-x squared +12x+14 and 2x+30 solve this system of equations

The type of experimental design where the assignment of Experimental units to treatment and control groups is random is called a randomized controlled trial (RCT).

The type of experimental design where the assignment of experimental units to treatment and control groups is random is called a randomized controlled trial (RCT).

Randomized controlled trials are widely used in various fields of research, including medicine, psychology, and social sciences. They are considered the gold standard for evaluating the effectiveness of interventions or treatments. The key feature of an RCT is the random assignment of participants or experimental units to either the treatment group or the control group.

Randomization helps to ensure that the treatment and control groups are similar in terms of both observed and unobserved characteristics, reducing the potential for bias and confounding variables. By randomly assigning participants, researchers can make causal inferences about the effects of the treatment, as any observed differences between the groups can be attributed to the intervention.

In an RCT, experimental units can be individuals, groups, organizations, or any other defined units depending on the research context. The random assignment process involves using a randomization procedure, such as coin flipping, random number tables, or computer-generated randomization, to assign participants to the treatment and control groups.

By comparing the outcomes or responses of the treatment and control groups, researchers can determine the effectiveness or impact of the intervention being studied. Statistical techniques, such as hypothesis testing and analysis of variance, are commonly used to analyze the data collected from the RCT and draw conclusions.

a randomized controlled trial is the type of experimental design where the assignment of experimental units to treatment and control groups is random. It is a rigorous approach to evaluating the effects of interventions and minimizing biases, providing robust evidence for decision-making and policy development.

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Answer:

The domain of a radical function is the set of all real numbers for which the function is defined. In this case, we have the function f(x) = √(x + 1) - 3.

For the function to be defined, the value inside the square root (√) must be non-negative, since the square root of a negative number is undefined in the real number system.

So, to determine the domain, we set the expression inside the square root greater than or equal to zero:

x + 1 ≥ 0

Solving for x:

x ≥ -1

Therefore, the domain of the given radical function is all real numbers greater than or equal to -1. In interval notation, the domain can be expressed as (-1, +∞).

Answer:

x = 1

Step-by-step explanation:

To solve the given equation, we'll start by setting up the equation and simplifying it step by step:

The product of (x + 3) and (2x + 3) is 14 more than the product of (x + 1) and (2x + 1).

(x + 3)(2x + 3) = (x + 1)(2x + 1) + 14

Expanding both sides of the equation:

2x^2 + 3x + 6x + 9 = 2x^2 + x + 2x + 1 + 14

Combining like terms:

2x^2 + 9x + 9 = 2x^2 + 3x + 15

Subtracting (2x^2 + 3x + 15) from both sides:

2x^2 + 9x + 9 - 2x^2 - 3x - 15 = 0

Simplifying:

6x - 6 = 0

Adding 6 to both sides:

6x = 6

Dividing both sides by 6:

x = 1

Therefore, the value of x that satisfies the equation is x = 1.

Hope this helps!

(a) The probability of selecting exactly two white balls and two red balls is 5/11.

(b)The probability of selecting at least two white balls is 208/33, or about 0.63

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

There are several approaches to this problem, but one popular option is to employ combinations. The combination formula gives the number of possibilities to pick k things from a set of n objects:

C(n, k) = n! / (k!(n-k)!)

where n! represents n factorial (the sum of all positive integers up to and including n).

a) To calculate the chance of picking exactly two white balls and two red balls, we must count the number of possibilities to select two white balls and two red balls from a set of six white balls and five red balls. We may then divide this number by the total number of ways to select any four balls from the 11 available.

Number of favorable outcomes:

C(6, 2) x C(5, 2) = 15 x 10 = 150

Total number of outcomes:

C(11, 4) = 330

Probability of selecting exactly two white balls and two red balls:

P(2 white and 2 red) = 150/330 = 5/11

Therefore, the probability of selecting exactly two white balls and two red balls is 5/11.

b)To calculate the probability of picking at least two white balls, count the number of ways to select 2, 3, or 4 white balls and then sum the probabilities. We may also remove the probability  of picking 0 or 1 white balls from 1 (the overall probability).

Number of favorable outcomes:

C(6, 2) x C(5, 2) + C(6, 3) x C(5, 1) + C(6, 4) x C(5, 0)

= 150 + 120 + 15

= 285

Total number of outcomes:

C(11, 4) = 330

Probability of selecting at least two white balls:

P(at least 2 white) = 1 - P(0 white) - P(1 white)

To calculate P(0 white), we count the number of ways to select four red balls from a possible five and divide by the total number of outcomes:

C(5, 4) / C(11, 4) = 5/33

To find P(1 white), we count the number of ways to choose 1 white ball and 3 red balls, and multiply by the number of ways to arrange these balls (4!):

C(6, 1) x C(5, 3)x 4! / C(11, 4) = 120/33

Therefore, we have:

P(at least 2 white) = 1 - 5/33 - 120/33 = 208/33

The chance of picking at least two white balls is thus 208/33, or approximately 0.63 (rounded to two decimal places).

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Answer:

Hector watches Jaden swim in the ocean

Answer:

[tex]\mathrm{\frac{n(n-1)}{2}}[/tex]

Step-by-step explanation:

[tex]\mathrm{The\ formula\ for\ the\ number\ of\ handshakes\ possible\ among\ n\ participants\ is:}\\ \mathrm{ \frac{n(n-1)}{2}}\\\mathrm{It's\ because\ each\ of\ the\ n\ participants\ may\ shake\ hands\ with\ n-1\ people}\mathrm{(they}\\\mathrm{cannot\ shake\ their\ own\ hands)\ and\ the\ handshake\ between\ two\ people\ is\ not}\\ \mathrm{counted\ twice.}[/tex]

The minimum distance between the two balls is: 5 + (Robinson's vertical velocity) * t - (1/2) * g * [tex]t^2[/tex] = 6 + (Derek's vertical velocity) * t - (1/2) * g * [tex]t^2[/tex]

Using the given information, we can calculate the horizontal and vertical components of Robinson's initial velocity:

Robinson's horizontal velocity: 45 ft/sec * cos(44 degrees)

Robinson's vertical velocity: 45 ft/sec * sin(44 degrees)

Using the given information, we can calculate the horizontal and vertical components of Derek's initial velocity:

Derek's horizontal velocity: 41 ft/sec * cos(39 degrees)

Derek's vertical velocity: 41 ft/sec * sin(39 degrees)

For Robinson's ball:

Robinson's y-coordinate at time t = 5 ft + (Robinson's vertical velocity) * t - (1/2) * g * [tex]t^2[/tex]

For Derek's ball:

Derek's y-coordinate at time t = 6 ft + (Derek's vertical velocity) * [tex]t - (1/2) * g * t^2[/tex]

Set these two equations equal to each other and solve for t:

5 + (Robinson's vertical velocity) *[tex]t - (1/2) * g * t^2 = 6[/tex] + (Derek's vertical velocity) * t - (1/2) * g * [tex]t^2[/tex]

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[tex]2^3 + 3^3 - 5[/tex] :

[tex]\sf\:2^3 + 3^3 - 5 = 8 + 27 - 5 \\ = 35 - 5 \\ = 30[/tex]

Therefore, [tex]2^3 + 3^3 - 5[/tex] equals 30.

The points with black dots on the number line represent the fractions.

In elementary mathematics -

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Given are the fractions -

5/6 and 2 2/3

We can write

2 2/3 = 8/3 = 16 / 6

And, 5/6 = 5/6

Refer to the number line attached.

The points with black dots represent the numbers.

Therefore, the points with black dots on the number line represent the fractions.

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Answer:

To convert feet to yards, we can use the conversion factor:

1 yard = 3 feet

To find out how many yards long Joey's truck is, we divide the length of the truck in feet by 3:

Length in yards = Length in feet / 3

Length in yards = 18 feet / 3

Length in yards = 6 yards

Therefore, Joey's truck is 6 yards long.

Answer:

he covered a distance of 210km

Step-by-step explanation:

distance is calculated by speed multiplied by time, therefor we need to multiply 70 with 3.

70km/hr means that for every hour that has passed he drove 70km

he drove for 3 hours, so the answer is 210km

The pulse rate of 133.9 beats per minute is significantly high.

We have to use the range rule of thumb. The range rule of thumb states that values within two standard deviations of the mean are considered typical, while values outside this range may be considered significantly low or significantly high.

The range in this case would be calculated as follows:

= 2 * standard deviation

= 2 * 11.3

= 22.6 beats per minute.

Lower Limit = Mean - Range

Lower Limit = 71.3 - 22.6

Lower Limit = 48.7 beats per minute.

Upper Limit = Mean + Range

Upper Limit = 71.3 + 22.6

Upper Limit = 93.9 beats per minute.

Since the pulse rate of 133.9 beats per minute is higher than the upper limit of 93.9 beats per minute, it is considered significantly high.

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Answer:

[tex]\displaystyle{f(x)=(x+4)(x-3)}[/tex], the second choice.

Step-by-step explanation:

Since the problem gives us that the quadratic function has roots of -4 and 3. Therefore, this means that:

[tex]\displaystyle{x=-4,3}[/tex]

Which can be reverted back to:

[tex]\displaystyle{f(x)=(x+4)(x-3)}[/tex]

However, we cannot assume that a = 1 in this case, so:

[tex]\displaystyle{f(x)=a(x+4)(x-3)}[/tex]

To clear any confusions, a means how narrow or wide the graph is, the same a-term in standard form or vertex form.

As the point (2, -6) is said to lie on f(x), therefore, substitute x = 2 and y = -6 to solve for a:

[tex]\displaystyle{-6=a(2+4)(2-3)}\\\\\displaystyle{-6=a(6)(-1)}\\\\\displaystyle{-6=-6a}\\\\\displaystyle{a=1}[/tex]

Therefore, a = 1. Thus, the equation of f(x) is:

[tex]\displaystyle{f(x)=(x+4)(x-3)}[/tex]

The probability of drawing a number more than 5​ is 0.167

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

A number cube of 6 faces

Where we have

Total outcomes = 6

Outcome greater than 5 = 1 i.e. face e

Using the above as a guide, we have the following:

P(Number greater than 5) = 1/6

Evaluate

P(Number greater than 5) = 0.167

Hence, the the probability of drawing a number more than 5​ is 0.167

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Complete question

A number cube with faces labeled from 1 to 6 is rolled once.

Find the probability of drawing a number more than 5​

The length of each of the remaining sides of the isosceles trapezoid is 11 meters.

Let's denote the length of the remaining sides of the isosceles trapezoid as "x" meters each.

The perimeter of the trapezoid is the sum of all its side lengths. In this case, we have:

Shorter base + Longer base + Side 1 + Side 2 = Perimeter

Plugging in the given values:

4 + 6 + x + x = 32

Simplifying the equation:

10 + 2x = 32

Subtracting 10 from both sides:

2x = 22

Dividing both sides by 2:

x = 11

Therefore, the length of each of the remaining sides of the isosceles trapezoid is 11 meters.

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Answer:

[tex]\mathrm{x=34^o}[/tex]

Step-by-step explanation:

[tex]\mathrm{Since\ A\ and\ B\ are\ complementary\ angles,}\\\mathrm{\angle A+\angle B=90^o}\\\mathrm{or,\ (x+22)^o+x^o=90^o}\\\mathrm{or,\ 2x+22^o=90^o}\\\mathrm{or,\ 2x=68^o}\\\mathrm{or,\ x=34^o}[/tex]

The value of x is :

Solution:

If two angles are complementary, their sum is 90°.

Since A and B are complementary, we know that :

[tex]\rm{A+B=90}[/tex]

The values are x + 22 and x, respectively.

[tex]\rm{x+22+x=90}[/tex]

Combine like terms.

[tex]\rm{2x+22=90}[/tex]

[tex]\rm{2x=68}[/tex]

Divide each side by 2.

[tex]\rm{x=34}[/tex]

The value of the other angle is:

[tex]\rm{x=34+22}[/tex]

[tex]\rm{x=56}[/tex]

Based on the information provided, it seems like there is a dataset that contains three values: 30, 39, and 45. The prompt states that each value appears a certain number of times in the dataset.

For example, the value 30 appears "time(s)" in the dataset, although we don't know exactly how many times it appears. Similarly, the value 39 appears a certain number of times, as does the value 45.

Without more information about the dataset, it is difficult to draw any conclusions about the significance or pattern of these values. It is possible that they are part of a larger dataset and represent only a small portion of the data.

Alternatively, they could be outliers or represent a significant trend in the data. Further analysis would be necessary to determine their meaning and significance.

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The integer representation of a debt of R16,00 would be -1600.

In integer representation, debts are typically represented as negative numbers.

In this case, since the debt is R16,00, we would represent it as -1600.

The negative sign indicates that it is a debt or a negative value, and the number 1600 represents the magnitude or amount of the debt.

By using a negative integer, we can accurately represent the concept of a debt in mathematical calculations and representations.

Hence, the integer representation of a debt of R16,00 would be -1600.

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The equation is 13x + 2 = 15x - 2.

The value of x is 2.

The measure of the angles are:

BGF is 28.

EHC is 28.

EGB is 152.

FHD is 28.

We have,

From the figure,

BGF and EHC are alternate angles.

Since AB and CD are parallel lines.

Now,

FHC and EHD are opposite angles.

Since they share the same common point.

Now,

The equation is:

BGF and EHC are alternate angles.

This means,

13x + 2 = 15x - 2

2 + 2 = 15x - 13x

4 = 2x

x = 2

Now,

BGF = 13x + 2 = 13 x 2 + 2 = 26 + 2 = 28

EHC = 15x - 2 = 15 x 2 - 2 = 30 - 2 = 28

Now,

BGF + EGB = 180

EGB = 180 - 28 = 152

And,

EHC and FHD are alternate angles.

so,

FHD = 28

Thus,

The equation is 13x + 2 = 15x - 2.

The value of x is 2.

The measure of the angles are:

BGF is 28.

EHC is 28.

EGB is 152.

FHD is 28.

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The two Skyscrapers are approximately 7670.51 feet apart.

The distance between the two skyscrapers, we can use trigonometry and the given information about the angle of inclination and the height of skyscraper B. Let's break down the problem step by step.

1. Let's denote the distance between the bases of the two skyscrapers as d.

2. We can visualize the situation as a right triangle, where the height of skyscraper B (1463 feet) represents the opposite side and the distance between the two buildings (d) represents the adjacent side. The angle of inclination (10.5°) is the angle between the adjacent side and the hypotenuse.

3. The trigonometric function that relates the opposite side, adjacent side, and the angle of inclination is the tangent (tan) function: tan(angle) = opposite/adjacent.

4. Plugging in the known values, we have tan(10.5°) = 1463/d.

5. To solve for d, we can rearrange the equation: d = 1463 / tan(10.5°).

6. Evaluating the tangent of 10.5° using a calculator, we find that tan(10.5°) is approximately 0.1908.

7. Now, substituting this value into the equation, we have d = 1463 / 0.1908.

8. Calculating the right side of the equation, we find that d is approximately 7670.51 feet.

Therefore, the two skyscrapers are approximately 7670.51 feet apart.

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The Price per gram is $60, you will receive 2/3 of a gram of the product.

The product get $40 out of the $60 cost, we can set up a proportion based on the price per gram.

1. Let's denote the amount of product you will receive as x grams.

2. According to the given information, the price per gram is $60.

3. The total cost of the product can be calculated by multiplying the price per gram by the amount of product: $60/gram * x grams.

4. The amount of money you have available is $40.

5. We can set up a proportion to find the amount of product you will receive:

  ($60/gram * x grams) / $40 = 1

6. To solve for x, we can cross-multiply and solve for x:

  ($60/gram * x grams) = $40 * 1

7. Simplifying the equation, we have:

  $60x = $40

8. To isolate x, we divide both sides of the equation by $60:

  x = $40 / $60

9. Calculating the right side of the equation, we find:

  x = 2/3

Therefore, if you only have $40 and the price per gram is $60, you will receive 2/3 of a gram of the product.

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hello

the answer to the question is:

[tex]surface \: area = 2bs + {b}^{2} \\ = 2 \times 2 \times 6 + {2}^{2} = 28[/tex]

Rina will earn approximately $28.13 in interest in one quarter on her 12-month CD.

To calculate the amount of interest Rina will earn in one quarter on her 12-month CD, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount (including both principal and interest)

P is the principal amount (initial deposit)

r is the annual interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, Rina deposited $3,000 into a 12-month CD, so:

P = $3,000

r = 3.75% = 0.0375 (as a decimal)

n = 4 (compounded quarterly)

t = 1/4 (one quarter, or 1/4 of a year)

Substituting these values into the formula, we have:

A = 3000(1 + 0.0375/4)^(4 * 1/4)

= 3000(1 + 0.009375)^1

= 3000(1.009375)^1

= 3000(1.009375)

= 3028.13

The final amount (including both principal and interest) after one quarter is approximately $3,028.13.

To calculate the amount of interest earned in one quarter, we subtract the principal amount from the final amount:

Interest earned in one quarter = $3,028.13 - $3,000

= $28.13

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The total amount of money Share is £700, Peter would receive approximately £300.

The problem, let's assign variables to the amounts of money received by each person. Let's say Nick receives N pounds, Oliver receives O pounds, and Peter receives P pounds.

According to the given ratio, the amounts of money shared can be expressed as:

Nick:Oliver:Peter = 3:5:6

Since Nick receives £250 less than Oliver, we can set up the equation:

N = O - £250

Now we have two equations:

1) N + O + P = Total amount of money shared (unknown)

2) N = O - £250

To find the amount Peter receives (P), we need to substitute the values from the ratio into equation 1 and solve for P.

The ratio sums up to 3 + 5 + 6 = 14. So, the total amount of money shared is divided into 14 equal parts.

P = (6/14) * Total amount of money shared

Simplifying the fraction:

P = (3/7) * Total amount of money shared

Now, to determine the value of P, we need the total amount of money shared. If you have that information, substitute it into the equation and calculate P using a calculator.

For example, if the total amount of money shared is £700, we can calculate:

P = (3/7) * £700

P ≈ £300

Therefore, if the total amount of money shared is £700, Peter would receive approximately £300.

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The expected value is X/1000.

To find the expected value for this game, we need to calculate the average value of the winnings over the long run. In this case, the player has a 1 in 1000 chance of winning $X and a 999 in 1000 chance of winning $0. Let's assume that X is the amount won when the selected number is chosen.

The expected value (EV) can be calculated using the following formula:

EV = (Probability of winning $X) * (Amount won) + (Probability of winning $0) * (Amount won)

In this game, the probability of winning $X is 1/1000, and the probability of winning $0 is 999/1000. The amount won is $X when the selected number is chosen. Therefore, the expected value can be calculated as follows:

EV = (1/1000) * X + (999/1000) * 0

= X/1000 + 0

= X/1000

The expected value is X/1000. This means that on average, for every game played, the player can expect to win X/1000 dollars. It represents the long-term average winnings per game.

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To map Figure T to Figure U, we can use the following sequence of transformations:

Translation: Move the figure 10 units to the right and 12 units down.

This will shift all the points in Figure T by the specified distances.

Reflection: Reflect the figure across the vertical axis.

This will reverse the order of the points horizontally.

Translation: Move the figure 5 units to the right and 10 units up.

This will shift all the points in Figure T (which is now reflected) by the specified distances.

The resulting sequence of transformations would be:

Translation (10 units right, 12 units down) -> Reflection (across the vertical axis) -> Translation (5 units right, 10 units up)

Applying these transformations to Figure T should result in Figure U.

The scale factor used in the dilation is 3.

First, the distance between points A and B in triangle ABC is:

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

AB = √[(1 - (-1))² + (1 - (-1))²]

AB = √[(2)² + (2)²]

AB = √[4 + 4]

AB = √8

The distance between points A' and B' in triangle A'B'C' is:

A'B' = √[(x₂' - x₁')² + (y₂' - y₁')²]

A'B' = √[(3 - (-3))² + (3 - (-3))²]

A'B' = √[(6)² + (6)²]

A'B' = √[36 + 36]

A'B' = √72

The scale factor can be determined by dividing the corresponding side lengths:

Scale factor = A'B' / AB

Scale factor = √72 / √8

Scale factor = (√(72/8))

Scale factor = √9

Scale factor = 3

Therefore, the scale factor used in the dilation is 3.

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