A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.


Outcome Frequency
Heart 6
Spade 4
Club 7
Diamond 3


Determine the experimental probability of drawing a spade.
0.15
0.20
0.40
0.45

Answer:

10 inches

Step-by-step explanation:

The rule for a 45-45-90 triangle is if the two legs equal x then the hypotenuse is x√2.

So if the hypotenuse is 10√2 then the length of the leg d is 10

The best description of the area under the normal curve that would be used to approximate binomial probability is 'Area to the left of 46.5'.

To approximate the binomial probability, we can use the normal distribution as an approximation for the binomial distribution when the sample size is large enough, and the probability of success is not too close to 0 or 1. The mean of the normal distribution is equal to the mean of the binomial distribution, which is np, and the standard deviation of the normal distribution is equal to the square root of npq, where q is the probability of failure.

In this case, the number of DVDs that may malfunction follows a binomial distribution with parameters n = 319 and p = 1/100, where 1/100 is the probability of a DVD malfunctioning. Therefore, the mean of the binomial distribution is np = 3.19, and the standard deviation is [tex]\sqrt{npq}[/tex] = [tex]\sqrt{3.19*0.99}[/tex] ≈ 1.77.

To find the probability that at most 46 out of 319 DVDs will malfunction, we need to find the area under the normal curve to the left of 46.5 (since we are interested in the probability of at most 46 malfunctions, which includes 46.5 as well). Therefore, the answer is 'Area to the left of 46.5'.

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the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

How to solve the question?

To calculate the probability that a randomly selected part-time student has a gym membership, we need to use conditional probability. Specifically, we need to use Bayes' theorem:

P(Gym Membership | Part-Time) = P(Part-Time | Gym Membership) * P(Gym Membership) / P(Part-Time)

Where:

P(Gym Membership | Part-Time) is the probability that a student has a gym membership given that they are part-time.

P(Part-Time | Gym Membership) is the probability that a student is part-time given that they have a gym membership.

P(Gym Membership) is the overall probability of a student having a gym membership (regardless of whether they are full-time or part-time).

P(Part-Time) is the overall probability of a student being part-time (regardless of whether they have a gym membership).

Let's start by filling in the values we know from the table:

P(Part-Time) = (40 + 25) / 155 = 0.5484

P(Gym Membership) = (30 + 25) / 155 = 0.3226

P(Part-Time | Gym Membership) = 25 / (30 + 25) = 0.4545

To find P(Gym Membership | Part-Time), we need to calculate P(Part-Time and Gym Membership). We can use the formula:

P(Part-Time and Gym Membership) = P(Part-Time | Gym Membership) * P(Gym Membership)

Plugging in the values we know, we get:

P(Part-Time and Gym Membership) = 0.4545 * 0.3226 = 0.1463

Now we can use this value, along with P(Part-Time) and P(Gym Membership), to calculate P(Gym Membership | Part-Time):

P(Gym Membership | Part-Time) = 0.1463 / 0.5484 ≈ 0.2667

Therefore, the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

It's worth noting that this result is based on the assumption that the sample of 155 students is representative of the larger population of the university. If there are any biases or other factors that make this sample unrepresentative, then our calculated probability may not be accurate. Additionally, the results could be affected by other factors, such as the cost of gym membership or the availability of on-campus fitness facilities.

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Answer: We can use the formula for exponential decay to find the mass of substance A in the dish after 12 hours:

A = A0 * e^(-kt)

where:

A0 = initial mass of substance A (500 grams)

A = mass of substance A after time t

k = decay constant

t = time (in hours)

Since the mass of substance A decreases at the rate of 20% every 6 hours, we can find the decay constant as follows:

20% = 0.2 = e^(-k*6)

Taking the natural logarithm of both sides, we get:

ln(0.2) = -k*6

k = -ln(0.2)/6

k ≈ 0.1155

Substituting the values of A0, k, and t into the formula for exponential decay, we get:

A = 500 * e^(-0.1155*12)

A ≈ 169.2 grams

Therefore, the mass of substance A in the dish at the end of 12 hours is approximately 169.2 grams.

Step-by-step explanation:

The mass of substance A in the dish at the end of 12 hours would be 320 grams.

The mass of substance A decreases at a rate of 20% every 6 hours. After 6 hours, the mass of substance A remaining in the dish would be:

500 - (20/100) * 500

500 - 100

400 grams

After another 6 hours (i.e. at 12 hours), the remaining mass of substance A would be:

400 - (20/100) * 400

400 - 80

320 grams

Therefore, the mass of substance A in the dish at the end of 12 hours would be 320 grams.

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Answer:

the answer is 2) m11 p18.

Step-by-step explanation:

m5 p8 m6 p10 = (m5 m6) (p8 p10) = m11 p80

Therefore, the answer is 2) m11 p18.

a) His monthly salary is, 555.6

b) Total amount spent on his parent​ is, 111.1

Given that;

Mr. Ade plans to spend his monthly salary as follows

food-20%

children-25%

parents-20%

car-10%

entertainment-10%

saving-2½

miscellenceous-2½

And, the amount of saving kept for saving is Ghc 250.00.

Hence, We get;

Monthly salary is,

Since, We have;

Percent of savings = 100% - 20% - 10% - 10% - 12.5% - 2.5%

                             = 45%

Hence, We get;

45% of salary = 250

45/100 x salary = 250

Monthly salary = 25000 / 45

Monthly salary = 555.6

And, Money spent on parents;

20% of 555.6

20/100 x 555.6

111.1

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Answer:

9

Step-by-step explanation:

Based on the Pythagorean theorem, A equals the square root of C squared minus B squared. By plugging in these numbers, you get 9.

The one less likely to be picked is the one with less & (Vice Versa).

To find the probability: (#of paper clips/total amount of items)

Answer:  The mean of data set K is greater than the mean of data set L.

The median of data set K is greater than the median of data set L

Step-by-step explanation:

we need to calculate the mean (average) of each data set and compare them.

Mean of data set K = (28 + 145 + 112 + 57 + 130) / 5 = 112.4

Mean of data set L = (141 + 171 + 68 + 124 + 43) / 5 = 109.4

'Arranging the values in data set K in ascending order, we get:

28, 57, 112, 130, 145

The median of data set K is the middle value, which is 112.

The mean of data set L is 109.4.

The probability that a randomly chosen junior who volunteers in their community volunteers at least twice a week is approximately 0.4444, or 44.44%

Explain the term probability

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is used in various fields, including mathematics, statistics, and science, to analyze and predict the outcomes of experiments, games of chance, and real-world events.

According to the given information

Using Bayes' theorem, we can write:

P(T|V) = P(V|T) * P(T) / P(V)

We know that two-thirds of the juniors volunteer in their community, so P(V) = 2/3.

We also know that 45% of the juniors who volunteer do so at least twice a week, so P(T) = 0.45.

To find P(V|T), we can use the conditional probability formula:

P(V|T) = P(V and T) / P(T)

We can interpret P(V and T) as the probability of junior volunteering at least twice a week AND volunteering in their community. We don't have that information directly, but we can use the fact that P(T|V) = 0.45 to estimate it:

P(T|V) = P(V and T) / P(V)

0.45 = P(V and T) / (2/3)

P(V and T) = 0.45 * (2/3) = 0.3

Now we can substitute all these values into the original Bayes' theorem formula:

P(T|V) = P(V|T) * P(T) / P(V)

P(T|V) = (P(V and T) / P(T)) * P(T) / P(V)

P(T|V) = 0.3 / (0.45 * (2/3))

P(T|V) = 0.4444...

Therefore, the probability that a randomly chosen junior who volunteers in their community volunteers at least twice a week is approximately 0.4444, or 44.44%

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Roehr Corporation Additional Paid-in Capital--Common account will increase by $110,000 by issuing 20,000 shares of $0.50 par common stock for $6 per share.

When a corporation issues common stock, the par value of the stock is recorded in the Common Stock account, and any amount received above the par value is recorded in the Additional Paid-in Capital--Common account. In this case, Roehr Corporation The par value of the common stock is

Total par value = Par value per share x Number of shares

= $0.50 x 20,000

= $10,000

The total amount received from issuing the stock is $6 per share x 20,000 shares = $120,000.

The additional paid-in capital is calculated as the difference between the total amount received and the total par value:

Additional paid-in capital = Total amount received - Total par value

= $120,000 - $10,000

= $110,000

Therefore, the answer is (B) $110,000.

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After rounding , The calculated result of 15.58 - 7.237 is therefore around  8.4

When a number is rounded, it is approximated by using a smaller, more straightforward number that is near to the original value. For instance, 3.141 is the result of rounding 3.14159 to two decimal points.

We can round 15.58 to 15.6 and 7.237 to 7.2 to estimate 15.58 - 7.237 by first rounding each number to the nearest tenth

. After that, we may take 7.2 away from 15.6 to get:

15.6 - 7.2 = 8.4

The calculated result of 15.58 - 7.237 is therefore around  8.4

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Answer:

if you go into your reading lessone on one of the sentences in page 2 or 4 there is the answer hope this helped

Step-by-step explanation:

The incorrect measurements of the right triangle is 36² + 60² = 48²

Given data ,

Let the triangle be represented as ABC

Now , let the height of the triangle be AB = 36 miles north

Let the base of the triangle be BC = 48 miles east

Now , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , 36² + 48² = 60²

So , the incorrect option from the data is 36² + 60² = 48²

Hence , the triangle is formed

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The amount of space that the flower pot will take up is: 38.47 cm²

We are given that the bottom of the given flower pot has a diameter of 7 cm.

Now, the space that the flower pot will cover is simply the area the the circle base.

Formula for the area of a circle is:

A = πr²

where:

A is area

r is radius

We have d = 7 cm

Thus: r = 7/2 = 3.5 cm

A =  π * 3.5²

A = 3.14 * 3.5²

A = 38.47 cm²

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Answer:

When the red lines in a geometric figure are not parallel, the congruency of angles may vary. Vertical angles formed by the intersection of non-parallel lines are always congruent, while corresponding angles and alternate interior angles may or may not be congruent. The congruency of angles depends on the specific relationship between the angles and the lines in the figure, and further analysis of the figure would be necessary to determine which angles are congruent.

It will take approximately 25 years for $7,000 to double in an account that pays 2.8% simple interest.

The 70 rule is a helpful shortcut for calculating the number of years it will take an investment to double in value using simple interest. The formula is 70 divided by the interest rate.

In this case, we have an interest rate of 2.8%, so we can calculate that it will take approximately 70/2.8 = 25 years for $7,000 to double in value. It's important to note that this rule assumes the interest rate remains constant over the entire period, which may not always be the case in real-world investments.

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Around 21.13% of the batteries will final(last) between 90.6 and 109.8 hours. 

To unravel this issue, ready to utilize the standard typical conveyance by standardizing the values utilizing the equation:

z = (x - μ) / σ

where

x is the esteem we need to discover the likelihood

μ is cruel(mean), and σ is the standard deviation.

So, for the lower conclusion of the extent, we have:

z1 = (90.6 - 105) / 12 ≈ -1.20

z1 = -1.20

And for the upper conclusion of the extension, we have the:

z2 = (109.8 - 105) / 12 ≈ 0.45

z2 =  0.45

We need to discover the rate of batteries that will final(last) between these two values, which compares to the area under the typical bend between z1 and z2.

Able to utilize a standard ordinary conveyance table or calculator to discover this zone, or we will utilize the properties of the typical conveyance to inexact it.

Since the typical conveyance is symmetric around the cruel, we know that the zone between z1 and z2 is the same as the range between -z2 and -z1 (i.e., the comparing values on the other side of the mean).

So, ready to discover the range between -z2 and -z1, which compares to the rate of batteries that will final between 90.6 and 109.8 hours:

P(-z2 < z < -z1) ≈ P(z < -z1) - P(z < -z2)

Employing a standard typical dissemination table or calculator, we discover:

P(z < -1.20) ≈ 0.1151

P(z < -0.45) ≈ 0.3264

So, the rate of batteries that will final between 90.6 and 109.8 hours is rough:

P(-z2 < z < -z1) ≈ 0.3264 - 0.1151 ≈ 0.2113

Increasing by 100%, we get:

0.2113 * 100% ≈ 21.13D

44 Subsequently, roughly 21.13% of the batteries will final between 90.6 and 109.8 hours. 

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Answer:

Answers down below!

Step-by-step explanation:

Mean: 58.75

Median: 63

Range: 70

Mode: 63

Hope this helps!

The test score that is 0.6 standard deviations above the mean is 111.

We can use the formula for z-score to find the test score that is 0.6 standard deviations above the mean:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.

In this case, we want to find x when z = 0.6, μ = 105, and σ = 10:

0.6 = (x - 105) / 10

Multiplying both sides by 10, we get:

6 = x - 105

Adding 105 to both sides, we get:

x = 111

Therefore, the test score that is 0.6 standard deviations above the mean is 111.

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The test score that is 0.6 standard deviations above the mean is 111.

To find the test score that is 0.6 standard deviations above the mean, we can use the formula

z = (x - μ) / σ

where z is the number of standard deviations from the mean,

x is the test score we want to find,

μ is the mean of the distribution (105), and

σ is the standard deviation of the distribution (10).

We know that the desired test score is 0.6 standard deviations above the mean,

so we can set z = 0.6 and solve for x:

0.6 = (x - 105) / 10

Multiplying both sides by 10, we get:

6 = x - 105

Adding 105 to both sides, we get:

x = 111

Therefore, the test score that is 0.6 standard deviations above the mean is 111.

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Answer:

Step A: The third quartile is 9.5, choice d.

Step B: The median of the data set is 6.5.

Step C: The IQR of the data set is 6, and we found this value by subtracting the first quartile from the third quartile (9.5 - 3.5 = 6).

Step-by-step explanation:

First, let's analyze the data set.

1 2 3 4 5 6 7 8 9 10 11 12

Since this data set is already sorted in numerical order, we can determine the median by finding the middle value that divides the data set in half. With 12 values in the data set, the median would be between the 6th and 7th numbers, so we can find this by using the calculation (6+7)/2 = 6.5.

                 6.5

{1 2 3 4 5 6} | {7 8 9 10 11 12}

With this median, we split our data set into two halves. Now, we can find the first quartile, or the 25th percentile, by finding the median of the first half. This would be the value between 3 and 4, so (3+4)/2 = 3.5.

       3.5        6.5

{1 2 3} | {4 5 6} | {7 8 9 10 11 12}

We can repeat this step in the second half in order to find the third quartile or the 75th percentile. The median of the second half would be between 9 and 10, so (9+10)/2 = 9.5.

       3.5         6.5        9.5

{1 2 3} | {4 5 6} | {7 8 9} | {10 11 12}

Now we know Q1 (first quartile) and Q3 (third quartile), we can find the IQR which is Q3 - Q1, so Q3 - Q1 = 9.5 - 3.5 = 6.

So now we can answer the question:

Step A: The third quartile is 9.5, choice d.

Step B: The median of the data set is 6.5.

Step C: The IQR of the data set is 6, and we found this value by subtracting the first quartile from the third quartile (9.5 - 3.5 = 6).

The distance that the car travelled on 1 gallon of gasoline is 71 1/20. (option d).

Let's start by finding how far the car can travel on 1/3 gallon of gasoline. We can do this by dividing 50 3/4 by 1 2/3. To divide fractions, we invert the divisor and multiply. So we have:

50 3/4 ÷ 1 2/3 = 50 3/4 × 3/5 = 153/4

This means that the car can travel 153/4 miles on 1 2/3 gallons of gasoline.

Now, we can use the unitary method to find how far the car can travel on 1 gallon of gasoline. We know that the car can travel 153/4 miles on 1 2/3 gallons of gasoline, so we can set up a proportion:

1 2/3 gallons ÷ 153/4 miles = 1 gallon ÷ x miles

To solve for x, we can cross-multiply:

1 2/3 × x = 1 × 153/4

We can simplify the left side by converting 1 2/3 to an improper fraction:

5/3 × x = 153/4

To solve for x, we can cross-multiply again:

5/3x = 153/4 × 3/5

Simplifying both sides, we have:

x = 153/4 × 3/5 ÷ 5/3 = 229/20

So the car can travel 229/20 miles on 1 gallon of gasoline.

To check our answer, we can use the unitary method again to find how far the car can travel on 1 2/3 gallons of gasoline using our answer for how far the car can travel on 1 gallon of gasoline. We have:

1 gallon ÷ 229/20 miles = 1 2/3 gallons ÷ y miles

Simplifying both sides, we have:

20/229y = 3/5

Solving for y, we have:

y = 3/5 × 229/20 ÷ 20/229 = 71 1/20

Therefore, the answer to the question is (d) 71 1/20.

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The area covered by grass in the nursery school playground is 5760 square meters.

To find the area covered by grass in the nursery school playground, we first need to calculate the total area of the playground, and then subtract the areas of the swings and the paths.

Given:

Length of playground = 160 m

Width of playground = 80 m

Width of swings = 80 m

Width of paths = 1.5 m

Total area of the playground = Length × Width = 160 m × 80 m = 12800 m²

Area of the swings = Width of swings × Width of swings = 80 m × 80 m = 6400 m²

Since there are two sides of the swings that are parallel to the length of the playground, we need to subtract the area of the paths along those two sides. The total width of the paths is 1.5 m + 1.5 m = 3 m.

Area of the paths along the length = Length of playground × Width of paths = 160 m × 3 m = 480 m²

Similarly, since there are two sides of the swings that are parallel to the width of the playground, we need to subtract the area of the paths along those two sides.

Area of the paths along the width = Width of playground × Width of paths = 80 m × 3 m = 240 m²

Now, we can calculate the remaining area covered by grass by subtracting the area of the swings and the areas of the paths from the total area of the playground:

Area covered by grass = Total area of playground - Area of swings - Area of paths along length - Area of paths along width

Area covered by grass = 12800 m² - 6400 m² - 480 m² - 240 m²

Area covered by grass = 5760 m²

So, the area covered by grass in the nursery school playground is 5760 square meters.

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Answer:

  A: x +y = 60; y = x +20

  B: 20 minutes on math

  C: no

Step-by-step explanation:

You have some relations and some questions about dance times and math practice times with dance times longer than math practice by 20 minutes.

The given relations can be written as two equations:

  x + y = 60 . . . . . total time is 60 minutes

  y = x + 20 . . . . . dance time is 20 minutes longer than math time

We want the value of x. We can find that by using the second equation to substitute for y in the first equation:

  x + (x +20) = 60

  2x = 40 . . . . . . . . . subtract 20

  x = 20 . . . . . . . . divide by 2

Jordyn practices math 20 minutes every day.

If Jordyn dances for 60 minutes, then she will practice math for 60 -20 = 40 minutes. That brings her total practice time to 60 +40 = 100, which is more than 80.

It is not possible to spend 80 minutes total if she spends 60 minutes dancing.

(She could spend 50 minutes dancing, 30 minutes on math, and have a total practice time of 80 minutes.)

Jordyn spends 20 minutes each day practicing math. However, if her total practice time is 80 minutes, it would not be possible for her to spend 60 minutes practicing dance.

The total time Jordyn spends practicing both dancing and math is 60 minutes. If we establish the time she spends on math as 'x' and the time she spends dancing as 'y', we can establish the following and equations:

To solve for 'x', substitute the first equation into the second to get x + (x + 20) = 60. Simplify to get 2x + 20 = 60. Subtract 20 from each side to get 2x = 40, and finally divide by 2 to get x = 20. Therefore Jordyn spends 20 minutes practicing math each day.

To answer Part C, if Jordyn practices for a total of exactly 80 minutes and dances 20 minutes longer than she does math, it would not be possible for her to spend 60 minutes practicing dance. The most amount of time she could spend dancing is 50 minutes (80 total minutes- 30 minutes for math).

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The division expressions are given below.

Given are divisions, we need to write their division expressions,

5/6 = 5÷6

9/15 = 9÷15 = 3÷5

10/25 = 10÷25 = 2÷5

16/31 = 16÷31

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The ratio of the lengths of the corresponding sides of the similar right triangles indicates that the length of the segment [tex]\overline{BD}[/tex] = 8 units

Similar triangles are triangles that have the same shape, and therefore, the interior angles of each triangle are congruent to the three angles in the similar triangle, however, the sizes of the triangles may be different.

The similar triangles are; ΔABD, ΔBCD, ΔACB

∠ABD ≅ ∠BCD ≅ ∠ACB (Corresponding angles in similar triangles are congruent)

[tex]\overline{AD}[/tex]/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/[tex]\overline{DC}[/tex]

4/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/16

4 × 16 = 64 = [tex]\overline{BD}[/tex]²

[tex]\overline{BD}[/tex] = √(64) = 8

The length of the segment [tex]\overline{BD}[/tex] = 8 units

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Carrie will have $15,481.24 after taxes for a year assuming she works 52 weeks.

First, let's calculate the total taxes she pays each week:

Federal income tax rate = 10% of $350.15 = $35.02

State income tax rate = 5% of $350.15 = $17.51

Total taxes per week = $35.02 + $17.51 = $52.53

Now, we can calculate the total amount of taxes she pays for a year:

Total taxes for a year = $52.53 x 52 weeks = $2,731.56

Amount Carrie will have after taxes for a year:

Annual income before taxes = $350.15 x 52 weeks = $18,212.80

Net income after taxes = Annual income before taxes - Total taxes for a year

Net income after taxes = $18,212.80 - $2,731.56 = $15,481.24

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--The complete Question is, Carrie Burnside is single, earns $350.15 weekly, and claims 1 allowance. If the federal income tax rate is 10% plus an additional 5% state income tax rate, how much will Carrie have after taxes for a year assuming she works 52 weeks? --

The width of the rectangle is x + 4

Since the area of the rectangle is x^2 + 15x + 44, the product that give the value can be solved by factorization

To factorize the expression x^2 + 15x + 44, we need to find two numbers whose product is 44 and whose sum is 15. These numbers are 11 and 4, because 11 times 4 is 44 and 11 plus 4 is 15.

Now we can write the expression as:

x^2 + 11x + 4x + 44

Grouping the terms in pairs:

(x^2 + 11x) + (4x + 44)

Factoring out the greatest common factor from each pair:

x(x + 11) + 4(x + 11)

Now we can see that we have a common factor of (x + 11):

(x + 11)(x + 4)

Therefore, the factored form of x^2 + 15x + 44 is:

(x + 11)(x + 4)

the width of the rectangle is x + 4

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If 15% of "x" is 20% of "y", then "y" is 75 percent of "x", the correct option is (c).

The "Percentage" is defined as a way to express the proportions or rates in terms of a "relative-scale" out of 100,

We know that, 15% of "x" equals 20% of "y".

Mathematically, this can be expressed as,

0.15x = 0.20y,           ...because 15% = 0.15 and 20% = 0.20;

To find what percentage of x is y, we need to express "y" as a percentage of "x".
On solving further,

We get,

⇒ 0.15x = 0.20y,

⇒ y = (0.15x)/0.20,

⇒ y = 0.75x

It is read as "y" is read as 75% of "x".

Therefore, "y" is 0.75 times "x", or 75% of "x", Option(c) is correct.

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Answer:

[tex] log_{7}(a) \times log_{b}(7) [/tex]

[tex] \frac{ log(a) }{ log(7) } \times \frac{ log(7) }{ log(b) } = \frac{ log(a) }{ log(b) } = log_{b}(a) [/tex]