}{17.5}[/tex]

The angle is equal to

[tex]\theta = sin^{-1}(\frac{3.5}{17.5} )\\\theta = 11.54\°[/tex]

The angle that the ramp makes with the ground can be found using the concept of tangent in trigonometry. By dividing the height of the loading platform by the length of the ramp and taking the inverse tangent of the result, we find the angle to be approximately 11.3 degrees.

This question can be solved by using trigonometric principles, specifically the tangent of an angle in a right triangle. The tangent of an angle θ (theta) can be defined as the ratio of the side opposite the angle to the side adjacent to it.

In this scenario, the ramp forms a right triangle with the ground and the vertical line from the loading platform to the ground directly below it. The height of the platform, or the 'opposite' side, is 3 1/2 feet, and the ramp, or the 'adjacent' side, is 17 1/2 feet.

Therefore, we can say that: tan θ = (3.5 / 17.5)

To find the value of θ, we take the inverse tangent (or arc tangent) of the quotient. Using a calculator to do this (remember to set your calculator to degree mode), we find θ to be approximately 11.3 degrees.

Thus, the angle that the ramp makes with the ground is about 11.3 degrees.

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Answer:

Area: 180 units2 (units 2 is because since the are no specific unit given but every area should have a unit  of measurement)

Step-by-step explanation:

The area enclosed by the graph of the function, the horizontal axis, and vertical lines is the integral of the function between thos two points (x=2 and x=4)

So , let's solve the integral of f(x)

Area =[tex]\int\limits^2_4 3{x}^3 \, dx = 3*x^4/4[/tex]+C

C=0

So if we evaluate this function in the given segment:

Area= 3* (4^4)/4-3*(2^4)/4= 3*(4^4-2^4)/4=180 units 2

Goos luck!

Answer:

[tex]x = 0[/tex] or [tex]x = \pi[/tex].

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

[tex]\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}[/tex].

[tex]\displaystyle \sec{x} = \frac{1}{\cos{x}}[/tex].

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, [tex]\sin^{2}{x} = 1 - \cos^{2}{x}[/tex]. Therefore, for the square of tangents,

[tex]\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}[/tex].

This equation will thus become:

[tex]\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2[/tex].

To simplify the calculations, replace all [tex]\cos^{2}{x}[/tex] with another variable. For example, let [tex]u = \cos^{2}{x}[/tex]. Keep in mind that [tex]0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1[/tex].

[tex]\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2[/tex].

[tex]\displaystyle \frac{(1 - u) + u - u \cdot (1- u)}{u^{2}} = 2[/tex].

Solve this equation for [tex]u[/tex]:

[tex]\displaystyle \frac{u^{2} + 1}{u^{2}} = 2[/tex].

[tex]u^{2} + 1 = 2 u^{2}[/tex].

[tex]u^{2} = 1[/tex].

Given that [tex]0 \le u \le 1[/tex], [tex]u = 1[/tex] is the only possible solution.

[tex]\cos^{2}{x} = 1[/tex],

[tex]x = k \pi[/tex], where [tex]k\in \mathbb{Z}[/tex] (i.e., [tex]k[/tex] is an integer.)

Given that [tex]0 \le x < 2\pi[/tex],

[tex]0 \le k <2[/tex].

[tex]k = 0[/tex] or [tex]k = 1[/tex]. Accordingly,

[tex]x = 0[/tex] or [tex]x = \pi[/tex].

Answer:

Step-by-step explanation:

Consider the cubic polynomial,

[tex](x+a)(x+b)(x+c)[/tex]

Expanding this gives

[tex]x^3+(a+b+c)x^2+(ab+ac+bc)x+abc=x^3+x^2-4x-4[/tex]

We can factor this by grouping,

[tex]x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x^2-4)(x+1)=(x-2)(x+2)(x+1)[/tex]

Then letting [tex]a=-2[/tex], [tex]b=2[/tex], and [tex]c=1[/tex] gives [tex]a^3+b^3+c^3=-8+8+1=\boxed1[/tex]

Answer:

There were 49 people that chose chocolate and vanilla twist.

Step-by-step explanation:

This problem can be solved by building a Venn diagram of this set, where:

-A is the number of the people that tasted the vanilla

-B is the number of the people that tasted the chocolate.

The most important information in this problem is that some of those people tasted both. It means that [tex]A \cap B = x[/tex], and x is the value we want to find.

The problem states that 97 people tasted the vanilla sample of frozen yogurt.  This includes the people that tasted both samples. It means that x people tasted the chocolate and vanilla twist and 97-x people tasted only the vanilla twist.

72 people tasted the chocolate, also including the people that tasted both samples. It means that x people that tasted the chocolate and vanilla twist and 72-x that tasted only the chocolate twist.

So, recapitulating, there are 120 people, and

97-x  tasted only the vanilla twist.

72 - x tasted only the chocolate twist

x people tasted both

So

97 - x + 72 - x + x = 120

-x = 120 - 72 - 97

-x = -49 *(-1)

x = 49

There were 49 people that chose chocolate and vanilla twist.

To find out how many people chose the chocolate and vanilla twist, we need to subtract the number of people who tasted only vanilla and only chocolate from the total number of people who tasted the frozen yogurt.

To find out how many people chose the chocolate and vanilla twist, we need to subtract the number of people who tasted only vanilla and only chocolate from the total number of people who tasted the frozen yogurt. We know that 97 people tasted vanilla and 72 people tasted chocolate. However, some people chose the chocolate and vanilla twist, so we need to subtract the overlapping cases.

To calculate the number of people who chose the chocolate and vanilla twist, we can use the principle of inclusion-exclusion. We add the number of people who tasted only vanilla and the number of people who tasted only chocolate, and then subtract the total number of people who tasted the frozen yogurt.

Using the formula:

(# of people who tasted vanilla) + (# of people who tasted chocolate) - (# of people who tasted both) = Total # of people who tasted the frozen yogurt

97 + 72 - X = 120

X = 97 + 72 - 120

X = 169 - 120

X = 49

Therefore, 49 people chose the chocolate and vanilla twist.

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