A truck driver who covers the interstate in 4 1/2hours traveling at the posted speed of 55 mph. If the speed limit is raised to 65 mph, how much time will the same trip require

To estimate the percentage of seniors attending college with a 4% margin of error and 90% confidence, a sample size of 424 is needed. For constructing a confidence interval and hypothesis testing about military enlistment, various statistical formulas are applied, including adjustments for undecided responses.

To estimate the percentage of this year’s seniors planning to attend college with a margin of error no greater than 4% and 90% confidence, we use the formula for determining sample size for a proportion, which is n = (Z^2 * p * (1-p)) / E^2, where Z is the Z-score corresponding to the confidence level, p is the estimated proportion, and E is the margin of error. With a 90% confidence level, the Z-score is approximately 1.645, and assuming we don't have a preliminary estimate, we use p = 0.5 for maximum variability, thus maximizing the required sample size.

To calculate: n = (1.645^2 * 0.5 * 0.5) / 0.04^2 = 423.3. Therefore, a sample size of 424 is required to achieve the desired margin of error and confidence level.

For the second question regarding the confidence interval for the percentage of seniors planning to go to college this year, the total sample size is the sum of students from all categories, which is 500. The proportion planning to go to college is 289/500. Using a formula for constructing a confidence interval for a proportion, C.I. = p ± (Z*sqrt(p(1-p)/n)), we can find our interval.

Testing the hypothesis regarding military enlistment involves setting up a null hypothesis (H0: p = 0.045) and an alternative hypothesis (H1: p ≠ 0.045), where p is the proportion of high school seniors enlisting in the military. The test statistic is calculated using a formula, and the P-value associated with this statistic is compared against the alpha level to decide whether to reject H0.

If considering undecided or no response students as potential enlistees changes this calculation significantly, we reassess by including an adjusted number of potential enlistees.

The time for the fastest 10 % is less than 89.4 seconds

Here's how to find the qualifying task times:

Calculate the z-score for the 10th percentile:

A z-score represents the number of standard deviations a specific point is away from the mean. In this case, we want the z-score for the lower 10th percentile, which can be found using a z-score table or online calculators. The approximate z-score for the 10th percentile is -1.28.

Translate the z-score to task time:

We know the z-score for the 10th percentile (-1.28) and the standard deviation (20 seconds). We can use the formula to find the corresponding task time (t):

t = mean + (z-score) * standard deviation

t = 115 seconds + (-1.28) * 20 seconds

t ≈ 89.4 seconds

Therefore, task times less than 89.4 seconds qualify individuals for advanced training, as they fall within the lower 10th percentile of the normal distribution.

Complete question:

The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 115 sec and a standard deviation of 20 sec. The fastest 10% are to be given advanced training. What task times qualify individuals for such training? (Round the answer to one decimal place.)

Answer:

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^t

Where

y represents the population, t years after 2010.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 2.13 × 10^6

r = 2.4% = 2.4/100 = 0.024

Therefore, the equation that you can use to predict the population for the number of years after 2010 is

y = 2.13 × 10^6(1 + 0.024)^t

y = 2.13 × 10^6(1.024)^t

Answer:

$118,791.2985

Step-by-step explanation:

Given that,

A = 160,000

T = 18 - 8 = 10 years

Rate = 3%

since it is semi annual, n = 2

A = P ( 1 + R/2) ∧ 2T

160000 = P ( 1 + 3/2*100) ∧ 2 * 10

160000 = P ( 1 + 3/200) ∧20

160000 = P( 1 + 0.015) ∧20

160000 = P(1.015)∧20

P= 160000/ (1.015)∧20

P = 160000/ 1.3469

= $118,791.2985

Answer:

sampling error i think

Step-by-step explanation:

Answer:

[tex]A(x)=x(\sqrt{2500-x^{2} } )[/tex] is the area expressed as function of x,

and x: >0, <50 is the domain of the function.

Step-by-step explanation:

Draw an appropriate figure and then express the area of the rectangle as a function of x.

We know that the diagonal of a rectangle inscribed in a circle, will be equal to the diameter of the circle. 50 feet

let w = the width of the rectangle

therefore

[tex]x^2 + w^2 = 50^2\\w^2 = 2500 - x^2\\w = \sqrt{2500-x^{2} }[/tex]

recall

Area = x*w

replace w

[tex]A(x)=x(\sqrt{2500-x^{2} } )[/tex] is the area expressed as function of x

b)state the domain of the function

x: >0, <50

To find the area of the rectangle inscribed in a circle, we can use the Pythagorean theorem to find the length of the rectangle. Then, we can calculate the area by multiplying the width and length. The function that represents the area of the rectangle as a function of x is A(x) = x * sqrt(2500 - x^2), and the domain is x >= 0 and x <= 50.

To find the area of the rectangle, we need to consider that the diagonal of the rectangle is equal to the diameter of the circle, which is twice the radius. Therefore, the diagonal measures 50 feet.

We can use the Pythagorean theorem to find the length of the rectangle. Let's denote the length as y. We have:

x^2 + y^2 = 50^2

This equation represents the relationship between the width and length of the rectangle. By solving for y, we can express the length as a function of x.

Once we have the width and length of the rectangle, we can calculate the area by multiplying them:

A = x * y = x * sqrt(50^2 - x^2)

The function that represents the area of the rectangle as a function of x is A(x) = x * sqrt(2500 - x^2). The domain of this function is x >= 0 and x <= 50.

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Answer:

D

Step-by-step explanation:

Depending on the number of defects in 6th car,  we have 3 cases:

To find mean we can use the sum of numbers given (= 36) and add either 3, 7, or 12 to it and then divide by 6 (number of cars).

(36 + 3) /6 = 39/6 = 6.5 (== median above)

(36 + 7) /6 = 43/6 = 7.1 (does not equal median above)

(36 + 12) /6 = 48/6 = 8 (== median above)

Answer: D (I and III only).

Answer:

Pamela = 30

Jiri = 40

Step-by-step explanation:

Two equations needed:

J-10 = P

P+J = 70

Plug and solve:

(J-10) + J = 70

2J - 10 =70

2J = 80

J = 40

40 - 10 = P

P=30

Answer:

30

Step-by-step explanation:

Let Jiri's age be x

Let Pamela's age be (x - 10)

The sum of their ages becomes

x + (x - 10) = 70

x + x - 10 = 70

2x - 10 = 70

2x =70+10

2x = 80

x = 40

Therefore, it means that Jiri's age is 40

Pamela's age is 40-10= 30

Answer:

756 is a reasonable estimate because the proportion of the sample whose favorite pizza is pepperoni is about 27 %

Step-by-step explanation:

given data

random sample = 150 people

favorite pepperoni pizza = 40

total of residents = 2800

number of residents favorite pizza = 750

solution

we get here first Proportion favorite pizza that is

Proportion = [tex]\frac{40}{150}[/tex]

Proportion = 0.27 = 27%

and now we get 27% of total of residents that is = 27% × 2800  

= 756

so we can say  756 is a reasonable estimate because here proportion of an sample whose favorite pizza are pepperoni pizza about 27 %

The probability of rolling a sum of 5 when rolling two fair, six-sided dice is 1/18.

The probability that the sum of the two rolls is 5 can be found by considering the possible outcomes. There are a total of 36 equally likely outcomes when rolling two fair, six-sided dice.

Out of these, the prime sums are 5, 7, 11, and 17. The sum of 5 can only be obtained by rolling a 1 and a 4 or a 2 and
a 3. Since each die has 6 sides, the probability of rolling a 1 and a 4 is 1/6 × 1/6 = 1/36.

Similarly, the probability of rolling a 2 and a 3 is also 1/36. Therefore, the overall probability of rolling a sum of 5 is
1/36 + 1/36 = 2/36 = 1/18.

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The accumulator pattern for calculating the sum of numbers using variables number and total in programming is correctly represented by 'total = total + number'. This demonstrates the commutative property of addition, indicating that 'total += number' updates the running total with the new number.

The correct representation of an accumulator to calculate the sum of numbers in a programming context, when the current number is stored in a variable number and the total is stored in a variable total, would be to update the total by adding the number to it. This would look like total = total + number or in a more simplified form as total += number.

Addition in programming is similar to addition in mathematics; it's commutative and associative. This means that the order of adding numbers does not change the sum, as represented by A + B = B + A. Whether we are dealing with numbers, such as integers or real numbers, or other structures like vectors, the concept of addition remains fundamentally the same.

The accumulator pattern is commonly used to build a sum or total by updating a running total each time a new value is added, which is also illustrated by the expression total += number. This pattern is essential in various programming tasks, such as summing a series of numbers in a loop.

Answer:

(a) P(X = 0) = 1/3

(b) P(X = 1) = 2/9

(c) P(X = −2) = 1/9

(d) P(X = 3) = 0

(a) P(Y = 0) = 0

(b) P(Y = 1) = 1/3

(c) P(Y = 2) = 1/3

Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 : Result on 1st die.

- Random Variable X_2: Result on 2nd die.

- Random Variable X = X_2 - X_1.

Solution:

- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }

- The corresponding probabilities for each outcome are:

                 ( X = -2 ):  { X_2 = 1 , X_1 = 3 }  

                P ( X = -2 ):  P ( X_2 = 1 ) * P ( X_1 = 3 )  

                                :  ( 1 / 3 ) * ( 1 / 3 )  

                                : ( 1 / 9 )    

                ( X = -1 ):  { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }

                P ( X = -1 ):  P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)

                                :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )        

 ( X = 0 ):  { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } +  { X_2 = 3 , X_1 = 3 }

               P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )

                                :  3*( 1 / 3 ) * ( 1 / 3 )

                                : ( 3 / 9 ) = ( 1 / 3 )        

                  ( X = 1 ):  { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }

               P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )

                                : 2* ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )

                  ( X = 2 ):  { X_2 = 1 , X_1 = 3 }

                 P ( X = 2 ):  P ( X_2 = 3 ) * P ( X_1 = 1 )  

                                   :  ( 1 / 3 ) * ( 1 / 3 )  

                                   : ( 1 / 9 )                  

- The distribution Y = X_2,

                         P(Y=0) = 0

                         P(Y=1) =  1/3

                         P(Y=2) = 1/ 3

- The probability for each number of 3 sided die is same = 1 / 3.

In this exercise we have to use the knowledge of probability to calculate the chance of an event to occur, so:

A) P(X = 0) = 1/3

B) P(X = 1) = 2/9

C) P(X = −2) = 1/9

D) P(X = 3) = 0

A) P(Y = 0) = 0

B) P(Y = 1) = 1/3

C) P(Y = 2) = 1/3

organizing the following information given in the text we have that:

Then calculating the probability we find that:

A)  For P(X = 0) we have

[tex]( X = -2 ): { X_2 = 1 , X_1 = 3 } \\P ( X = -2 ): P ( X_2 = 1 ) * P ( X_1 = 3 ) \\ : ( 1 / 3 ) * ( 1 / 3 ) \\ : ( 1 / 9 )[/tex]

B)   For  P(X = 1) er have:

[tex]( X = -1 ): { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }\\ P ( X = -1 ): P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)\\ : ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )\\ : ( 2 / 9 )[/tex]  

C) For  P(X = −2)  we have:

[tex]( X = 0 ): { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } + { X_2 = 3 , X_1 = 3 }\\ P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )\\ : 3*( 1 / 3 ) * ( 1 / 3 )\\ : ( 3 / 9 ) = ( 1 / 3 )[/tex]    

D) For P(X = 3), we have:

[tex]( X = 1 ): { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }\\ P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )\\ : 2* ( 1 / 3 ) * ( 1 / 3 )\\ : ( 2 / 9 )\\ ( X = 2 ): { X_2 = 1 , X_1 = 3 }\\ P ( X = 2 ): P ( X_2 = 3 ) * P ( X_1 = 1 ) \\ : ( 1 / 3 ) * ( 1 / 3 ) \\ : ( 1 / 9 )[/tex]            

In this next case we have to take into account that the number will be the probability of falling 3, that is:

A) P(Y=0) = 0

B) P(Y=1) =  1/3

C) P(Y=2) = 1/ 3

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Answer:

(1) The expected number of people who would have consumed alcoholic beverages is 34.9.

(2) The standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3) It is surprising that there were 45 or more people who have consumed alcoholic beverages.

Step-by-step explanation:

Let X = number of adults between 18 to 20 years consumed alcoholic beverages in 2008.

The probability of the random variable X is, p = 0.697.

A random sample of n = 50 adults in the age group 18 - 20 years is selected.

An adult, in the age group 18 - 20 years, consuming alcohol is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 50 and p = 0.697.

The probability mass function of a Binomial random variable X is:

[tex]P(X=x)={50\choose x}0.697^{x}(1-0.697)^{50-x};\ x=0,1,2,3...[/tex]

(1)

Compute the expected value of X as follows:

[tex]E(X)=np\\=50\times 0.697\\=34.85\\\approx34.9[/tex]

Thus, the expected number of people who would have consumed alcoholic beverages is 34.9.

(2)

Compute the standard deviation of X as follows:

[tex]SD(X)=\sqrt{np(1-p)}=\sqrt{50\times 0.697\times (1-0.697)}=10.55955\approx10.56[/tex]

Thus, the standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3)

Compute the probability of X ≥ 45 as follows:

P (X ≥ 45) = P (X = 45) + P (X = 46) + ... + P (X = 50)

                [tex]=\sum\limits^{50}_{x=45} {50\choose x}0.697^{x}(1-0.697)^{50-x}\\=0.0005+0.0001+0.00002+0.000003+0+0\\=0.000623\\\approx0.0006[/tex]

The probability that 45 or more have consumed alcoholic beverages is 0.0006.

An unusual or surprising event is an event that has a very low probability of success, i.e. p < 0.05.

The probability of 45 or more have consumed alcoholic beverages is 0.0006. This probability value is very small.

Thus, it is surprising that there were 45 or more people who have consumed alcoholic beverages.

THE ANSWER FOR CUP A IS 660 divided by 157

the answer to cup b is 660 divided by 628.319

brainliest plz

Answer:

(1) 3628800

(2) 0.00000028

Step-by-step explanation:

We are given that a puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column.

(1) If we make the matches randomly, number of possible matches are given by = 10!

Because after making each match the number will decrease so,

Number of possible matches = 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 .

(2) The probability all 10 of your matches are correct is given by;

      Number of outcomes in favor ÷ Total number of matches

So, there will be only 1 case when all 10 of the matches are correct.

Therefore, required probability = [tex]\frac{1}{10!}[/tex] = [tex]\frac{1}{3628800}[/tex] = 0.00000028 .

Answer:

Option C) 115 / square of 100 = 11.5

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 496

Standard Deviation, σ = 115

Sample size, n = 100

a) Mean of scores

[tex]\bar{x} = \mu = 496[/tex]

b) The standard Deviation

[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{115}{\sqrt{100}} = \dfarc{115}{10} = 11.5[/tex]

Thus, the correct answer is

Option C) 115 / square of 100 = 11.5

Answer:

Option C.  115 / square of 100 = 11.5.

Step-by-step explanation:

We are given that Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 496 and standard deviation 115.

An SRS of 100 students is chosen and average their SAT reading scores.

The z score normal probability is given by;

  Z = [tex]\frac{xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

So, the mean of the average scores will be close to [tex]\frac{\sigma}{\sqrt{n} }[/tex] i.e.;

      = 115 / square root of 100 = [tex]\frac{115}{\sqrt{100} }[/tex] = 115/10 = 11.5

Answer:

[tex]\frac{9}{4}[/tex]

Step-by-step explanation:

Given

x² + 3x - 13 = 0 ( add 13 to both sides )

x² + 3x = 13

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2([tex]\frac{3}{2}[/tex] )x + ([tex]\frac{3}{2}[/tex] )² = 13 + ([tex]\frac{3}{2}[/tex] )², that is

x² + 2([tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] = 13 + [tex]\frac{9}{4}[/tex]

(x + [tex]\frac{3}{2}[/tex] )² = [tex]\frac{61}{4}[/tex]

The required number to be added to complete the square is [tex]\frac{9}{4}[/tex]

Hence, required number to be added to complete the square is 9/4

A quadratic equation is any equation that can be rewritten in standard form as ax2+bx+c=0 in algebra. When x is an unknown and a, b, and c are known numbers, and an is less than 0. Because there is no ax2 term when a = 0, the equation is linear rather than quadratic.

Given equation =x² + 3x - 13 = 0 ( add 13 to both sides )

=x² + 3x = 13

using complete the square and add ( half the coefficient of the x- term )² to both sides

=x² + 2(3/2 )x + ( 3/2)² = 13 + (3/2 )², that is

=x² + 2(3/2 )x +  = 13 + 9/4

=(x + 3/2 )² = 61/4

The required number to be added to complete the square is 9/4

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Answer:

2 workers

Step-by-step explanation:

Here is additional information for your question:

The questions below deal with the Gizmo Company, which has the following production function.

# Workers # Produce

0 0

1 10

2 19

3 26

4 31

5 34

If the real wage is equal to 8 widgets and only an integer number of workers can be hired the Gizmo company should hire?

My answer:

2 workers. (where MPL is less than real wage)

Answer:

22 rows and 22 flags are needed

Step-by-step explanation:

Total number of vendors = 88

Existing number of rows and flags= 4

Number of rows and flags needed= 88/4 =22

Answer:

4rows and 16flags

Step-by-step explanation:

Since there were 88 vendors at the craft fair and 4flags on each rows. To set up equal number of vendors on each row, we will use the expression;

Number of vendors per row = Total number of vendors/total number of flags per row = 88/4 = 22 vendors

If there are 22 vendors in a rows and there are 88vendors in total, the total of rows will be;

Total number of vendors/number of vendors per row

= 88/22

= 4 rows

If there are four rows in total and 4flags in each row, the total of flags needed will be;

Total number of row × total flag per row

= 4×4

= 16flags

This shows that there are 4rows and 16flags were needed.

Answer:

5%

Step-by-step explanation:

According to fisher equation

Nominal rate = Real rate + Inflation

N = R + I

N is calculated when there is no inflation and for the current year = 8%

The Real rate is calculated from the base year

Real rate is consider "Inflation factor" and R is unknown

Inflation rate (I) = 3%

Hence, N = R + I

8 = R + 3

R = 8 - 3

R = 5%

Answer:

  a. 90°

  b. 180°

  c. 180°

Step-by-step explanation:

For these problems there is a bit of a shortcut you can take. Each figure is entirely within one quadrant, and the rotation is said to be by 90° (one quadrant), 180° (two quadrants), or 270° (three quadrants) clockwise.

a. The image is in the adjacent clockwise quadrant, so rotation is 90°.

b, c. The image is in the diagonally opposite quadrant, so rotation is 180°.

Answer:

Part 1) [tex]m\angle 1=39^o[/tex]

Part 2) [tex]m\angle 3=51^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

Part 1) Find the measure of angle 1

we know that

The longer diagonal of a kite bisects the kite into two equal parts

That means

[tex]m\angle 1=39^o[/tex]

In this problem the longer diagonal is the segment AC

Part 2) Find the measure of angle 3

we know that

The intersection of the diagonals of a kite form 90 degrees.

That means ----> The triangle ADO (O is the intersection point both diagonals) is a right triangle

so

[tex]39^o+m\angle 3=90^o[/tex] ----> by complementary angles in a right triangle

[tex]m\angle 3=90^o-39^o=51^o[/tex]

Answer:

[tex]\sqrt{29}\ units[/tex]

Step-by-step explanation:

we know that

In a right triangle

Applying the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse (the greater side)

a and b are the legs (perpendicular sides)

In this problem we have

[tex]a=2\ units\\b=5\ units[/tex]

substitute

[tex]c^2=2^2+5^2[/tex]

[tex]c^2=29[/tex]

[tex]c=\sqrt{29}\ units[/tex]

Answer:

Supply curve vs Aggregate Supply

Step-by-step explanation:

- Supply express a direct relationship between what producers supply and how that relationship affects the price of a specific product or service. Hence, expresses a linear increase - or a constant slope

- Aggregate supply are the total supply in an economy at a particular period of time and a particular price threshold. Aggregate supply is an economy's gross domestic product (GDP), the total amount a nation produces and sells.

-  Aggregate supply convey how much firms are willing to produce at a specific price point.

- Aggregate supply is a response to increasing prices that drive firms to utilize more inputs to produce more output. The incentive is that if the price of inputs remains the same but if the price of outputs increase, the firm will generate larger profits and margins by producing and selling more. The aggregate supply curve is represented by a curve that slopes upward, which indicates that as the price per unit goes up, a firm will supply more. Increasing slope - Not constant.

- The supply curve eventually becomes vertical, indicating that at a certain price point a firm cannot produce anymore, as they are limited by certain inputs, e.g. number of employees and number of factories.

Answer:

Total length of the Nylon rope will be 5.8 feet.

Step-by-step explanation:

Given:

Height of the tent = 5 ft

ground Distance from stake to tent = 3 ft

We need to find the Total length of the nylon rope.

Solution:

Now we can say that the total length of the nylon rope, the height of the tent, the ground distance from the stake to the tent, forms a right angle triangle.

From above we can see that;

the height of the tent, the ground distance from the stake to the tent are the two legs of the right angled triangle.

While the Total length of the nylon rope is the hypotenuse.

Now using Pythagoras theorem we get;

[tex]h^2=l_1^2+l_2^2[/tex]

[tex]l_1[/tex] ⇒ the height of the tent

[tex]l_2[/tex] ⇒  the ground distance from the stake to the tent

[tex]h[/tex] ⇒ the Total length of the nylon rope

substituting the values we get;

[tex]h^2=5^2+3^2\\\\h^2=25+9\\\\h^2=34[/tex]

Taking square root on both side we get;

[tex]\sqrt{h^2} =\sqrt{34} \\\\h=5.8\ ft[/tex]

Hence Total length of the Nylon rope will be 5.8 feet.

Answer:

Just find the hypotenuse by doing a^2 + B^2 = C^2

Step-by-step explanation:

Answer:

3x-7y=-6

Step-by-step explanation:

Answer:

28 minutes spent in washing the dishes.

Step-by-step explanation:

Given the table

Chore             time in minutes

Sweeping           42

Dishes                  ?

Amanda spent a total of 70 minutes competing her chores this week

Total of 70 minutes spent

42 minutes spent in sweeping . to find the number of minutes Amanda spent in washing the dishes , subtract 42 minutes from the total time spent

let x be the number of minutes spent washing the dishes

[tex]42+x=70[/tex]

To solve for x , subtract 42 from both sides

[tex]42+x=70\\x= 70-42\\x=28[/tex]

28 minutes spent in washing the dishes.

Final answer:

The set of ordered pairs that correctly satisfies the equation y = 1/8x + 11 is (0,11) (8,12) (16,13). This is determined by substituting the x-values into the equation to check if the y-values correspond.

Explanation:

The question is asking which set of ordered pairs satisfies the equation y = 1/8x + 11. To determine the correct set, we will plug in the x-values from each ordered pair into the equation and see if the resulting y-value matches the one provided in the ordered pair. Let's examine each set:

(0,11) - If we plug in x=0, we get y=1/8*0+11=11. This matches the ordered pair, so (0,11) is correct.

(5,12) - With x=5, y becomes 1/8*5+11=11.625. This does not match the ordered pair (5,12), so this set is incorrect.

(7,13) - With x=7, y is 1/8*7+11=11.875. This does not match the ordered pair (7,13), so this set is also incorrect.

(8,12) - With x=8, y is 1/8*8+11=12. This matches the ordered pair, so (8,12) is correct.

(16,13) - With x=16, y is 1/8*16+11=13. This matches the ordered pair, so (16,13) is correct.

(6,12) - With x=6, y is 1/8*6+11=11.75. This does not match the ordered pair (6,12), so this set is incorrect.

(8,13) - Again, with x=8, y should be 12, not 13, so the ordered pair (8,13) is incorrect.

The only set with all matching ordered pairs for the equation y = 1/8x + 11 is (0,11) (8,12) (16,13).

Answer: the length of the kite string is 183.6 feet

Step-by-step explanation:

The string of the kite forms an angle of 57° with the ground thus, a right angle triangle is formed. Richard's distance from the point on the ground directly below the kite represents the adjacent side of the right angle triangle. The length of the kite, h represents the hypotenuse of the right angle triangle. To determine h, we would apply the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 57 = 100/h

h = 100/Cos57

h = 100 /0.5446

h = 183.6 feet

Answer:

it was B

Step-by-step explanation:

The algorithm employing "Nearest Neighbour" to determine one of the cheaper routes to visit every city and get back home again would be:

B). ATL-CHI-BOS-DEN-ATL

Thus, option B is the correct answer.

Learn more about "Algorithm" here

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