In January 2013 a country‘s first class mail rates increased to 42 cents for the 1st ounce and 22 cents for each additional ounce. Is Sabrina spent $16.24 for a total of 52 stamps of these two denominations how many stamps of each denomination did she buy?

She bought ___ 42 cent stamps
And _____ 22 cent stamps

Answer: The altitude and the base of the sign are 6 meters and 11 meters respectively.

Step-by-step explanation:

Since we have given that

Area of triangular sign = 33 sq. meters

Let the altitude of the triangle be 'x'.

Let the base of the triangle be ' 2x-1'.

As we know the formula for "Area of triangle ":

[tex]Area=\dfrac{1}{2}\times base\times height\\\\33=\dfrac{1}{2}\times x(2x-1)\\\\33\times 2=2x^2-x\\\\66=2x^2-x\\\\2x^2-x-66=0\\\\2x^2-12x+11x-66=0\\\\2x(x-6)+11(x-6)=0\\\\(2x+11)(x-6)=0\\\\x=-\dfrac{11}{2},6\\\\x=-5.5,6[/tex]

Discarded the negative value of x for dimensions:

So, altitude of triangle becomes 6 meters

Base of triangle would be [tex]2(6)-1=12-1=11\ meters[/tex]

Answer:     [tex]\text{Mean length}=590.5\ mm\\\\\text{Variance of the lengths}=0.03\ mm[/tex]

Step-by-step explanation:

The mean and variance of a continuous uniform distribution function with parameters m and n is given by :-

[tex]\text{Mean=}\dfrac{m+n}{2}\\\\\text{Variance}=\dfrac{(n-m)^2}{12}[/tex]

Given : [tex] m=590.2\ \ \ n=590.80[/tex]

[tex]\text{Then, Mean=}\dfrac{590.2+590.8}{2}=590.5\ mm\\\\\text{Variance}=\dfrac{(590.8-590.2)^2}{12}=0.03\ mm[/tex]

Answer: Simple random sampling

Step-by-step explanation:

Simple random sampling is a technique of sampling in which an experimenter selects the group of samples or subjects randomly from a large group of population. Each sample is chosen randomly by chance and each entity of a population has equal possibility of being selected as sample.

According to the given situation, simple random sampling is the technique that should be used for sampling.

Answer:

{chocolate, strawberries, peanuts}

Step-by-step explanation:

Given that three sets are

Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}

Let B = {vanilla, hot fudge, sprinkles, whipped cream}  

Let C = {chocolate, hot fudge, peanuts, whipped cream}

Then Universal set U = AUBUC

= {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}

B'=elements in U but not in B

={chocolate, strawberries, peanuts}

The resulting set is B' = {chocolate, strawberries, peanuts}.

To solve for B', we first need to understand that B' (B complement) consists of elements that are in set A but not in set B.

Given the sets:

Set B includes: vanilla, hot fudge, sprinkles, and whipped cream. Therefore, B' will be the elements of set A excluding those in B.

Thus, B' is:

Therefore, the set B' = {chocolate, strawberries, peanuts}.

This method can help you understand combinations without repetition effectively.

       [tex]f'(x)= \dfrac{-1}{2\sqrt{9-x}}[/tex]

The function f(x) is given by:

   [tex]f(x)=\sqrt{9-x}[/tex]

The domain of the function is the possible values of x where the function is defined.

We know that the square root function [tex]\sqrt{x}[/tex] is defined when x≥0.

Hence, [tex]\sqrt{9-x}[/tex] will be defined when [tex]9-x\geq 0\\\\i.e.\\\\x\leq 9[/tex]

Hence, the domain of the function f(x) is: [tex]x\leq 9[/tex]

Also, the definition of derivative of x is given by:

[tex]f'(x)= \lim_{h \to 0}  \dfrac{f(x+h)-f(x)}{h}[/tex]

Hence, here by putting the value of the function we get:

[tex]f'(x)= \lim_{h \to 0} \dfrac{\sqrt{9-(x+h)}-\sqrt{9-x}}{h}\\\\i.e.\\\\f'(x)= \lim_{h \to 0} \dfrac{\sqrt{9-(x+h)}-\sqrt{9-x}}{h}\times \dfrac{\sqrt{9-(x+h)}+\sqrt{9-x}}{\sqrt{9-(x+h)}+\sqrt{9-x}}\\\\\\f'(x)= \lim_{h \to 0} \dfrac{(\sqrt{9-(x+h)}-\sqrt{9-x})(\sqrt{9-(x+h)}+\sqrt{9-x})}{(\sqrt{9-(x+h)}+\sqrt{9-x})\times h}\\\\\\f'(x)= \lim_{h \to 0} \dfrac{9-(x+h)-(9-x)}{(\sqrt{9-(x+h)}+\sqrt{9-x})\times h}[/tex]

Since,

[tex](a-b)(a+b)=a^2-b^2[/tex]

Hence, we have:

[tex]f'(x)= \lim_{h \to 0} \dfrac{-h}{(\sqrt{9-(x+h)}+\sqrt{9-x})\times h}\\\\\\f'(x)= \lim_{h \to 0} \dfrac{-1}{(\sqrt{9-(x+h)}+\sqrt{9-x})}\\\\\\i.e.\\\\\\f'(x)= \dfrac{-1}{2\sqrt{9-x}}[/tex]

Since, the domain of the derivative function is equal to the derivative of the square root function.

Also, the domain of the square root function is: [tex]x\leq 9[/tex]

Hence, domain of the derivative function is:  [tex]x\leq 9[/tex]

Answer:

-1/sqrt(1-9x)

Step-by-step explanation:

This is the answer

The line y = 3 means that x = 0.

The point (-3, y) tells me that x = -3 when y is 3.

So, y = 3 completes the point (-3, 3).

Answer:

Option C

Step-by-step explanation:

96ft2

Answer:

Area of pyramid = [tex]96[/tex]. square feet.

Step-by-step explanation:

Given : A square pyramid is 6 feet on each side. The height of the pyramid is 4 feet.

To find:  What is the total area of the pyramid.

Solution : We have given

Each side of square pyramid = 6 feet .

Height = 4 feet .

Area of pyramid = [tex](side)^{2} + 2* side\sqrt{\frac{(side)^{2}}{4} +height^{2}}[/tex].

Plug the values side =  6 feet  , height = 4 feet .

Area of pyramid = [tex](6)^{2} + 2* 6\sqrt{\frac{(6)^{2}}{4} + 4^{2}}[/tex].

Area of pyramid = [tex]36+ 12\sqrt{\frac{36}{4} + 16}[/tex].

Area of pyramid = [tex]36+ 12\sqrt{9 +16}[/tex].

Area of pyramid = [tex]36+ 12\sqrt{25}[/tex].

Area of pyramid = [tex]36+ 12 *5[/tex].

Area of pyramid = [tex]36+ 60[/tex].

Area of pyramid = [tex]96[/tex]. square feet.

Therefore, Area of pyramid = [tex]96[/tex]. square feet.

Answer:

4th Option is correct.

Step-by-step explanation:

Given:

Number of apples in refrigerator = 6

Number of oranges in refrigerator = 5

Number of bananas in refrigerator = 10

Number of pears in refrigerator = 3

Number of peaches in refrigerator = 7

Number of plums in refrigerator = 11

Number of mangoes in refrigerator = 2

A piece is randomly taken out from refrigerator.

To find: Sample Space of the experiment

Sample Space : It is a set which contain all the possible outcome / results of the experiment.

So, here Sample Space = { 6 apples , 5 oranges , 10 bananas , 3 pears , 7 peaches , 11 plums , 2 mangoes }

Therefore, 4th Option is correct.

Answer:

[tex]26.12\:<\:\mu\:<\:31.48[/tex]

Step-by-step explanation:

Since the population standard deviation [tex]\sigma[/tex] is unknown, and the sample standard deviation [tex]s[/tex], must replace it, the [tex]t[/tex] distribution  must be used for the confidence interval.

The sample size is n=8.

The degree of freedom is [tex]df=n-1[/tex], [tex]\implies df=8-1=7[/tex].

With 95% confidence level, the [tex]\alpha-level[/tex](significance level) is 5%.

Hence with 7 degrees of freedom, [tex]t_{\frac{\alpha}{2} }=2.365[/tex]. (Read from the t-distribution table see attachment)

The 95% confidence interval can be found by using the formula:

[tex]\bar X-t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )\:<\:\mu\:<\:\bar X+t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )[/tex].

The sample mean is [tex]\bar X=28.8[/tex] hours.

The sample sample standard deviation is [tex]s=3.2[/tex] hours.

We now substitute all these values into the formula to obtain:

[tex]28.8-2.365(\frac{3.2}{\sqrt{8} } )\:<\:\mu\:<\:28.8+2.365(\frac{3.2}{\sqrt{8} } )[/tex].

[tex]26.12\:<\:\mu\:<\:31.48[/tex]

We are 95% confident that the population mean is between 26.12 and 31.48  hours.

Answer:

First type of fruit drinks: 160 pints

Second type of fruit drinks: 80 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 5.5% pure fruit juice

Let's call B the amount of second type of fruit drinks. 100% pure fruit juice

The resulting mixture should have 70% pure fruit juice and 240 pints.

Then we know that the total amount of mixture will be:

[tex]A + B = 240[/tex]

Then the total amount of pure fruit juice in the mixture will be:

[tex]0.55A + B = 0.7 * 240[/tex]

[tex]0.55A + B = 168[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:

[tex]-A -B = -240[/tex]

[tex]-A -B = -240[/tex]

                  +

[tex]0.55A + B = 168[/tex]

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

[tex]-0.45A = -72[/tex]

[tex]A = \frac{-72}{-0.45}[/tex]

[tex]A = 160\ pints[/tex]

We substitute the value of A into one of the two equations and solve for B.

[tex]160 + B = 240[/tex]

[tex]B = 80\ pints[/tex]

To make 240 pints of a mixture that is 70% pure fruit juice, you will need 160 pints of the first type of fruit drink (55% pure fruit juice) and 80 pints of the second type of fruit drink (100% pure fruit juice).

To solve this problem, we can set up a system of equations. Let's say x represents the number of pints of the first type of fruit drink (55% pure fruit juice) and y represents the number of pints of the second type of fruit drink (100% pure fruit juice). We know that the total number of pints of the mixture is 240, so we can write the equation x + y = 240. We also know that the desired percentage of pure fruit juice in the mixture is 70%, so we can write the equation (55% * x + 100% * y) / 240 = 70%. To solve this system of equations, we can use substitution or elimination method. Let's use substitution:

From the first equation, we can solve for x in terms of y: x = 240 - y. Substituting this into the second equation, we get ((55% * (240 - y)) + 100% * y) / 240 = 70%. Simplifying the equation, we have (0.55(240 - y) + y) / 240 = 0.70. Distributing and combining like terms, we get (132 - 0.55y + y) / 240 = 0.70. Simplifying further, we have (132 + 0.45y) / 240 = 0.70. Cross multiplying, we get 132 + 0.45y = 0.70 * 240. Simplifying, we have 132 + 0.45y = 168. Multiplying 0.45 with y, we get 0.45y = 168 - 132. Subtracting 132 from 168, we get 0.45y = 36. Dividing both sides of the equation by 0.45, we get y = 36 / 0.45. Evaluating this expression, we get y = 80. So, the number of pints of the second type of fruit drink (100% pure fruit juice) needed is 80. Substituting this value back into the first equation, we can solve for x: x + 80 = 240. Subtracting 80 from both sides of the equation, we get x = 240 - 80. Evaluating this expression, we get x = 160. Therefore, the number of pints of the first type of fruit drink (55% pure fruit juice) needed is 160.

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Answer:

a(12) = 35

Step-by-step explanation:

Given

a(12) = 50- 1.25x

Value of x is 12

50 - 1.25(12)

Simplify

50 - 15

Solve

a(12) = 50 - 15

a(12) = 35

Answer:

There are 13 families had a parakeet only

Step-by-step explanation:

* Lets explain the problem

- There are 180 families

- 67 families had a dog

- 52 families had a cat

- 22 families had a dog and a cat

- 70 had neither a cat nor a​ dog, and in addition did not have a​

 parakeet

- 4 had a​ cat, a​ dog, and a parakeet (4 is a part of 22 and 22 is a part

 of 67 and 520

* We will explain the Venn-diagram

- A rectangle represent the total of the families

- Three intersected circles:

 C represented the cat

 D represented the dog

 P represented the parakeet

- The common part of the three circle had 4 families

- The common part between the circle of the cat and the circle of the

 dog only had 22 - 4 = 18 families

- The common part between the circle of the dog and the circle of the

 parakeet only had a families

- The common part between the circle of the cat and the circle of the

 parakeet only had b families

- The non-intersected part of the circle of the dog had 67 - 22 - a =

  45 - a families

  had dogs only

- The non-intersected part of the circle of the cat had 52 - 22 - b =  

  30 - b families

  had cats only

- The non-intersected part of the circle of the parakeet had c families

  had parakeets only

- The part out side the circles and inside the triangle has 70 families

- Look to the attached graph for more under stand

∵ The total of the families is 180

∴ The sum of all steps above is 180

∴ 45 - a + 18 + 4 + 30 - b + b + c + a + 70 = 180 ⇒ simplify

- (-a) will cancel (a) and (-b) will cancel (b)

∴ (45 + 18 + 4 + 30 + 70) + (-a + a) + (-b + b) + c = 180

∴ 167 + c = 180 ⇒ subtract 167 from both sides

∴ c = 180 - 167 = 13 families

* There are 13 families had a parakeet only

Answer:

(a) The probability of P(A), P(B), and P(C) are 0.35, 0.6 and 0.65 respectively.

(b) The probability of P(A ∩ B) is 0.2.

(c) The probability of P(A ∪ B) is 0.75.

(d) Events A and C mutually exclusive because the intersection of set A and C is null set or ∅.

Step-by-step explanation:

The given sample space is

[tex]S=\{E_1,E_2,E_3,E_4,E_5,E_6,E_7\}[/tex]

[tex]P(E_1)=0.1, P(E_2)=0.15,P(E_3)=0.15,P(E_4)=0.2,P(E_5)=0.1,P(E_6)=0.05, P(E_7)=0.25[/tex]

It is given that

[tex]A=\{E_1,E_4,E_6\}[/tex]

[tex]B=\{E_2,E_4,E_7\}[/tex]

[tex]C=\{E_2,E_3,E_5,E_7\}[/tex]

(a)

[tex]P(A)=P(E_1)+P(E_4)+P(E_6)=0.1+0.2+0.05=0.35[/tex]

[tex]P(B)=P(E_2)+P(E_4)+P(E_7)=0.15+0.2+0.25=0.6[/tex]

[tex]P(C)=P(E_2)+P(E_3)+P(E_5)+P(E_7)=0.15+0.15+0.1+0.25=0.65[/tex]

Therefore the probability of P(A), P(B), and P(C) are 0.35, 0.6 and 0.65 respectively.

(b)

A ∩ B represent the common elements of set A and set B.

[tex]A\cap B=\{E_4\}[/tex]

[tex]P(A\cap B)=P(E_4)=0.2[/tex]

The probability of P(A ∩ B) is 0.2.

(c)

A ∪ B represent all the elements of set A and set B.

[tex]A\cup B=\{E_1,E_2,E_4,E_6,E_7\}[/tex]

[tex]P(A\cup B)=P(E_1)+P(E_2)+P(E_4)+P(E_6)+P(E_7)[/tex]

[tex]P(A\cup B)=0.1+0.15+0.2+0.05+0.25=0.75[/tex]

The probability of P(A ∪ B) is 0.75.

(d)

Set A and C has no common element. So, the intersection of set A and C is empty set.

Yes, events A and C mutually exclusive because the intersection of set A and C is null set or ∅.

The probability of events A, B, and C are calculated by summing the individual probabilities of their constituent sample points. The probability of the intersection of events A and B is equal to the probability of the common sample point. The probability of the union of events A and B is obtained by subtracting the probability of the intersection from the sum of their individual probabilities. Events A and C are not mutually exclusive because they have common sample points.

(a) Probability of events A, B, and C:

(b) Probability of intersection of events A and B:

P(A ∩ B) = P(E4) = 0.2

(c) Probability of union of events A and B:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.35 + 0.6 - 0.2 = 0.75

(d) Mutually exclusive events A and C:

No, events A and C are not mutually exclusive because they have common sample points in E2 and E7.

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Final answer:

Train B travels at a speed of 30 miles per hour and train A travels at a speed of 50 miles per hour.

Explanation:

Let's say the speed of train B is x miles per hour. Since train A is 20 miles per hour faster, the speed of train A is x + 20 miles per hour.

Distance = Speed x Time

For train A, Distance = (x +20) * 3

For train B, Distance = x * 3

Since they meet 240 miles apart, the sum of their distances is 240:

(x + 20) * 3 + x * 3 = 240

3x + 60 + 3x = 240

6x = 180

x = 30

Hence, train B travels at a speed of 30 miles per hour and train A travels at a speed of 50 miles per hour.

[tex](f+g)(x)=3x^2-2+4x+2=3x^2+4x\\\\(f+g)(2)=3\cdot2^2+4\cdot2=12+8=20[/tex]

Answer:

The cost of 1 pint of the medication would be $1.875.

Step-by-step explanation:

The AWP of 3785 ml ( 1 gallon ) cough syrup = $18.75

After an additional 20% discount from wholesaler the price would be

New price = 18.75 - (0.20 × 18.75)

                 = 18.75 - 3.75

                 = $15.00

Since 1 gallon ( 3785 ml) = 8 pints

Therefore, the price for 1 pint = [tex]\frac{15}{8}[/tex] = $1.875

The cost of 1 pint of the medication would be $1.875.

Answer: 0.16

Step-by-step explanation:

Given: The probability that a student graduating from Suburban State University has student loans to pay off after graduation is =0.60

Then the probability that a student graduating from Suburban State University does not have student loans to pay off after graduation is =[tex]1-0.6=0.4[/tex]

Since all the given event is independent for all students.

Then , the probability that neither of them has student loans to pay off after graduation is given by :-

[tex](0.4)\times(0.4)=0.16[/tex]

Hence, the probability that neither of them has student loans to pay off after graduation =0.16

The equation of the line indicates that the x and y-intercept and the formula for the area of the triangle are;

x-intercept (c, 0)

y-intercept (0, 1/(c² + 7))

A(c) = c/(2·(c² + 7))

The steps used to find the x-intercept and the y-intercept are presented as follows;

The equation of the line c·(c² + 7)·y = c - x, can be expressed in the slope intercept form to find the coordinates of the x-intercept and the coordinates of the y-intercept as follows;

c·(c² + 7)·y = c - x

y = (c - x)/(c·(c² + 7))

y = c/(c·(c² + 7)) - x/(c·(c² + 7))

y = 1/((c² + 7)) - x/(c·(c² + 7))

The above equation is in the slope-intercept form, y = m·x + c

Where c is the y-coordinate of the y-intercept, and (0, c) ids the coordinate of the y-intercept; Therefore, the coordinates of the y-intercept is; (0,  1/((c² + 7)))

The coordinate of the x-intercept can be found by plugging in y = 0, in the above equation to get;

0 = 1/((c² + 7)) - x/(c·(c² + 7))

x/(c·(c² + 7)) = 1/((c² + 7))

x = (c·(c² + 7))/((c² + 7))

(c·(c² + 7))/((c² + 7)) = c

x = c

Therefore coordinates of the x-intercept is; (c, 0)

The triangle enclosed by the line and the x-axis and y-axis is a right triangle, therefore;

The positive x and y-values of the x-intercept and y-intercept indicates that the area of the triangle is the product half the distance from the origin to the y-intercept and the distance from the origin to the x-intercept

Area = (1/2) × (1/((c² + 7)) - 0) × (c - 0)

(1/2) × (1/((c² + 7))) × (c) = c/(2·(c² + 7)

Area of the triangle, A(c) = c/(2·(c² + 7)

The complete question found through search can be presented as follows;

Consider the equation of the line c·(c² + 7)·y = c - x where c > 0 is a constant

(a) Find the coordinates of the x-intercept and the y-intercept

x-intercept (  ,  )

y-intercept (  ,  )

(b) Find a formula for the area of the triangle enclosed between the line, the x-axis and the y-axis

Answer: 0.59

Step-by-step explanation:

Probability is a measure that quantifies the likelihood that events will occur.

Probabilities can be numerically described by the number of desired outcomes divided by the total number of all outcomes .

In this case, the number of desired outcomes is 307 (surveyed voters who plan to vote to reelect the mayor), and the total number of all outcomes is 520 (total of surveyed voters) .

Then, the probability that a surveyed voter plans to vote to reelect the mayor is calculated as:

[tex]\frac{307}{520}=0.59[/tex]

The probability that a surveyed voter plans to vote to reelect the mayor is 0.59.

To find the probability that a surveyed voter plans to vote to reelect the mayor, we divide the number of surveyed voters who plan to reelect the mayor by the total number of surveyed voters.

Given that 307 out of 520 likely voters plan to reelect the incumbent mayor, the probability is:

Probability = Number of surveyed voters who plan to reelect the mayor / Total number of surveyed voters

Probability = 307 / 520 = 0.59 (rounded to two decimal places)

Answer:

Step-by-step explanation:

The formula of an area of a square with side length a:

[tex]A=a^2[/tex]

The big square:

[tex]a=x+5[/tex]

Substitute:

[tex]A_B=(x+5)^2[/tex]           use  [tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex]A_B=x^2+2(x)(5)+5^2=x^2+10x+25[/tex]

The small square:

[tex]a=x-2[/tex]

Substitute:

[tex]A_S=(x-2)^2[/tex]       use  [tex](a-b)^2=a^2-2ab+b^2[/tex]

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

The area of a shaded region:

[tex]A=A_B-A_S[/tex]

Substitute:

[tex]A=(x^2+10x+25)-(x^2-4x+4)=x^2+10x+25-x^2+4x-4[/tex]

combine like terms

[tex]A=(x^2-x^2)+(10x+4x)+(25-4)=14x+21[/tex]

Answer: 19.77%

Step-by-step explanation:

Given: Mean : [tex]\mu=74[/tex]

Standard deviation : [tex]\sigma = 7.1[/tex]

The formula to calculate z-score is given by :_

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 80, we have

[tex]z=\dfrac{80-74}{7.1}\approx0.85[/tex]

The P-value = [tex]P(z>0.85)=1-P(z<0.85)=1-0.8023374=0.1976626[/tex]

In percent , [tex]0.1976626\times100=19.76626\%\approx19.77\%[/tex]

Hence, the approximate percentage of the test scores during the past year exceeded 80 =19.77%

The probability of writing the first 7 digits of your phone number is 1/60480.

To determine the probability of choosing the first 7 digits of your phone number in the given scenario, we need to calculate the probability of choosing each digit correctly and in order. Since there are 10 digits to choose from, the probability of choosing the first digit correctly is 1/10. The probability of choosing the second digit correctly is 1/9, since one digit has already been chosen. Continuing this pattern, the probability of choosing all 7 digits correctly and in order is:

P(choosing all seven numbers correctly) = P(choosing 1st number correctly) * P(choosing 2nd number correctly) * ... * P(choosing 7th number correctly)

So, the probability is:

1/10 * 1/9 * 1/8 * 1/7 * 1/6 * 1/5 * 1/4 = 1/60480

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The probability of writing the first 7 digits of your phone number is 1/604,800.

The probability of writing the first 7 digits of your phone number depends on the specific digits in your phone number. However, assuming that all digits are equally likely to be chosen, the probability can be calculated by multiplying the probabilities of choosing each digit correctly. Since there are 10 digits to choose from and you are picking 7, the probability would be:

To calculate the overall probability, you multiply these individual probabilities together:

So, the probability of writing the first 7 digits of your phone number is 1/604,800.

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[tex]\textbf{Transform}\\ \textrm{log} (7(3x -2)^2) \textbf{ into} \textrm{ log}(7) + \textrm{log}(3x-2)^2\\\\ \textbf{Expand} \\ \text{log}(3x-2)^2\\\\ \text{You can move 2 outside of }\text{log}(3x-2)^2\\\\ \textbf{Answer}\\ \text{log }7 + 2\text{ log}(3x-2)[/tex]

You probably know that

[tex]\sin x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)!}[/tex]

Then

[tex]\mathrm{sinc}\,x=\displaystyle\frac1x\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)!}=\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}[/tex]

when [tex]x\neq0[/tex], and 1 when [tex]x=0[/tex].

By the ratio test, the series converges if the following limit is less than 1:

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(-1)^{n+1}x^{2n+2}}{(2n+3)!}}{\frac{(-1)^nx^{2n}}{(2n+1)!}}\right|=|x^2|\lim_{n\to\infty}\frac{(2n+1)!}{(2n+3)!}[/tex]

The limit is 0, so the series converges for all [tex]x[/tex].

For this case we propose a system of equations:

x: Variable representing the weight of large boxes

y: Variable that represents the weight of the small boxes

So

[tex]x + y = 80\\55x + 70y = 4850[/tex]

We clear x from the first equation:

[tex]x = 80-y[/tex]

We substitute in the second equation:

[tex]55 (80-y) + 70y = 4850\\4400-55y + 70y = 4850\\15y = 450\\y = 30[/tex]

We look for the value of x:

[tex]x = 80-30\\x = 50[/tex]

Large boxes weigh 50 pounds and small boxes weigh 30 pounds

Answer:

Large boxes weigh 50 pounds and small boxes weigh 30 pounds

Answer: A large box weighs 50 pounds and a small box weighs 30 pounds.

Step-by-step explanation:

Set up a system of equations.

Let be "l" the weight of a large box and "s" the weight of a small box.

Then:

[tex]\left \{ {{l+s=80} \atop {55l+70s=4,850}} \right.[/tex]

You can use the Elimination method. Multiply the first equation by -55, then add both equations and solve for "s":

[tex]\left \{ {{-55l-55s=-4,400} \atop {55l+70s=4,850}} \right.\\.............................\\15s=450\\\\s=\frac{450}{15}\\\\s=30[/tex]

Substitute [tex]s=30[/tex] into an original equation and solve for "l":

[tex]l+(30)=80\\\\l=80-30\\\\l=50[/tex]

Answer:

  $270,314.08

Step-by-step explanation:

The multiplier each month is 1+0.08/12 ≈ 1.0066667, so after 120 months, the amount is multiplied by (1.0066667)^120 ≈ 2.2196402. The amount needed is ...

  $600,000/2.2196402 ≈ $270,314.08

To reach a retirement goal of $600,000 in 10 years with an 8% interest rate compounded monthly, you would need to deposit approximately $277,002.66 now.

In this case, we're using a formula to determine the amount needed to deposit today (P) for a future goal ($600,000) using an interest rate (r) of 8% compounded monthly for ten years. The formula to use is P = F / (1 + r/n)^(nt), where:

So, you need to plug these figures into the equation: P = 600,000 / (1 + 0.08/12)^(12*10). After doing the math, you would need to deposit around $277,002.66 now to reach your retirement goal of $600,000 in ten years given an 8% annual interest rate compounded monthly.

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Answer:

Bailey family's sprinkler was used for 35 hours and Harris family's sprinkler was used for 20 hours.

Step-by-step explanation:

 Set up a system of equations.

Let be "b" the time Bailey family's sprinkler was used and "h" the time Harris family's sprinkler was used.

Then:

[tex]\left \{ {{b+h=55} \atop {15b+40h= 1,325}} \right.[/tex]

You can use the Elimination method. Multiply the first equation by -15, then add both equations and solve for "h":

[tex]\left \{ {{-15b-15h=-825} \atop {15b+40h= 1,325}} \right.\\.............................\\25h=500\\\\h=\frac{500}{25}\\\\h=20[/tex]

Substitute [tex]h=20[/tex] into an original equation and solve for "b":

[tex]b+20=55\\\\b=55-20\\\\b=35[/tex]

Answer: c) The number 75 is an outlier on the stem and leaf plot.

Step-by-step explanation:

When we look in the given stem-leaf plot, there is no leaf attached to the stem with value 6.

It mean there is no value between 50 and 75.

It shows that the value of 75 is detached from the other values in the data.

⇒ The number 75 is an outlier on the stem and leaf plot.

Answer:

The answer is C

Step-by-step explanation:

You must know that percent are ALWAYS taken out of 100. This means that 100 subtracted by 65 will give the percent that this event won't happen:

100 - 65 = 35

This event has 65% probability of happening and a 35% of NOT happening

Hope this helped!

~Just a girl in love with Shawn Mendes