Determine whether each ordered pair is a solution or not a solution to this system of inequalities.

y< −x

2x+y>2

The probability of drawing 5 cards from Ms Q's deck such that three cards have the same number is 876 / 98 = approximately 0.089.

There are a total of 28 possible combinations of 5 cards from Ms Q's deck since there are 4 colours and 7 numbers.

To have three cards with the same number, Yunseol must choose 3 cards with the same number and 2 cards with different numbers. There are 7 possible choices for the number of the three cards, and 4 choices for the colour of each card, so there are 7 × 4³ = 196 ways to choose the 3 cards.

For the other 2 cards, Yunseol must choose 2 different numbers and 2 different colours, so there are 7 choose 2 (or 21) ways to choose the numbers and 4 choose 2 (or 6) ways to choose the colours. Therefore, there are 21 × 6 = 126 ways to choose the other 2 cards.

So, the total number of ways to have 3 cards with the same number is 196 × 126 = 24536.

The probability of having three cards with the same number is 24536 / 28 = 876 / 98.

Therefore, the probability of drawing 5 cards from Ms Q's deck such that three cards have the same number is 876 / 98 = approximately 0.089.

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Answer: -4c + 16

Step-by-step explanation:

So to expand all you do is simply multiply the number outside the bracket (-4) but the numbers inside the bracket one by one as such:
-4 * c = -4c
-4 * -4 = 16

Therefore your answer is -4c + 16 as it can not be simplified further because there as no more like terms to be collected. Hope this helped! ^^

Step-by-step explanation:

-4c+16=

divide both sides by -4

-4c\-4=16\-4

c=16\-4

c=-4

The probability of rolling a specific sequence of numbers on three eight-sided dice is 1/8 x 1/8 x 1/8, or 1/512. To calculate the probability of rolling three strictly increasing numbers, we need to consider all possible combinations of numbers that meet this condition.

For the first die, any number from 1 to 6 can appear, for the second die, any number from 2 to 6 can appear, and for the third die, any number from 3 to 6 can appear.

Therefore, the number of possible combinations is 6 x 5 x 4 = 120.

The probability of rolling three strictly increasing numbers is 120/512 = approximately 0.234 or 23.4%.

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Scott picked x pounds of blueberries from a local farm and if Scott picked x pounds of blueberries, he now has 5 pounds, so x = 5(2) = 10 pounds.

Pounds is a unit of mass or weight used in the imperial and United States customary systems of measurement. It is equal to 16 ounces or 0.45 kilograms. In the United Kingdom and the other countries that use the imperial system of measurement, it is the standard unit used to measure the weight of people, animals and other objects. In the United States, the pound is often referred to as the avoirdupois pound to differentiate it from other units of measure.

He gave 3 pounds of his pick to his brother, Dean. This leaves x-3 pounds of blueberries. He then shared the remaining blueberries equally with his sister Georgia, so each of them got (x-3)/2 pounds of blueberries. This means that Scott has (x-3)/2 + 3 = (x+3)/2 pounds of blueberries. Therefore, if Scott picked x pounds of blueberries, he now has 5 pounds, so x = 5(2) = 10 pounds.

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The simplified form of the expression (42x + 62y) + (38x - 4y) is 80x + 58y.

Given the expression in the question

(42x + 62y) + (38x - 4y)

To simplify, collect and add like terms.

(42x + 62y) + (38x - 4y)

42x + 62y + 38x - 4y

Collect like term

42x + 38x - 4y + 62y

Add 42x and 38x

80x - 4y + 62y

Add -4y and 62y

80x + 58y

Therefore, the simplified form is 80x + 58y.

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In order to achieve a bigger splash in their next trial, all the students must need to do is use a ball with a larger circumference.

Displacement and volume are defined as a dimensional object dropped into a liquid that will always displace its own volume from the liquid.

For a basketball, the circumference is a function of its volume. In other words, the larger the circumference, the larger the volume.

This defines that a basketball with a larger volume will displace more water from the pool than one with a lower volume.

Finally, to make a bigger splash, a basketball with a larger circumference would be needed.

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This is Single-Blinded Randomized Controlled trial type of study because the recipient is unaware that they are receiving a treatment, only the researchers are aware of who is receiving which treatment. So the option d is correct.

One of the most rigorous research designs is experimental research, which is frequently referred to as the "gold standard" in research designs.

This design involves the researcher manipulating one or more independent variables (as treatments), randomly assigning individuals to various treatment levels (random assignment), and observing the effects of the treatments on outcomes (dependent variables).

Experimental research has a distinct advantage in that it may link cause and effect through treatment manipulation while controlling for the erroneous effect of unrelated variables, which is known as internal validity (causality).

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The complete question is:

A team of researchers randomly separates their study's participants into two groups, giving one group a placebo and the other a new treatment to be tested. As the treatment is somewhat experimental, participants do not know whether they receive the placebo but researchers do know whether a specific participant receives the placebo. What type of study is this?

a. Standard Deviation Study

b. Type 1 Study

c. Case-Control Study

d. Non-Blinded Randomized Controlled Trial

e. Single-Blinded Randomized Controlled trial

The solution is, 5orange = 1.25 cup

                          24orange= 6 cup

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Abby squeezed the juice from 4 oranges and made 1 cup of orange juice. Each orange provides the same amount of juice.

now,

from 5 orange we get = 5/4

                                     =1.25 cup

and, 6 cup from = 4*6

                          =24 orange

Hence, The solution is, 5orange = 1.25 cup

                                      24orange= 6 cup

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Answer:

the answer is m =-2

beause my teacher told me

The slope of the line is [tex]$\frac{3}{2}$[/tex] containing the midpoint of the segment with certain given endpoints.

The slope is a measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change between any two points on the line. It represents the rate of change in the y-coordinate with respect to the x-coordinate.

The midpoint of the first segment is[tex]$\left(\frac{2+0}{2}, \frac{4+(-2)}{2}\right)[/tex]= (1,1) and the midpoint of the second segment is [tex]$\left(\frac{5+1}{2}, \frac{1+5}{2}\right)[/tex] = (3, 3). To find the slope of the line between these two points, we use the formula for the slope of a line: [tex]$\frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex] = [tex]\frac{3 - 1}{3 - 1}[/tex] =[tex]\frac{3}{2}[/tex]. So, the slope of the line is [tex]$\frac{3}{2}$[/tex].

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Answer:

well i don't know but i wish you the best of luck sorry always remember YOUR SMART ♥️♥️♥️♥️♥️

Step-by-step explanation:

It would be appropriate to construct a t-interval to estimate the population mean.

To determine whether it is appropriate to construct a t interval to estimate the population means, we need to consider if the sample size is large enough and if the population standard deviation is known.

If the sample size is less than 30 and the population standard deviation is not known, then it would be appropriate to use a t-interval.In this case, the sample size is 32, which is large enough to assume that the sample mean is an accurate representation of the population mean.

However, the population standard deviation is not known, so it would be appropriate to use a t interval. The t interval can be calculated using the sample mean, sample standard deviation, and degrees of freedom, which is the sample size minus 1.

The t interval will provide a range of values that we can be confident the population mean falls within, given the sample mean and variability.

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How much time do students spend on the internet? We collect data from the 32 members of our AP Statistics class and calculate the mean amount of time that each student spent on the Internet yesterday. Discuss whether it would be appropriate to construct a t interval to estimate the population mean.

The solution to the quadratic equation is ±6

From the question, we have the following steps that can be used in our computation:

2x^2 - 20 = 52

2x^2 = 32x^2

16x = ±4

The error in the above steps is appending x^2 to 32 after collecting the like terms.

Also, the like terms are not properly added

The correct solution is as follows

2x^2 - 20 = 52

Collect the like terms

2x^2 = 72

Divide by 2

x^2 = 36

Take the square root of both sides

x = ±6

Hence, the solution is ±6

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It is difficult to estimate the exact percentage of adult Americans who feel this way without further information, however 63% is a good indication that the majority of adult Americans favor capital punishment.

Based on the data provided, it is reasonable to assume that the majority of adult Americans favor capital punishment. This is supported by the survey results which show that 63% of respondents favor capital punishment (63.2% favor capital punishment; gss, 2018). However, without further information such as the survey sample size and what demographics were surveyed, it is difficult to estimate the exact percentage of adult Americans who feel this way. Nonetheless, the survey results indicate that the majority of adult Americans are in favor of capital punishment.

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Answer:

Alex deleted 45 selfies.

The probability that at least two bulbs must be selected to obtain one that is rated 75W is 2/3.

Number of 40W bulbs = 7

Number of 60W bulbs = 5

Number of 75W bulbs = 6

We are to find the probability that at least two bulbs must be selected to obtain one that is rated 75 w

Let's say the x is the event in which at least 2 bulbs must be selected to obtain one that is rated 75W and y is the event in which just one bulb was selected which is rated 75 W

So, P(x) = 1 - P(y)

P(x) = 1 - 6/(7 + 5 + 6)

P(x) = 1 - 6/18

P(x) = 1 - 1/3

P(x) = 2/3

Hence, the probability that at least two bulbs must be selected to obtain one that is rated 75W is 2/3.

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The expression can be used to find the number of CDs that are not country music is 52-c. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Kayla has 52 CDs in her music collection. Let c represent the number of country music CDs in Kayla's collection.

The expression can be used to find the number of CDs that are not country music is written as below:-

E =  52-c

The correct option is D for the required expression.

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The probability he can hit at least 9 of 10 shots anyway is 0.0463 or 4.63%

Divide the total number of outcomes by the entire number of different ways an event could happen to arrive at the probability. There are differences between probability and odds. Odds are determined by dividing the probability of a situation happening by the probability that it won't happen. Probability is a metric used to determine how likely an event is to occur. The likelihood that the coin will land with the heads side up is measured using the probability concept when we toss it in the air. Here is an example of how probability is used in everyday life that you probably already know about. Prior to a major outing, we always consult the weather prediction.

Given[tex]=60[/tex]%[tex]=0.60[/tex]

n[tex]=10[/tex]

Definition binomial probability:

[tex]P(X=k)=(n^{k} )*(P^{k} )*(1-P)^{n-k}[/tex]

Evaluate for [tex]k=9[/tex] and [tex]k=10[/tex]

P[tex](X=9)=0.0403[/tex]

P[tex](X=10)=0.0060[/tex]

Add the corresponding probabilities:

P[tex](x\geq 9)=P(X=9)+P(X=10)=0.0403+0.0060=0.0463=4.63[/tex]%

Command Ti83/84 command: binompdf(10,0.60,9)+binompdf(10,0.60,10)

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The distance between the top of the ladder and the ground is decreasing at a rate of 10 meters per minute.

Let's call the distance between the bottom of the ladder and the wall as "x".

At a certain instant, x = 3636 meters

The rate of change of x with respect to time is 10 meters per minute, so dx/dt = 10 m/min.

At that same instant, the height of the ladder above the ground can be expressed as

h = (3939 - x)

since the ladder is 3939 meters long

The rate of change of h with respect to time can be found using the chain rule of differentiation.

dh/dt = dh/dx * dx/dt = -10 m/min

So, at the instant when the bottom of the ladder is 3636 meters from the wall, the rate of change of the distance between the top of the ladder and the ground is -10 meters per minute. This means that the distance between the top of the ladder and the ground is decreasing at a rate of 10 meters per minute.

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Answer:

x=43

Step-by-step explanation:

since we know already two values (90 which is the right angle and 47)

we can do 90+47 =137

180(angles in a triangle)- 137= 43

The two column proof that shows that AE ≅ CE, and BE ≅ DE is as shown below.

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Statement 1: ABCD is a parallelogram

Reason 1: Given

Statement 2: AB ≅ CD

Reason 2: Parallelogram Side Theorem

Statement 3: ∠ABE and ∠CDE are alt. interior angles

Reason 3: Def. of alt. interior angles

Statement 4: ∠BAE and ∠DCE are alt. interior angles

Reason 4: Def. of alt. interior angles

Statement 5: AB ║ CD

Reason 5: Def. of Parallelogram

Statement 6: ∠BAE ≅ ∠DCE

Reason 6: alt. interior angles theorem

Statement 7: ∠ABE ≅ ∠CDE

Reason 7: alt. interior angles theorem

Statement 8: ΔBAE ≅ ΔDCE

Reason 8: ASA

Statement 9: AE ≅ CE

Reason 9: CPCTC

Statement 10: BE ≅ DE

Reason 10: CPCTC

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The triangles ∆DEF and ∆DGF are isosceles triangles, and the values of the following lengths are: EF = 44, FG = 36, and DF = 62.

EH is a perpendicular bisector of FD implies triangle ∆DGF is an isosceles triangle so:

FE is equal to ED and FG is equal to GD

7x + 9 = 9x - 1

9x + 7x = 9 + 1 {collect like terms}

2x = 10

x = 10/5 {divide through by 5}

x = 2

7y + 8 = 10y - 4

10y - 7y = 8 + 4 {collect like terms}

3y = 12

y = 12/3 {divide through by 3}

y = 4

EF = 7(5) + 9 = 44

FG = 7(4) + 8 = 36

DF = 2(FH)

FH = 3(5) + 4(4) = 31

DF = 2(31) = 62.

Therefore, the isosceles triangles ∆DEF and ∆DGF have the values of the following lengths as: EF = 44, FG = 36, and DF = 62.

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The largest group of students that the study results represent is "all UCLA graduate student apartments in the three sampled buildings".

The number of graduate student apartments in the three sampled buildings can be represented mathematically as:

N = 25 * 3

Where N is the number of apartments sampled and 25 is the number of apartments randomly selected in each of the three buildings.

This expression represents the total number of apartments in the largest group that the study results represent, which is "all UCLA graduate student apartments in the three sampled buildings."

This is because the survey only included data from 25 apartments in each of the three randomly selected buildings. The results of the study cannot be generalized to represent all UCLA graduate student apartments or even all apartments in the group of seven buildings as the sample size is limited to only three buildings. The results only provide information about the energy efficiency of the apartments in the three sampled buildings.

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Let's call the time it takes for the birds to be 25 miles apart t, in hours. In this time, the first bird will fly a distance of 8t miles to the east, and the second bird will fly a distance of 6t miles to the north.

To determine t, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the distance between the birds) is equal to the sum of the squares of the other two sides.

So, for the two birds to be 25 miles apart, we have:

25^2 = (8t)^2 + (6t)^2

25^2 = 64t^2 + 36t^2

25^2 = 100t^2

t^2 = 25^2 / 100

t^2 = 0.25

t = √0.25

t = 0.5

So, it will take the birds 0.5 hours, or 30 minutes, to be 25 miles apart.

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The value of x in the diagram is 100 degrees

From the question, we have the following parameters that can be used in our computation:

The figure

On the figure, we can see that:

The angle x and 100 degrees are alternate angles

Alternate angles have equal values

So, we have

x = 100

Hence, the value is 100 degree

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Answer:

[tex]\angle HLG=18 \textdegree[/tex]

Step-by-step explanation:

The sum of the angles in the top quadrant must add up to 90º.

We are given

[tex]25m+22[/tex]  and  [tex]9m[/tex]

The sum of those must equal 90.

Therefore we can write

[tex](25m+22)+(9m)=90[/tex]

Rearrange and remove the parenthesis.

[tex]9m+25m+22=90[/tex]

Add [tex]9m[/tex] and [tex]25m[/tex].

[tex]34m+22=90[/tex]

Subtract 22 form both sides of the equation.

[tex]34m=68[/tex]

Divide both sides of the equation by 34.

[tex]m=2[/tex]

Now we can evaluate [tex]\angle HLG[/tex].

[tex]\angle HLG=9m\\m=2\\\angle HLG=9*2\\\angle HLG=18 \textdegree[/tex]

The number of RPM flown on this flight from Los Angeles to Sydney is 2,150,960 Miles.

Revenue Passenger Miles (RPM) is a measure of how much passenger traffic an airline is serving, and is calculated by multiplying the number of revenue passengers (passengers paying a fare) by the distance travelled in miles. For this flight, the number of RPM is calculated as follows:

RPM = (Number of Revenue Passengers) x (Distance Travelled in Miles)

RPM = (285 Passengers) x (7,536 Miles)

RPM = 2,150,960 Miles

Therefore, the number of RPM flown on this flight from Los Angeles to Sydney is 2,150,960 Miles.

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Answer:

x = 8

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{RT}{WU}[/tex] = [tex]\frac{RS}{WV}[/tex] ( substitute values )

[tex]\frac{6x+15}{28}[/tex] = [tex]\frac{108}{48}[/tex] ( cross- multiply )

48(6x + 15) = 28 × 108 = 3024 ( divide both sides by 48 )

6x + 15 = 63 ( subtract 15 from both sides )

6x = 48 ( divide both sides by 6 )

x = 8