here are 5 cards: 2,5,7,8,9. one of the cards is removed and then mean average is 6. which card was removed

The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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Answer:

28.

Step-by-step explanation:

I just did the question and I got it right. The answer above is right. The image below is where I did the question and has the picture attached next to it too.

*And I accidentally clicked the one star option, that's why it has such a low score.

An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.

The value of y is 28.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.

m∠CAB = 34

m∠CBA = x - 5

m∠ACB = 4y

Triangle ABC is an isosceles triangle.

AC and BC are sides are equal.

This means,

m∠CAB = m∠CBA

34 = x - 5

34 + 5 = x

x = 39

Now,

The sum of the angles in a triangle is 180 degrees.

This means,

34 + (x -5) + 4y = 180

34 + (39 - 5) + 4y = 180

34 + 34 + 4y = 180

68 + 4y = 180

4y = 180 - 68

y = 112 / 4

y = 28

We can cross-check.

34 + 34 + 4 x 28 = 180

34 + 34 + 112 = 180

180 = 180

Thus,

The value of y is 28.

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The correct option is 50.

Given that `N = 56` and `k = 6`.

We need to find the total degrees of freedom (df) which can be calculated using the formula below:

df(total) = N - kdf(total) = 56 - 6df(total) = 50

Therefore, the total degrees of freedom (df) is 50. Hence, the correct option is 50.

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(a) Using quarters, dimes, nickels, and pennies, the greedy algorithm for 87 cents returns the following solution: 6 coins

(b) Using quarters, dimes, and pennies (no nickels), the greedy algorithm for 87 cents returns the following solution:6 coins

(a) Using quarters, dimes, nickels, and pennies, the greedy algorithm for 87 cents returns the following solution:

3 quarters (75 cents)

1 dime (10 cents)

2 pennies (2 cents)

Total: 3 + 1 + 2 = 6 coins

(b) Using quarters, dimes, and pennies (no nickels), the greedy algorithm for 87 cents returns the following solution:

3 quarters (75 cents)

1 dime (10 cents)

2 pennies (2 cents)

Total: 3 + 1 + 2 = 6 coins

In both cases, the greedy algorithm returns the optimal solution, which uses the fewest coins possible. This is because the denominations used (quarters, dimes, nickels, and pennies or quarters, dimes, and pennies) are in descending order of value, and the greedy algorithm always selects the largest denomination that is less than or equal to the remaining amount.

For (a) 87 cents, the greedy algorithm starts by selecting the largest denomination, which is a quarter. It continues to select quarters until the remaining amount is less than 25 cents. Then, it moves on to the next largest denomination, which is a dime and repeats the process. Finally, it selects pennies to make up the remaining amount.

For (b) 80 cents, the same process is followed. The greedy algorithm selects quarters until the remaining amount is less than 25 cents, then proceeds with dimes, and finally uses pennies.

In both cases, the greedy algorithm returns the optimal solution, as it always chooses the largest denomination possible at each step, resulting in the fewest number of coins needed to make the given amount.

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Answer:

27 x 52  = ( 20 + 7 ) x ( 50 + 2 )  = 1404

Step-by-step explanation:

27 x 52

( 20 + 7 ) x ( 50 + 2 )

(20 x 50) + (20 x 2) + (7 x 50) + (7 x 2)

= 1000 + 40 + 350 + 14

= 1404  

Answer:

Are you asking for the selling price? If yes the answer should be $50 x (1+25%) = $62.5

Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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Answer:

True

Step-by-step explanation:

Four-sided polygons are usually referred to as quadrilaterals, quadrangles or sometimes tetragons. In geometry the term quadrilateral is commonly used.

Answer: True

Step-by-step explanation: :D

The probability of a even number less than 8 will be 3/10.

What is the definition of probability?

The possibility of an event is expressed by probability. This field of mathematics is concerned with the occurrence of a random event. The value varies from 0 to 1. In mathematics, probability is used to forecast the likelihood of occurrences occurring.

The potential of something happening is referred to as probability. The probability distribution makes use of this fundamental principle in probability theory. Before we can evaluate the likelihood of an event occurring, we must first know the total number of alternatives.

P(E) is the chance that an event will occur divided by the total number of outcomes.

Now,

Given sample space  S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

and Event E="Even number less than 8"

{2,4,6}

Then, Probability of event E=3/10

Hence,

          The probability of a even number less than 8 will be 3/10.

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The probability  that the average scholarshi[s in the samle greater than 20,000 is (69.729, 74.271).

Let X: Marks of students and be the population average marks.

X ~ N(72, 16)

The formula for the CI for is,

CI = mean + tₐ/₂ , ₙ₋₁ s/n

= 72 ± 2.539 × 4/20

= 72 ± (2.539 × 0.8944)

= 72 ± 2.27

= 72 - 2.27 , 72 + 2.27

= (69.729, 74.241)

Therefore, the required 98% CI for the average marks of the students is (69.729, 74.271).

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The fraction of water Libby drinks is 1 6/8 more liters of water than Jack.

In mathematics, a fraction is represented by a numerical value that designates a portion of an entire. A fraction is a piece or section of a whole, where the whole can be any number, a particular value, or an object. Let's use an example to better comprehend this idea. A pizza cut into 8 equal pieces is depicted in the following diagram. Now, to describe a single portion of the pizza, we may use the notation 1/8, which indicates that, out of 8 equally sized portions, we are speaking of one portion.

Given that, Libby drinks 2 7/8 liters of water.

Coverting the mixed fraction into improper fraction:

2 7/8 = 2(8) + 7/ 8 = 23/8

Jack drinks 1 1/8 liters of water.

Coverting the mixed fraction into improper fraction:

1 1/8 = 8 + 1/8 = 9/8

The difference between is:

D = 23/8 - 9/8 = 14/8

14/8 = 1 6/8

Hence, Libby drinks 1 6/8 more liters of water than Jack.

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If the sample has the same mix of people, in the same proportions, as the population being studied then sociologists know if the sample they are using is representative. So the option c is correct.

No subject is off-limits when sociologists use the sociological lens and start asking questions. Every facet of human behaviour has the potential to be studied. Sociologists cast doubt on the society that people have built and inhabit. They observe behavioral patterns as individuals navigate that world.

Sociologists have uncovered workplace patterns that have revolutionized industries, family patterns that have educated parents, and educational patterns that have supported structural changes in classrooms by using sociological methodologies, methodical research, and a scholarly interpretive approach.

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The complete question is;

How do sociologists know if the sample they are using is representative?

a. If the people in the sample freely volunteered to serve as representatives

b. If the sample has an even number, decided by the researcher, of people from several different categories or backgrounds

c. If the sample has the same mix of people, in the same proportions, as the population being studied

d. If the participants have been interviewed to reveal possible bias.

The rule for reflection along y-axis is:

So the point (3,4) when reflected along y-axis becomes (-3,4).

So (-3,4) is the answer.

The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

What is function?

For the parent function f(x) and a constant k >0,

then, the function given by  

g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)

if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k

As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e

k = 3 >1

so, by definition

g(x) = 3 f(x) = 3 . 8(3)ˣ

= 8(3)ˣ⁺¹

= 24 (3)ˣ

Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

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Answer:

New price = 90 dollars

Step-by-step explanation:

25% of 120 = 30

Price is reduced 25% from 120 so,

120 - 30 = 90

Amount of discount = 30

new price = $90

method #1 -

25% = 0.25

0.25(120) = 30

120 - 30 = 90

method #2 -

25 = 1/4 of 100

120 ÷ 4 = 30

120 - 30 = 90

First: info on point-slope form.

We need to find the slope of the line first.

\(m = \frac{2 + 1}{5 - 1} = \frac{3}{4}\)

Slope: \(\frac{3}{4}\)

Now we can complete the point-slope equation of the line.

\(y - (-1) = \frac{3}{4}(x - 1)\\\\y + 1 = \frac{3}{4}(x - 1)\)

*These equations are equivalent.

Given the expression :

The expression will be equal:

so, the answer is option 4)

Answer:

33.75°

Step-by-step explanation:

Given data

Ratio=  3:3:10

combined  ratio= 3+3+10= 16

The sum of angles in a triangle is 180°

Hence the smallest angle is represented by the ratio 3

therefore let the angle be x

Applying the part to all method

3/16= x/180

16x= 180*3

16x=540

x= 540/16

x= 33.75°

Hence the smallest angle is 33.75°

According to the Lotka-Volterra equations, the species with the higher K, or carrying capacity, that is, the resource's more effective user, should prevail in exploitative competition for resources in stable ecosystems.

Alfred J. Lotka first introduced the Lotka-Volterra predator-prey model in the science of autocatalytic chemical reactions in 1910.

This was essentially the logistic equation, which Pierre François Verhulst first deduced

Using a plant species and a herbivorous animal species as an example, Lotka extended the model to "organic systems" in 1920 through Andrey Kolmogorov.

In 1925, he utilized the equations to analyze predator-prey interactions in his book on biomathematics.

The same set of equations were first published in 1926 by mathematician and physicist Vito Volterra, who had recently developed an interest in mathematical biology.

Umberto D'Ancona, a marine biologist who was courting Volterra's daughter at the time and would subsequently marry her, provided the impetus for Volterra's investigation. D'Ancona did research.

Hence, the Lotka-Volterra equations, the species with the higher K, or carrying capacity, that is, the resource's more effective user, should prevail in exploitative competition for resources in stable ecosystems.

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Answer:

62

Step-by-step explanation:

DEH is an isoceles triangle, so Angle DEH anf angle EHD are congruent.

180-56 = 124

124 / 2= 62

Based on the properties of a kite, the statement that is true is: D. KPE = TPE.

A kite is a quadrilateral in which its diagonals intersect at right angles.

Also, the non-vertex angles of a kite are congruent, that is they have equal measure.

Angle KPE and angle TPE in the given kite are right angles formed at the point of intersection of the two diagonals of the kite. They both equal 90 degrees.

Therefore, the true statement is:

D. KPE = TPE

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Answer: 6.24

Step-by-step explanation:

To round 6.235 to the nearest hundredth means to round the numbers so you only have two digits in the fractional part (numbers after the decimal)

The last digit in the fractional part of 6.235 is 5 or more and less than 9, so add 1 to the second digit of the fractional part and remove the third digit.

Therefore, the answer is 6.24

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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Answer: 180

Step-by-step explanation:

The difference in the dollar value of Assistantship (Stipend) between art and science fields with  standard errors is equal to 1.214.

Mean      24041.62203                 25952.36501

Sample mean difference between Assistantship (stipend) in arts and science is equal to

=  $25952.36501 - $24041.62203

= $1910.74298.

Hypothesized mean difference is 0 (there is no difference in stipend between the two fields).

Variance        621483.0801            615193.5853

Sample size    521                             479

Standard error of the difference is,

=√[(variance in arts / sample size in arts) + (variance in science / sample size in science)]

= √[(615193.5853 / 479) + (621483.0801 / 521)]

= $49.77

t-statistic

= (sample mean difference - hypothesized mean difference) / standard error of the difference

Substitute the values into the t-statistic formula,

⇒ t-statistic = ($1910.74298 - 0) / $49.77

⇒ t-statistic = 38.39

t-critical value for a two-tailed test with 992 degrees of freedom at a significance level of 0.05 is 1.9624.

t-statistic (38.39) > t-critical value (1.9624)

⇒Reject the null hypothesis that there is no difference in stipend between the two fields.

standard errors

= t-statistic / √(sample size)

= 38.39 / √(479 + 521)

= 38.39 /31.62

=1.214

Therefore,  the difference in the dollar value of Assistantship (Stipend) between these two fields is 1.214 standard errors away from the hypothesized difference.

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Answer:

Improper its 81/10

Step-by-step explanation:

8   1/10~ we should multiply denominator with whole number then add numerator:

10 x 8 = 80+ 1 = 81

In improper its- 81/10

Hope this helps :D

A bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and a standard deviation of 50.

We will find the score that separates the lower 60% of ratings from the top 40% of ratings.

Let x be the score that separates these two portions. We can find the corresponding z-scores using the standard normal distribution, since the ratings are normally distributed with mean 200 and standard deviation 50.

The z-score corresponding to the 60th percentile is the value z such that

P(Z ≤ z) = 0.6

With the help of standard normal tables, we can find that z = 0.25. Therefore, we have

(x - 200)/50 = 0.25

For x, we get

x - 200 = 0.25 * 50

x - 200 = 12.5

x = 212.5

Similarly, the z-score corresponding to the 40th percentile is the value z such that

P(Z ≤ z) = 0.4

With the help of standard normal tables, we can find that z = -0.25. Therefore, we have

(x - 200)/50 = -0.25

For x, we get

x - 200 = -0.25 * 50

x - 200 = -12.5

x = 187.5

Hence, the score that separates the lower 60% from the top 40% is between 187.5 and 212.5.

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