A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon, whereas they sell 3902 gallons on a day that they charge $1.40 per gallon. Find a linear function that expresses gallons sold as a function of price. (Hint: express the given information as two ordered pairs, and then find the equation of the line that goes through the two points.) Use this function to predict the number of gallons sold at a price of $1.22 per gallon.

Answer: Samantha's Recipe:

Ratio of lemonade = 2 1/2 : 6

Caden's Recipe:

Ratio of lemonade = 15 : 32

Step-by-step explanation:

Samantha's Recipe

3 1/2 parts cranapple juice

2 1/2 parts lemonade

Caden's Recipe

4 1/4 parts cranapple juice

3 3/4 parts lemonade

For each recipe, write a ratio that compares the number of parts of lemonade to the total number of parts.

Solution:

For Samantha's Recipe:

Total number of parts = cranapple juice parts + lemonade parts = 3.5 + 2.5 = 6.0

Ratio of lemonade to total number of parts = (2.5)/(6.0) = 2 1/2 : 6

For Caden's Recipe:

Total number of parts = cranapple juice parts + lemonade parts =(17/4)+(15/4) = (32/4) = 8

Therefore, Ratio of lemonade to total number of parts = (15/4) / (8) =(15)/(32) = 15:32

Answer:

74

Step-by-step explanation:

tan?=7/2

tan^-1(7/2)=?

?=74

Answer:

16°

Step-by-step explanation:

A ladder leans against a building . The foot of the ladder is 2 feet from the building and reaches to a point 7 feet high on the building . The measured angle formed by the ladder and building can be computed below.

The illustration forms a right angle triangle. Two sides are given and we are told to find an angle

Distance form the foot of the ladder to the building = 2 feet

The ladder reaches a point in the building which is the height of the building the ladder head started from = 7 feet

Using SOHCAHTOA principle

tan ∅ = opposite /adjacent

where

opposite = 2 ft

adjacent = 7 ft

∅ = angle formed by the ladder and the building

tan ∅ = 2/7

∅ = tan⁻¹ 2/7

∅ =  15.9453959

∅ ≈ 16°

Answer:

Reggie picked total 8 quarts of berries.

Step-by-step explanation:

Given:

Amount of Blueberries picked by Reggie = [tex]3\frac{3}{4} [/tex] quarts

[tex]3\frac{3}{4}[/tex] can be Rewritten as  [tex]\frac{15}{4}[/tex]

Amount of Blueberries picked by Reggie = [tex]\frac{15}{4}[/tex] quarts

Amount of Raspberries picked by Reggie = [tex]4\frac{1}{4} [/tex] quarts

[tex]4\frac{1}{4}[/tex] can be Rewritten as  [tex]\frac{17}{4}[/tex]

Amount of Raspberries picked by Reggie = [tex]\frac{17}{4}[/tex] quarts

We need to find Total quarts of berries he picked from fruit farm.

So we can say Total quarts of berries he picked from fruit farm is equal to sum of Amount of Blueberries and Amount of Raspberries.

Framing in equation form we get;

Total Quarts of Berries = [tex]\frac{15}{4}+\frac{17}{4} = \frac{15+17}{4}=\frac{32}{4} = 8\ quarts[/tex]

Hence Reggie picked Total 8 quarts of berries.

Answer:

Option D.

Step-by-step explanation:

It is given that a set of 15 different integers has a median of 25 and a range of 25.

Total number of integers is 15 which is an odd number.

[tex](\frac{n+1}{2}) th=(\frac{15+1}{2}) th=8th[/tex]

8th integers is median. It means 8th integers is 25.

7 different integers before 25 are 18, 19, 20, 21, 22, 23, 24.

It means the greatest possible minimum value is 18.

Range = Maximum - Minimum

25 = Maximum - 18

Add 18 on both sides.

25 +18 = Maximum

43 = Maximum

The greatest possible integer in the set is 43.

Therefore, the correct option is D.

Answer:

D. 43

Step-by-step explanation:

We have been given that a set of 15 different integers has a median of 25 and a range of 25.

Since each data point is different, so we can represent our data points as:

[tex]N_1,N_2,N_3,N_4,N_5,N_6,N_7,N_8, N_9,N_{10},N_{11},N_{12},N_{13},N_{14}, N_{15}[/tex]

Since there are 15 data points, this means that median will be 8th data point.

We have been given that median is 25, so [tex]n_8=25[/tex].

Since each data point is different, so 7 data points less than 25 would be:

18, 19, 20, 21, 22, 23, 24.

We know that range is the difference between upper value and lower value.

[tex]\text{Range}=\text{Upper value}-\text{Lower value}[/tex]

[tex]\text{Range}+\text{Lower value}=\text{Upper value}[/tex]

Upon substituting our given values, we will get:

[tex]25+18=\text{Upper value}[/tex]

[tex]43=\text{Upper value}[/tex]

Therefore, the greatest possible integer in this set could be 43 and option D is the correct choice.

The sub-questions for this question are:

a) construct a binomial distribution using n=6 and p=0.34

b) graph the binomial distribution using a histogram and describe it's shape

c) what values of the random variable would you consider unusual? Explain your reasoning.

Answer:

a)

P(X=0) =0.0827

P(X=1) = 0.255

P(X=2) = 0.329

P(X=3) = 0.226

P(X=4) = 0.087

P(X=5) = 0.018

P(X=6) = 0.0015

b) graph D

c) x=5 and x=6

Step-by-step explanation:

a)

Formula for binomial distribution:

nCx(p^x)(q^(n-x))

Number of sample, n = 6

probability of success, p = 0.34

probability of failure, q = 1-p = 0.66

P(X=0) = 6C0(0.34^0)(0.66^6)

= 1*1*0.0827 = 0.0827

P(X=1) = 6C1(0.34^1)(0.66^5)

= 6*0.34*0.1252 = 0.255

P(X=2) = 6C2(0.34^2)(0.66^4)

= 15*0.1156*0.1897 = 0.329

P(X=3) = 6C3(0.34^3)(0.66^3)

= 20*0.0113 = 0.226

P(X=4) = 6C4(0.34^4)(0.66^2)

= 15*0.0058 = 0.087

P(X=5) = 6C5(0.34^5)(0.66^1)

= 6*0.003 = 0.018

P(X=6) = 6C6(0.34^6)(0.66^0)

= 1*0.0015 = 0.0015

b) the shape of the graph is the graph shape. Referring to the attachment, the correct graph is D

c) the unusual values would be x=6 and x=5, because those values are too small and lower than 0.05

Answer:

a) Mean = 0.30, SD = 0.017

Step-by-step explanation:

The mean and sampling distribution of the sample proportion can be found using the equations

Mean= p

[tex]SD=\sqrt{\frac{p*(1-p)}{n} }[/tex]

where

Using these information:

Mean = 0.30

[tex]SD=\sqrt{\frac{0.30*0.70}{750} }[/tex] ≈ 0.017

Final answer:

The mean of the sampling distribution of the sample proportion is 0.30, and the standard deviation is found to be approximately 0.017. Therefore, the correct answer is Mean = 0.30, SD = 0.017.

Explanation:

To determine the mean and standard deviation of the sampling distribution of the sample proportion p, we use the formulas related to binomial distributions, since the survey outcome (believe that performance-enhancing drugs are a problem or not) follows a binomial distribution. The mean of the sampling distribution of the proportion is simply the population proportion, which is given as 0.30.

The standard deviation (SD) of the sampling distribution of p can be calculated using the formula SD = √[p(1-p)/n], where p is the population proportion and n is the sample size. In this case:

SD = √[0.30(1-0.30)/750] = √[0.21/750] = √[0.00028] ≈ 0.0167

Thus, the correct answer is a) Mean = 0.30, SD = 0.017

Answer:$308.44

Step-by-step explanation:

$70.00/5= $14.02 an hour

14.02*22 = $308.44

Amount of money earned in 22 hour is 308

Amount of money earned in 5 hour = 70

Amount of money earned in 22 hour

Amount of money earned in 22 hour = 22[70/5]

Amount of money earned in 22 hour = 22[14]

Amount of money earned in 22 hour = 308

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Answer:

[tex]P = \frac{2}{3}[/tex]

Step-by-step explanation:

All the points in the plane that are 20 inches from P constituing a circle with center in P and with radius 20 inch

We need find the angle in this circle by which the point R is closer to P than it is to Q. The limit situation occurs when the distances from P to R and from R to Q are equals and have the value 20 inches. In this situation the points P, R y Q form a equilater triangle with angles of value 60°.

Thus, the point R is closer to P than it is to Q in 240° of the circle, except 60° above of the line PQ and 60° below the line PQ.

Then the probability is

[tex]P= \frac{240}{360} = \frac{2}{3}[/tex]

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

Step-by-step explanation:

Part 1) Graph the system of inequalities

we have

[tex]y> 5x+5[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dashed line [tex]y=5x+5[/tex]

The slope pf the dashed line A is positive m=5

The y-intercept of the dashed line A is (0,5)

The x-intercept of the dashed line A is (-1,0)

[tex]y>-\frac{1}{2}x+1[/tex] ----> inequality B

The solution of the inequality B is the shaded area above the dashed line [tex]y=-\frac{1}{2}x+1[/tex]

The slope pf the dashed line B is negative m=-1/2

The y-intercept of the dashed line B is (0,1)

The x-intercept of the dashed line B is (2,0)

The solution of the system of inequalities is the shaded area above the dashed line A and above the dashed line B

using a graphing tool

see the attached figure

Part B) Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

substitute the value of x and the value of y in each inequality

For x=-2, y=5

Verify inequality A

[tex]5>5(-2)+5[/tex]

[tex]5>-5[/tex] ---> is true

so

The ordered pair satisfy inequality A

Verify inequality B

[tex]5>-\frac{1}{2}(-2)+1[/tex]

[tex]5>2[/tex] ---> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

Answer:

Jane has drive 390 miles to visit Grandma.

Step-by-step explanation:

Given:

Number of miles Susie drive = 65 miles

Meg drives 2 times as far as Susie.

It means Number of miles Meg drive is equal to twice the number of miles driven my Susie.

Framing equation we get;

Number of miles Meg drive = 2 × Number of miles Susie drive = [tex]65 \times 2=130\ miles[/tex]

Also Given:

Jane drives twice as far as Susie and Meg combined.

Number of Miles Driven by Jane is equal to twice the sum of Number of miles Susie drive and Number of miles Meg drive.

Framing equation we get;

Number of miles Meg drive = 2 × (Number of miles Susie drive + Number of miles Meg drive) = [tex]2\times (65+130) = 2\times 195 = 390\ miles[/tex]

Hence Jane has drive 390 miles to visit Grandma.

Answer:

The answer to your question is

a) [tex]\frac{480 mi}{min}[/tex]

b) distance = 2400 mi

Step-by-step explanation:

a) 8 mi/s  convert to mi/min

[tex]\frac{8 mi}{s}  x  \frac{60 s}{1 min}  = \frac{8 x 60 mi }{min}  = \frac{480 mi}{min}[/tex]

b) [tex]speed = \frac{distance}{time}[/tex]

          distance = speed x time

          distance = [tex]\frac{480 mi}{min} x 5 min[/tex]

         distance = 2400 mi

Answer:

Step-by-step explanation:

The domain is the horizontal extent, which is from x=0 to x=7.

The range is the vertical extent, which is from y=-2 to y=4.

The curve passes the vertical line test, so the relation IS A FUNCTION.

_____

The vertical line test asks whether any vertical line intersects the curve at more than one point. If so, the relation is NOT a function.

Answer:

See proof below

Step-by-step explanation:

Let x,y be arbitrary real numbers. We want to prove that if x≠y then f(x)≠f(y) (this is the definition of 1-1).

If x≠y, we can assume, without loss of generality that x<y using the trichotomy law of real numbers (without loss of generality means that the argument in this proof is the same if we assume y<x).

Because f is strictly increasing, x<y implies that f(x)<f(y). Therefore f(x)≠f(y) because of the trichotomy law, and hence f is one-to-one.

Answer:

[tex]\large\tt\boxed{D. \ \tt -5j^{2}-5j+5}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to simplify the Polynomial.}[/tex]

[tex]\large\underline{\textsf{What is a Polynomial?}}[/tex]

[tex]\textsf{A Polynomial is an \underline{expression} that is made up of 1 or more terms.}[/tex]

[tex]\textsf{Terms can be a single whole number, variables, or a combination.}[/tex]

[tex]\large\underline{\textsf{How to Simplify a Polynomial?}}[/tex]

[tex]\textsf{There are a few ways to simplify a Polynomial. Let's identify them.}[/tex]

[tex]\textsf{A way to simplify a polynomial is by using the Distributive Property.}[/tex]

[tex]\textsf{Another way is to combine like terms.}[/tex]

[tex]\textsf{For this problem, we will have to do both!}[/tex]

[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]

[tex]\textsf{Distributive Property is a property that allows us to distribute a number left to a set}[/tex]

[tex]\textsf{of parentheses inside the values of the parentheses.}[/tex]

[tex]\underline{\textsf{How the Distributive Property works;}}[/tex]

[tex]\textsf{Example;} \tt -2(x+y)[/tex]

[tex]\textsf{-2 would multiply with x and y.}[/tex]

[tex]\mathtt{ -2(x+y)=\boxed{-2x-2y}}[/tex]

[tex]\large\underline{\textsf{What is Combining Like Terms?}}[/tex]

[tex]\textsf{Combining Like Terms is a simple way to simplify an expression by adding/subtracting}[/tex]

[tex]\textsf{like terms. This helps to make the expression much simpler.}[/tex]

[tex]\textsf{Now, we should know how to simplify the given polynomial.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Begin by using the Distributive Property on the left side of the Polynomial.}[/tex]

[tex]\textsf{Afterwards, Combine Like Terms.}[/tex]

[tex]\large\underline{\textsf{Simplifying;}}[/tex]

[tex]\tt -(5j^{2}+2j-7)-(3j+2)[/tex]

[tex]\textsf{The negative sign on the left side of the parentheses is the same as -1. Turn terms}[/tex]

[tex]\textsf{into their opposite value.}[/tex]

[tex]\tt -(5j^{2}+2j-7) \rightarrow (-1 \times 5j^{2})+(-1\times2j)-(-1\times-7)[/tex]

[tex]\tt -(3j+2) \rightarrow (-1 \times3j) + (-1 \times 2)[/tex]

[tex]\underline{\textsf{After Simplifying;}}[/tex]

[tex]\tt -5j^{2}-2j+7-3j-2[/tex]

[tex]\underline{\textsf{Combine All Like Terms;}}[/tex]

[tex]\tt -5j^{2}\boxed{-2j}+7\boxed{-3j}-2[/tex]

[tex]\tt -5j^{2}-5j\boxed{+7}\boxed{-2}[/tex]

[tex]\large\tt\boxed{D. \ \tt -5j^{2}-5j+5}[/tex]

Answer:

Height of Cara at the end of the Third grade is 51 inches.

Step-by-step explanation:

Given:

Height of Cara at the start of second grade = 44 inches

In second grade she grew = 3 inches.

Hence height of Cara at the end of the second grade will be equal to sum of Height of Cara at the start of second grade and height she grew in second grade.

Framing the equation we get;

height of Cara at the end of the second grade = 44 + 4 = 48 inches

Also Given:

Height she grew in third grade = 3 inches

We need to find Height of Cara at end of third grade.

Hence height of Cara at the end of the Third grade will be equal to sum of Height of Cara at the end of second grade and height she grew in third grade.

Framing in equation form we get;

Height of Cara at the end of the Third grade = 48 + 3 = 51 inches

Hence Height of Cara at the end of the Third grade is 51 inches.

Answer:

51 inches

Step-by-step explanation:

44 + 4 + 3= 51

Answer:

Option a - [tex]xy^2+5[/tex]

Step-by-step explanation:

Given : Polynomial [tex]x^3y^2+8xy^2+5x^2+40[/tex]

To find : Select one of the factors of polynomial ?

Solution :

The polynomial  [tex]x^3y^2+8xy^2+5x^2+40[/tex]

We factor of above polynomial by taking common terms,

[tex]xy^2(x^2+8)+5(x^2+8)[/tex]

[tex](xy^2+5)(x^2+8)[/tex]

From the given options,

[tex]xy^2+5[/tex] is one of the factors of polynomial.

Therefore, option a is correct.

Answer:

As x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function [tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex].

Therefore, x = -5, x = 2 and y = 3 is the right option.

Step-by-step explanation:

As the given function is

[tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex]

Determining Vertical Asymptote:

The line x = L is a vertical asymptote of the function if if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

Such as

[tex]x^{2} +3x -10 = 0[/tex]

[tex](x-2)(x-5)=0[/tex]

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

x=−5 , check:

[tex]\lim_{x \to -5^{+}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = -\infty[/tex]

Since, the limit is infinite, then x = -5 is a vertical asymptote.

x = 2, check:

[tex]\lim_{x \to 2^{+}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = -\infty[/tex]

Since the limit is infinite, then x = 2 is a vertical asymptote.

Determining Horizontal Asymptote:

Line y=L is a horizontal asymptote of the function y = f(x), if either

[tex]\lim_{x \to \infty^{}}{f(x)=L}[/tex] or [tex]\lim_{x \to -\infty^{}}{f(x)=L},[/tex] and L is finite.

Calculating the limits:

[tex]\lim_{x \to \infty^{}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = 3[/tex]

[tex]\lim_{x \to -\infty^{}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = 3[/tex]

Thus, the horizontal asymptote is y=3.

So, x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function [tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex].

Therefore, x = -5, x = 2 and y = 3 is the right option.

Keywords: asymptote, vertical asymptote, horizontal asymptote, equation

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I believe the answer is a.

Answer:

A. The Long family paid $2.63 too little for their purchases.

Step-by-step explanation:

We have been given that the Long family spent $38.62 for school supplies and $215.78 for new school clothes. They paid 6.8% sales tax on their purchases.

First of all, we will add both amounts as:

[tex]\$38.62+$215.78=\$254.40[/tex]

Now, we will find 6.8% of 254.40.

[tex]\text{Amount of tax paid}=\$254.40\times \frac{6.8}{100}[/tex]

[tex]\text{Amount of tax paid}=\$254.40\times0.068[/tex]

[tex]\text{Amount of tax paid}=\$17.2992[/tex]

Upon adding $254.40 and $17.2992, we will get total amount paid by Long family.

[tex]\text{Total amount paid by Long family}=\$254.40+\$17.2992[/tex]

[tex]\text{Total amount paid by Long family}=\$271.6992[/tex]

Now, we will subtract $271.6992 from $269.07:

[tex]\$269.07-\$271.6992[/tex]

[tex]-\$2.6292\approx -\$2.63[/tex]

Since the long family paid $2.63 less than actual amount, therefore, the Long family paid $2.63 too little for their purchases and option A is the correct choice.

Answer:

A

Step-by-step explanation:

Answer:

  maybe

Step-by-step explanation:

If p is prime, then answer is NO. If p is not prime, the answer is YES.

__

Some positive integers are prime; some are not. We need to know more about p before we can give a better answer than this.

The rate of change of the function is -35.7

Step-by-step explanation:

The rate of change of a function [tex]f(x)[/tex] between two points [tex]x_1[/tex] and [tex]x_2[/tex] is given by the ratio between the increment of the function itself and the increment of the x-variable:

[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

The function of this problem is

[tex]f(x)=480 (0.3)^x[/tex]

For [tex]x_1=1[/tex], the value of the function is

[tex]f(1)=480(0.3)^1=144[/tex]

For [tex]x_2=5[/tex], the value of the function is

[tex]f(5)=480(0.3)^5=1.2[/tex]

Therefore, the rate of change of the function is

[tex]m=\frac{f(5)-f(1)}{5-1}=\frac{1.2-144}{5-1}=-35.7[/tex]

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Test hypothesis :

[tex]H_0 : \mu =5\\\\ H_a: \mu >5[/tex]

Since alternative hypothesis is right-tailed and population standard deviation is known σ = 1 , so we perform a right-tailed  z-test.

Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

, where [tex]\overline{x}[/tex] = sample mean

[tex]\mu[/tex] = population mean

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

n= Sample size

Substitute values, we get

[tex]z=\dfrac{ 5.3-5}{\dfrac{1}{\sqrt{500}}}[/tex]

[tex]z=\dfrac{ 0.3}{0.04472135955}\approx6.7[/tex]

Critical value for 0.01 significance level in z-table is 2.326.

Decision : Test statistic (6.7)> Critical value ( 2.326), it means we reject that null hypothesis.

i.e. [tex]H_a[/tex] is accepted.

We conclude that there is sufficient evidence that the mean time to approval is actually longer than advertised.

Answer:

e = 4796

Step-by-step explanation:

given,

mean of five distinct positive number = 1000

median of the number = 100

100 is median means two number will be less than 100 and two number will be greater than 100.

let five number be

a , b, c, d, e

'e' should be the largest number

As 100 is median so 'c' = 100.

'a' and 'b' should be as small as possible and d should be the number nearest to 100.

As all the number are distinct so the least number be equal to 1 and 2

now d will be equal to 101 (nearest to 100)

now,

sum of the five number = 5 x 1000 = 5000

a + b + c + d + e = 5000

1 + 2 + 100 + 101 + e = 5000

e = 5000 - 204

e = 4796

hence, the largest number will be equal to e = 4796

The required width of the mat around the photo is given as 3 inches.

Given that,
The combined area of the photo and mat needs to be 224 square inches. The equation that represents the combined area is (2w+8)(2w+10)=224, where w represents the width of the mat around the photo.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
(2w + 8)(2w + 10) = 224
4w² + 16w + 20w + 80 = 224
4w² + 36w - 144 = 0
w² + 9w - 36 = 0
[w -3][w + 12] = 0
w = 3 and w = -12
Since the measure of width cannot be negative so -12 can be neglected.
w = 3 preferred,

Thus, the required width of the mat around the photo is given as 3 inches.

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Answer:

The value of p would be [tex]\frac{1}{50}[/tex]

Step-by-step explanation:

Given,

[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right )[/tex]

[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{49} \right )\left ( 1 - \frac{1}{50} \right )[/tex]

[tex]p=\frac{2-1}{2}.\frac{3-1}{3}.\frac{4-1}{4}......\frac{49-1}{49}.\frac{50-1}{50}[/tex]

[tex]p=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{48}{49}.\frac{49}{50}[/tex]

[tex]p=\frac{1.2.3.4.........48.49}{2.3.4........49.50}[/tex]

[tex]p=\frac{1}{50}[/tex]

Hence, the value of p is 1/50.

P is the product, indicated above, of all the numbers of the form , where k is an integer from 2 to 50, inclusive. Value of P is 2) 1/50.

To find the value of [tex]\( P \)[/tex], we can simply multiply all the terms together:

[tex]\[ P = \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \ldots \left(1 - \frac{1}{50}\right) \][/tex]

We start with [tex]\( k = 50 \)[/tex]. and go up to [tex]\( k = 50 \)[/tex]. Let's calculate it:

[tex]\[ P = \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \ldots \left(1 - \frac{1}{50}\right) \][/tex]

[tex]\[ P = \left(\frac{1}{2}\right)\left(\frac{2}{3}\right)\left(\frac{3}{4}\right) \ldots \left(\frac{49}{50}\right) \][/tex]

[tex]\[ P = \frac{1}{50} \][/tex]

So, the value of [tex]\( P \) is \( \frac{1}{50} \).[/tex]

[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right[/tex]) P is the product, indicated above, of all the numbers of the form [tex]1 – \frac{1}{k}[/tex], where k is an integer from 2 to 50, inclusive. the value of P is  [tex]\( P \) is \( \frac{1}{50} \).[/tex]

Question:-

[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right )[/tex]

P is the product, indicated above, of all the numbers of the form [tex]1 – \frac{1}{k}[/tex], where k is an integer from 2 to 50, inclusive. What is the value of P ?

1.) [tex]\frac{1}{100}[/tex]

2.) [tex]\frac{1}{50}[/tex]

3.) [tex]\frac{1}{49}[/tex]

4.) [tex]\frac{49}{50}[/tex]

5.)[tex]\frac{99}{100}[/tex]

Answer:

6 dresses

Step-by-step explanation:

Given: sales price is $d

           Regular price is 3 times of sales price

           Janine has money to buy 2 dresses at regular price.

Now, finding the number of dresses Janine can buy at the sales price, if sale price is d

Regular price= [tex]3\times d= 3d[/tex]

Janine has total money= [tex]3d\times 2= 6d[/tex] (∵ regular price is 3d)

∴ Number of dresses bought by Janine= [tex]\frac{Total\ money}{sale\ price\ of\ one\ dress}[/tex]

⇒ Number of dresses bought by Janine= [tex]\frac{6d}{d} = 6\ dresses[/tex]

∴ Number of dresses bought by Janine is 6.

Answer:

Option a) 50% of output expected to be less than or equal to the mean.

Step-by-step explanation:

We are given the following in the question:

The output of a process is stable and normally distributed.

Mean = 23.5

We have to find the percentage of output expected to be less than or equal to the mean.

Mean of a normal distribution.

Thus, by property of normal distribution 50% of output expected to be less than or equal to the mean.

The distance between the two kites is approximately 380 ft.

To find the distance between the two kites, we can use the law of cosines. Let's call the distance between the two kites as 'd'. We can use the equation:

d^2 = 380^2 + 420^2 - 2 * 380 * 420 * cos(30)

By plugging in the values, we get:

d^2 = 144400

Taking the square root of both sides, we find:

d = 380 ft

So, the distance between the two kites is approximately 380 ft.

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Answer: Median

Step-by-step explanation:

Answer:the price of one large gift is $60

Step-by-step explanation:

Let x represent the cost of one large gift.

Melanie bought 4 large gifts and 2 small gifts. Since each small gift costs $10, it means that the total amount that Melanie spent is

4x + 2×10 = 4x + 20

Mary bought 1 large gift and 20 small gifts. It means that the total amount that Mary spent is

x + 20×10 = x + 200

They both spent the same amount of money. This means that

4x + 20 = x + 200

4x - x = 200 - 20

3x = 180

x = 60

To find the price of one large gift, we compare the total amount spent by Melanie and Mary. By setting up an equation and solving for the price of one large gift, we find that it is $60.

To find the price of one large gift, we need to calculate the total amount spent on gifts by both Melanie and Mary and divide it by the total number of large gifts they bought. Melanie bought 4 large gifts and 2 small gifts, while Mary bought 1 large gift and 20 small gifts. Let's assume the price of one large gift is x.

The total amount spent by Melanie can be calculated as (4x + 2*10), since each small gift costs $10. The total amount spent by Mary can be calculated as (x + 20*10). Since both of them spent the same amount of money, we can set up the equation: 4x + 2*10 = x + 20*10.

Simplifying the equation, we get 4x + 20 = x + 200. Subtracting x from both sides, we get 3x + 20 = 200. Subtracting 20 from both sides, we get 3x = 180. Dividing both sides by 3, we find that x = 60. Therefore, the price of one large gift is $60.

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Answer:

d) $18,390

Step-by-step explanation:

Let X be the amount of money he deposited on the first year of his study.

The question says that he earns 6% on his investment without specifying the investment return time. However, normally it's annually, so let's assume his earning is 6% per annum.

Given that he did not make any withdrawal until the end of the first year, in 2nd year, he'll get the earning of his investment minus 10,000 to pay for his first year study

2nd year Y = X(1.06 ) - 10000

The same goes with 3rd year

3rd year Z = Y(1.06) - 10000

In worst case scenario, let's assume all of the money is used up at the end of third year

Z = 0

Y(1.06) - 10000 = 0

Substitute the first year into the equation:

Y(1.06) - 10000 = 0

(X(1.06)-10000)1.06 -10000 = 0

(1.06^2)X -1.06(10000) - 10000 = 0

X = (10000+10600)/1.06^2 = 18333.92

So the minimum deposit he needs to make to survive for the whole 3 years is $18333.92.

From the answer selection, the nearest value is d) $18,390