A suit is sold for $68 while marked at $80. What
is the rate of discount?

Answer:

| -3 | = 3

Step-by-step explanation:

minus is removed

Answer:

For the 9% she invested $2,300

For the 10% she invested $2,500

Step-by-step explanation:

Let the amount invested be $x and $y in both cases respectively

Since the total invested is $4,800

This means that;

x + y = 4800 ••••••••••••(i)

Now let’s have a look at the interests.

For the 9%

Interest would be 9/100 * amount invested

= 9/100 * x = 9x/100

For the 10%, interest would be

10/100 * y = 10y/100

Adding both will give a total of 457

9x/100 + 10y/100 = 457

multiply through by 100

9x + 10y = 45700 •••••••• (ii)

From equation i, we can write x = 4800 - y

we can substitute this into the second equation

9(4800-y) + 10y = 45700

43200 -9y + 10y = 45,700

43200 + y = 45,700

y = 45,700-43,200 = $2,500

Recall

x = 4800 -y

so x = 4800 -2500 = 2300

Answer:

a) y = 0.55x + 75

b) $108

Step-by-step explanation:

a) to find the equation represent the sequence use the y=mx+b formula

y = total price

m = cost per mile

x = miles driven

b = flat fee

Therefore y = 0.55x+75

b) To figure out the cost of driving 60 miles you use the equation y = 0.55x + 75

y = 0.55 X 60 + 75

= 108

Therefore the cost of renting the truck and driving 60 miles is $108

The equation of the line parallel to the line is y = -4x + 10

The equation of the line perpendicular to the line is y = 1/4x +3/2

Using the point (1, 6) and (2, 2) on the line to get the slop:

Slope = 2-6/2-1

Slope = -4/1

Slope = -4

The equation is written in point slope form as y-y0 = m(x-x0)

Substitute a point and the given slope for the equation parallel to the line

y - 2 = -4(x-2)

y - 2 = -4x + 8

y+4x = 10

Hence the equation of the line parallel to the line is y = -4x + 10

The needed slope for the perpendicular line is 1/4.

Substitute a point and the given slope for the equation parallel to the line

y - 2 = 1/4(x-2)

4(y - 2) = x - 2

4y - 8 =x -2

4y = x + 6

y = 1/4x + 3/2

Hence the line perpendicular to the line is y = 1/4x + 3/2

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The following question may be like this:

write an equation of the line that passes through the given points and is perpendicular to the given line.

300 lbs = 136.078 kg.

Pounds (lbs) and kilograms (kg) are both units of measurement for weight, but they are not directly interchangeable. To convert a measurement of weight from pounds to kilograms, you will need to use a conversion factor.

1 pound is equal to 0.453592 kilograms. 300 pounds is equal to 136.078 kg. The conversion factor between pounds and kilograms is 1 lbs = 0.453592 kg.

To convert a measurement of weight from pounds to kilograms, you will multiply the number of pounds by the conversion factor of 0.453592.

For example,

if you have a measurement of 300 pounds, you would multiply 300 x 0.453592 to get 136.078 kg.

It's important to note that when measuring weight, it's important to use the same system of measurement as the requirement, as using the wrong measurements can greatly affect the outcome of the calculation. It's always good to know the conversion factors to make your calculations easier.

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(a) The probability that all the balls drawn are black is 1/11.

(b) The probability that the balls drawn are of different colors is 5/1.

To calculate this probability consider that after drawing the first ball, one less black ball in the bag and one less ball overall. The probability of drawing a black ball on the first draw is 7/22 (since there are 7 black balls out of 22 total balls).

After drawing a black ball, there will be 6 black balls left out of 21 total balls. The probability of drawing a second black ball is 6/21.

To find the probability of both events occurring probabilities together:

P(both black) = (7/22) × (6/21) = 42/462 = 1/11 (rounded to three decimal places)

Therefore, the probability that all the balls drawn are black is 1/11.

To calculate this probability consider the opposite event: that the balls are of the same color.

The probability of drawing two black balls is (7/22) × (6/21) = 1/11, as calculated above.

The probability of drawing two white balls can be calculated in a similar way. After drawing the first ball, there 15 white balls left out of 22 total balls. The probability of drawing a white ball on the first draw is 15/22

After drawing a white ball, there 14 white balls left out of 21 total balls. The probability of drawing a second white ball is 14/21.

P(both white) = (15/22) ×(14/21) = 210/462 = 5/11 (rounded to three decimal places)

Since drawing balls of different colors is the opposite event to drawing balls of the same color subtract the probability of drawing balls of the same color from 1:

P(different colors) = 1 - P(both black) - P(both white) = 1 - (1/11) - (5/11) = 5/11 (rounded to three decimal places)

Therefore, the probability that the balls drawn are of different colors is 5/11.

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functions can't be with exponents -

the correct answers are b,c,d

Answer:

These 3:

y = 2, y = 1/2x + 5, y = x

Step-by-step explanation:

Y can't be squared that would give a sideways function, that doesn't pass the vertical line test

the average waiting time cannot be determined when all five checkout lanes are being used.

To calculate the average waiting time when all five checkout lanes are being used, we can use queuing theory and the Little's Law formula.

Little's Law states that the average number of customers in a system (L) is equal to the average arrival rate (λ) multiplied by the average time a customer spends in the system (W).

L = λ * W

Given:

Number of checkout lanes (m) = 5

Average checkout time per customer (μ) = 3 minutes (since each clerk takes 3 minutes on average to checkout a customer)

Arrival rate (λ) = 70 customers per hour

First, we need to calculate the arrival rate per lane when all five lanes are being used. Since there are five lanes, the arrival rate per lane will be λ/m:

Arrival rate per lane = λ / m

= 70 customers per hour / 5 lanes

= 14 customers per hour per lane

Next, we can calculate the average time a customer spends in the system (W) using the formula:

W = 1 / (μ - λ)

where μ is the average service rate and λ is the arrival rate per lane.

W = 1 / (3 - 14)

W = 1 / (-11)

W = -1/11 (since the service rate is smaller than the arrival rate, resulting in negative waiting time)

However, negative waiting time is not meaningful in this context. It indicates that the system is not stable or the service rate is insufficient.

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Answer:

problem 2

Step-by-step explanation:

The feeding time constraint for cats can be written symbolically as:

12 minutes/day * number of cats <= 8 hours/day

The feeding time constraint for dogs can be written symbolically as:

20 minutes/day * number of dogs <= 8 hours/day

The pampering time constraint for cats can be written symbolically as:

16 minutes/day * number of cats <= 8 hours/day

The pampering time constraint for dogs can be written symbolically as:

20 minutes/day * number of dogs <= 8 hours/day

Statistical guidance should perform well in situations such as clinical trials and market research where rigorous data analysis and inference are necessary. Statistical methods provide a systematic approach to control biases, handle variability, and draw reliable conclusions, ensuring accurate decision-making and predictions based on the data.

Statistical methods are crucial in determining sample sizes, designing the study, and analyzing the data to draw valid conclusions about the effectiveness and safety of the treatment.

In this situation, statistical guidance should do well because it provides a systematic framework to control for biases, random variability, and confounding factors, ensuring robust and reliable results that can be generalized to a larger population.

One example where statistical guidance should perform well is in clinical trials for new drugs or treatments.

Another example is in market research and opinion polling. Statistical techniques can be used to collect and analyze data from a representative sample of the target population, allowing for accurate estimation and prediction of consumer preferences, market trends, or election outcomes.

Statistical guidance should do well in this situation because it provides methods for random sampling, hypothesis testing, and confidence interval estimation, which help minimize sampling errors and increase the reliability of the findings.

Additionally, statistical models can capture complex relationships and make accurate predictions based on the observed data.

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The information that is not sufficient to prove that a parallelogram is a square is the measurement of its angles alone. Additional information about the lengths of its sides is needed to confirm if a parallelogram is indeed a square.

To determine whether a parallelogram is a square, we need to consider both the angles and the side lengths. A parallelogram has opposite sides that are parallel and equal in length, and opposite angles that are congruent. While a square is a special type of parallelogram with four equal sides and four right angles, simply knowing that the angles of a parallelogram are equal is not enough to establish it as a square.

To confirm that a parallelogram is a square, we must also ensure that all four sides are of equal length. In a square, all angles are right angles, and all sides are congruent. Therefore, if we have information about the side lengths of a parallelogram and can verify that they are equal, along with the knowledge that the angles are right angles, then we can conclude that the parallelogram is indeed a square.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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To determine if the percentage of Contra Costa County residents supporting a ban is greater than the nationwide percentage reported by the Pew Research Center, we need to follow these steps.

1. Obtain the Pew Research Center's report on the nationwide percentage of people supporting a ban.
2. Gather data on the percentage of Contra Costa County residents supporting the ban. This data could come from local surveys, polls, or other relevant sources.
3. Compare the two percentages to see if the Contra Costa County percentage is greater than the nationwide percentage.

If the Contra Costa County percentage is greater than the nationwide percentage, we can be confident that a higher proportion of county residents support the ban. However, it is important to note that survey results may vary based on the sample size, methodology, and timing of the polls. To draw more accurate conclusions, it's essential to consider multiple sources of data and ensure the reliability of the information being used.

In summary, to confidently assert that the percentage of Contra Costa County residents supporting a ban is greater than the nationwide percentage, we must gather local data and compare it to the Pew Research Center's report. The reliability of this conclusion depends on the accuracy and representativeness of the data used.

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The equivalent expression of the rational exponent ∛a² is \((a)^{\frac{2}{3}\).

Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root.

So rational exponents (fractional exponents) are exponents that are fractions or rational expressions.

To determine the rational exponent equivalent to the expression given, we will apply the power rule of indices as shown below.

The given expression is ;

∛a²

The rational exponent is calculated as follows;

∛a² = \((a)^{\frac{2}{3}\)

Thus, based on exponent power rule, the given expression is equivalent to ∛a² = \((a)^{\frac{2}{3}\)

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The complete question is below:

Find the equivalent expression of the rational exponent ∛a². does anyone know it

Answer:

47.5

Step-by-step explanation:

The law of sines states that for any triangle:

side A (which is opposite to angle A) divided by sin(angle A) = side B (which is opposite to angle B) divided by sin(angle B).

Let's see if we can use this in the problem.

We have 2 angles, 1 side, and 1 variable for the side. we can set up an equation this way;

58/sin(39degrees) = v/sin(31degrees)

isolate v:

58sin(31degrees)/sin(39degrees) = v

We can plug this into a graphing calculator to get:

47.46740892

We round to the nearest 10th to get

47.5

Answer:

The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:

Pie Chart

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

given : x : 20 = 5 : x

x/20 = 5/x

 x² = 100

 x = 10

Hope this helps !

Answer:

15

Step-by-step explanation:

Answer:

there will only be one 3

Step-by-step explanation:

see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .

The necessary equation is \(L= 52+2D\), and the necessary overall length is \(114 miles\).

Given: A road is being extended by construction workers. The road already had a length of miles, and the crew is continuously extending it by miles. Let the number of days the crew has worked and the distance of the entire road (in miles) be represented by D and L respectively. Create a corresponding equation L to D.

According to the inquiry,

The road's initial length is 52 miles.

The daily length of roadways that a crew adds is 2 miles.

This number represents the number of days the crew worked.

The total length of the road that the crew built is represented by L.

A given condition-based equation can be written as \(L= 52+2D\).

Now, the crew's total length of the road after 31 days of construction is calculated.

\(L= 52+2*31\\L=52+62\\L=114 miles\)

As a result, the needed equation and the total length is \(L= 52+2D\)  and 114 miles respectively.

The complete question is:-

A construction crew is lengthening a road. The road started with a length of 52 miles, and the crew is adding 2 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 31 days.

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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To solve this problem, we will use the binomial probability formula.

a) Probability that less than 3 people will make a purchase:

We want to find P(X < 3), where X follows a binomial distribution with n = 15 (sample size) and p = 0.04 (probability of making a purchase).

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

where C(n, k) is the number of combinations of n items taken k at a time.

P(X = 0) = C(15, 0) * 0.04^0 * (1-0.04)^(15-0)

P(X = 1) = C(15, 1) * 0.04^1 * (1-0.04)^(15-1)

P(X = 2) = C(15, 2) * 0.04^2 * (1-0.04)^(15-2)

Calculate each term and sum them up to find the probability.

b) Probability that more than 1 person will make a purchase:

We want to find P(X > 1), which is the complement of P(X ≤ 1).

P(X > 1) = 1 - P(X ≤ 1)

Calculate P(X ≤ 1) using the binomial probability formula and subtract it from 1.

Note: Since the calculations involve combinations (C), the exact values will be quite lengthy. It's recommended to use a calculator or statistical software to compute these probabilities accurately.

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Before 5g left, 7.2 minutes had gone by.

Distance, time, and speed are all related to one another in their fundamental concepts. Distance traveled by a body in a given amount of time is its speed. That is Speed = Distance / Time. Normal Speed: Normal Total distance times speed Speed: Speed = Distance x Time Distance = D. (Speed x Time) Distance multiplied by speed equals time. mass This means that it would take 7.2 minutes before you had 5 g left: 0. 502.4. 254.8. 12.57.2. 6.259.6.

The amount of time it takes for a radioactive element to decay to half its original value is known as its half life. The time it takes for a source's activity to decrease to half its initial value is implied by this to be the definition of a half life.

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Answer: A=πr2=π·12≈3.14159ft²

Step-by-step explanation:

With the value of the circumference of the circle, find the radius of a circle. Then substitute the value of the radius of the circle in the formula of area of a quarter circle using radius which is πr2/4.

Answer:

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

Answer:

4 2/3

Step-by-step explanation:

Answer:

w = -1.3 (.3 repeating)

Step-by-step explanation:

3/2w = -20

3/2w time 2/3 (flip to get rid of fraction)

- 20 time 2/3 (what you do to one side, you must do to the other side)

w = 1.3 (.3 repeating)

1.3 as a fraction is 4/3

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

the given proportional relationship y=0.5x with proportional constant is 1/2.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

For every 1 scoop of ice cream, cup of milk is needed 1/2, and for every 5 scoops of ice cream, 2 cups of milk 2 1/2 are needed.

So the equation will be y = kx

or y = 0.5(x)

Here proportional constant is 1/2 or 0.5.

For 18 scoops of icecream, milk will be needed is 18/2 = 9 cups of milk.

Hence, we can say that the given proportional relationship y=0.5x with a proportional constant is 1/2.

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Jackie pays $130 monthly for her group health insurance.

To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.

First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.

To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.

Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.

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