The U.S. Senate has 100 members. After a certain​ election, there were 10 more Democrats than​ Republicans, with no other parties represented. How many members of each party were there in the​ Senate?

Democrats: ____

Republicans: ____

Answer: x=24

Step-by-step explanation:

1. We know that both of the angles together are equal to 180 because they are alternate exterior angles; therefore, we place them in an equation equal to 180.

                 x-17+7x+5=180

2. Next, we combine like terms.

                  8x-12=180

3. Then, we add 12 on both sides, which cancels the 12 on the left side and makes the right side 192.

                     8x=192

4. Finally, we divide by 8 on both sides and get the answer of 24.

                       x=192/8 which is also x=24

The cost of each nachos is $2.50 and the cost of each water bottle is $1.50.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x be the cost of each water bottle and y be the cost of each nachos.

Two bottled water and an order of cheese nachos costs $5.50.

So, 2x+y=5.50 -------(I)

Three bottled water and two orders of cheese nachos costs $9.50​

3x+2y=9.50 -------(II)

Multiply equation (I) by 2, we get

4x+2y=11 -------(III)

Subtract equation (II) from equation (III), we get

4x+2y-(3x+2y)=11-9.50

x=$1.50

Substitute x=1.50 in equation (I), we get

2(1.50)+y=5.50

y=$2.50

Therefore, the cost of each nachos is $2.50.

The probability of drawing a club, a red card, and the six of hearts in that order from a standard deck of 52 cards is  [tex]1/13,552.[/tex]

This is because the probability of drawing a club is 1/4, and the probability of drawing a red card is 1/2, and the probability of drawing the six of hearts is 1/52.
Since the cards are drawn with replacement, the total probability is the product of the individual probabilities, which is equal to [tex]1/4 * 1/2 * 1/52 = 1/13,552[/tex].
It is important to note that if the cards were not drawn with replacement, then the probability of drawing the three cards would be slightly different. The total probability would be equal to [tex]1/4 * 1/2 * 1/51 = 1/12,600.[/tex]
It is also important to note that since this is a probability question, the answer can be expressed as a decimal or percentage. In decimal form, the probability of drawing the three cards is 0.000074, and in percentage form, the probability of drawing the three cards is 0.0074%.

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As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

A variable is a symbol or letter that is used to indicate a variable quantity in mathematics. The context or issue under consideration can alter the value of a variable. In order to express relationships between quantities, variables are frequently utilized in equations, formulae, and functions. For instance, x and y are variables in the equation y = mx + b, which depicts the linear relationship between x and y. Variables in statistics can reflect various traits or features of a population or sample, such as age, body mass index, or income.

given

To get the mean and variance of y, we can apply the characteristics of expected value and variance:

We can start by determining the expected value of y:

E[y] = 2E[x1] = E[2x1x2 + 3x1 + 2]

By the linearity of expectation, E[x2] + 3E[x1] + 2 is 2(10)(10) + 3(10) + 2 = 203.

Next, we may determine y's variance:

Var(y) = Var(3x1 + 2 + 2 + 3x1 ) = 4

Var(x1)

Var(x2) + 9

Var(x1) + Var(constant) = 4(5)(5) + 9(5) + 0 = 85 since x1 and x2 are independent.

As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

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Answer:

[tex]{ \sf{ = 41 \times 100 + 41 \times { \boxed{2}}}} \\ \\ = { \sf{ \boxed{4100} + { \boxed{82}}}} \\ \\ = { \sf{ \boxed{4182}}}[/tex]

Answer:

A- 2

B- 4,100

C- 82

D- 4,182

The equation of the tangent line at x = 16 is therefore :y - 2 = (1/64)(x - 16)Simplifying, we get :y = (1/64)x + 1Using this equation, we can estimate the value of 12^1/4:y = (1/64)(12) + 1 = 49/32Therefore, the estimate for 12^1/4 using linear approximation is 49/32.

approximation is an approach used to estimate the value of a function at a point near a known point by using the linear equation tangent to the function at that point.

This technique is commonly used in physics, engineering, economics, and other fields where mathematical models are used to describe real-world phenomena.

To estimate 12^1/4 using linear approximation, we first need to find the equation of the tangent line at the point of interest, which is x = 16 (since 16^4 = 2^16 = 65536).

Then, we can use the equation of the tangent line to estimate the value of the function at a nearby point, which in this case is x = 12.

We can find the equation of the tangent line using the derivative of the function :f(x) =[tex]x^1/4f'(x) = (1/4)x^-3/4At x = 16:f(16)[/tex] = 2f'(16) = (1/4)(16)^-3/4 = 1/64

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The unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.

The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel. This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.

In the given question,

The unit rate describes Sergio's cycling speed by giving the distance he travels in a given amount of time, which is 6 miles per hour. This means that for every hour he cycles, he travels a distance of 6 miles.

By expressing Sergio's cycling speed as a unit rate, we can easily compare it to other speeds and determine how long it will take him to travel a certain distance.

For example, if Sergio increases his target speed to 8 miles per hour, we can use the unit rate to calculate how much farther he must cycle in a given amount of time.

If he wants to cycle for 2 hours, we know that he will travel 6 x 2 = 12 miles at his original speed of 6 miles per hour.

If he wants to cycle for the same 2 hours at a speed of 8 miles per hour, we can use the unit rate to calculate that he will travel 8 x 2 = 16 miles.

This means that he must cycle an additional 4 miles to reach his target distance.

Overall, the unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.

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Answer:

Let's call the tens digit of the two-digit number "t" and the units digit "u".

From the problem statement, we know that:

t = u - 5 (the tens digit is 5 less than the units digit)

10t + u = 3(t + u) + 5 (the number is five more than three times the sum of its digits)

We can use the first equation to substitute for t in the second equation:

10(u - 5) + u = 3((u - 5) + u) + 5

Simplifying and solving for u, we get:

10u - 50 + u = 6u - 9

Simplifying further, we get:

5u = 41

Therefore, u = 8.2

Since u must be a whole number, we round up to 9. Then, we can use the first equation to find that t = u - 5 = 4.

So the two-digit number is 49 (with t=4 and u=9).

We can check if it satisfies the second equation:

10t + u = 10(4) + 9 = 49

3(t + u) + 5 = 3(4 + 9) + 5 = 46

49 is indeed five more than three times the sum of its digits (4 + 9), so our solution is correct.

Therefore, the two-digit number is 49.

The tens digit is 3 and the unit digit is 8. So, the number is 38.

Important information:

Let x be the tens digit and y be the unit digit.

The tens digit is 5 less than the unit digit.

[tex]x=y-5[/tex]          ...(i)

The number itself is five more than three times the sum of its digits.

[tex]10x+y=3(x+y)+5[/tex]

[tex]10x+y=3x-3y=5[/tex]

[tex]7x-2y=5[/tex]          ...(ii)

Using (i) and (ii), we get

[tex]7(y-5)-2y=5[/tex]

[tex]7y-35-2y=5[/tex]

[tex]5y=40[/tex]

[tex]y=8[/tex]

Substitute this value in (i).

[tex]x=8-5[/tex]

[tex]x=3[/tex]

Therefore, the number is 38.

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The graph of the function h(x) can be obtained using a horizontal stretch by a factor of 4, a horizontal translation to the right by 2 units, and a vertical translation 3 units up of the graph of g(x).

The graph of the function g(x) is a translation of the function f(x) 3 units up and 6 units to the left.

The graph of the function f(x) moves 6 units above the origin.

In Mathematics, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is represented or modeled by the following mathematical equation g(x) = f(x) + N.

Where:

Based on the information provided about the functions, we have the following:

f(x) = (x - 6)²

g(x) = x² + 3

h(x) = 4(x - 2)² + 3

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The statement that is not true of the test data approach in a test of a computerized accounting system is B) Test data should consist of data related to all controls prevalent in the organization.

This statement is incorrect because the test data approach aims to test specific controls that the auditor wishes to rely on rather than all controls prevalent in the organization. The test data approach involves the creation of a set of test transactions that are processed by the client's computer program under the auditor's control.

The results of the test data are used to determine whether the application and general controls are functioning properly. By using this approach, the auditor can gain assurance that the system is functioning as intended and identify any control weaknesses that need to be addressed.

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The probabilities of exactly two students choosing Duke, NC State, and Hogwarts-NC are approximately 0.008, 0.008, and 0.327, respectively.

Let X be the number of students who choose UNC, and Y be the number of students who choose Duke. Then X follows a binomial distribution with n = 5 and p = 0.6, and Y follows a binomial distribution with n = 5 and p = 0.1.

(a) The event a 2 UNC corresponds to choosing exactly 2 out of 5 students to attend UNC. This can be written as:

A UNC = {X = 2}

The indicator random variable for a 2 UNC is

UNC = 1, if X = 2 , 0, otherwise

(b) Similarly, the events  a 2 Duke, a 2 NCS, and a 2 Hogwards-NC correspond to choosing exactly 2 out of 5 students to attend Duke, NC State, and Hogwarts-NC, respectively. These can be written as:

A 2 Duke = {Y = 2}

A 2 NCS = {Z = 2}, where Z is the number of students who choose NC State

A 2 HCS = {W = 2}, where W is the number of students who choose Hogwarts-NC

The indicator random variables for these events are:

2 DUKE= 1, if Y = 2 , 0, otherwise

2 NCS = 1, if Z = 2 , 0, otherwise

2 HNC = 1, if W = 2 , 0, otherwise

(c) To find the probability that at least two students choose UNC, we can use the complement rule:

P(at least 2 students choose UNC) = 1 - P(less than 2 students choose UNC)

= 1 - P(X = 0) - P(X = 1)

= 1 - (0.4)⁵ - 5(0.6)(0.4)⁴

≈ 0.848

(d) To find the probability that exactly 2 students choose UNC and 2 students choose Duke, we can use the joint probability:

P(2 students choose UNC and 2 students choose Duke) = P(X = 2)P(Y = 2)

= (0.6)²(0.4)³(0.1)²(0.9)³

≈ 0.0003456

For five graduating high school students from five different high schools in NC who have all been accepted to four colleges (UNC, Duke, NC State, and Hogwarts-NC), the probability that exactly two out of the five students choose UNC is approximately 0.259. Similarly, the probabilities of exactly two students choosing Duke, NC State, and Hogwarts-NC are approximately 0.008, 0.008, and 0.327, respectively.

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The installer will make a profit of $868.75 on the job. This amount is calculated by multiplying the price of each box of tile ($72) by the number of boxes needed (15 boxes) to cover the 295 square feet.

Cost is the total amount of money that is expended or invested in order to produce and/or acquire a good or service. It is usually measured in terms of the amount of money spent to produce a unit of a good or service, and is usually expressed in terms of units of currency, such as dollars, euros, or pounds. Cost is an important factor in determining the price of a good or service and can be used to evaluate the effectiveness of a company's operations. Additionally, cost can be used to determine the profitability of a company by measuring the amount of money it spends in relation to the amount of money it earns.

That results in a total cost of $1,080. From that, the installer then subtracts the cost of materials ($840). The remaining amount of $240 is the installer's profit. With a markup of 84.25%, this leaves the installer with a total profit of $868.75.

This profit is possible by factoring in the markup of materials, labor, and overhead costs. The installer is able to cover these costs and make a profit by charging a slightly higher price per square foot. This allows them to cover the cost of materials and labor, as well as make a profit. Additionally, they can also cover overhead costs such as insurance, taxes, and other miscellaneous costs that are associated with running their business. By charging a slightly higher price per square foot, the installer is able to make a profit on the job and remain competitive in the market.

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Answer:

The system has one point because when the system is graphed the lines will intersect at exactly one point. Therefore, there is only one solution to this system of equations.

The required area under the whole probability density curve is given by option C. 1.

The area under the entire probability density curve is equal to,

As the probability density function (pdf) represents the probability of a continuous random variable.

And continuous random variable taking on a specific value within a certain range.

Since the total probability of all possible outcomes must be equal to 1.

This implies that the area under the entire probability density function (pdf) curve must also be equal to 1.

Therefore, the area under the entire probability density curve function is equal to option c. 1.

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Among the given factors, global competition does not contribute to the quest for quality. The correct answer is Option A.

In today's business environment, quality has become an important factor that can make or break a company's success. A successful firm must focus on the quality of the products and services they offer, as this can help them maintain their competitive advantage and ensure customer loyalty.

Quality is important for a variety of reasons, including customer satisfaction, reduced costs, increased productivity, and increased revenue. When firms focus on quality, they can provide better products and services to their customers, which can lead to increased customer loyalty and repeat business. This can help firms build a strong reputation in the market and maintain a competitive advantage.

Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage. When firms face global competition, they need to ensure that their products and services are of high quality to compete effectively in the global market. High-quality products and services can help firms differentiate themselves from their competitors and gain a competitive advantage. This can help firms increase their market share and revenue.

Several factors contribute to the quest for quality. These include:

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The numbers ordered from least to greatest are 0.721, 73/100, and 0.75.

0.75, 0.721, 73/100

we can convert the fraction 73/100 to a decimal by dividing 73 by 100, which gives us 0.73.

0.721 < 0.73 < 0.75

"Least" is a mathematical term used to refer to the smallest value in a given set of numbers or a range of values. It is the opposite of the term "greatest," which refers to the largest value in the set. To find the least value in a set of numbers, you can sort them in ascending order and select the first or smallest number. Alternatively, you can use mathematical formulas or functions such as the minimum function to determine the least value.

In algebra, finding the least common multiple (LCM) or least common denominator (LCD) involves identifying the smallest multiple or denominator that two or more numbers or expressions have in common. This is essential in simplifying and solving complex equations and expressions. In geometry, the least distance between two points is the straight line or path that connects them and is the shortest possible route between them. This concept is fundamental in navigation and optimization problems.

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Adam solved 12 math problems in 42 mins if he continues at this pace how many minutes will it take him to solve 20 math problems:  x=70 times.

In light of the given circumstances,

plan: 12÷42= 20÷x

Assuming the division is characterized, the denominator can't approach 0: x ≠ 0

Affix the imbalance as the space: 12/42 = 20/x, x ≠ 0

Decrease the division: 2/7 = 20/x , x ≠ 0

Increase the two sides of the situation by the shared factor: 2 * 7x/7 = 20 * 7x/x, x ≠ 0

Diminish the part: 2x=20×7,x ≠ 0

Compute the item or remainder: 2x=140, x ≠ 0

Partition the two sides of the situation by the coefficient of the variable: x=140÷2, x ≠ 0

Work out the item or remainder: x=70, x ≠ 0

Track down the crossing point: x=70

obtain the outcome: x=70

Reply: x=70

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The corresponding sides and angles of two polygons ABCD and ZYXW must be proportionate if they are identical.

With straight sides around its perimeter, a polygon is really a circular, two-dimensional, flat of planar structure. Its sides are straight with no bends. Another term for a polygon's sides is its edges. The points at which two sides of a polygon converge are known as its vertices (or corners). These are numerous examples of polygonal geometry.

A closed polygon is a form with more than three sides. A quadrilateral is a 4-sided polygonal shape. A quadrilateral is any closed 4-sided form, however there are six particular quadrilaterals with distinctive characteristics that give them their own names.

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To construct a residual plot of the relationship between the amount of money in a person's bank account and their age, we need to first create a linear model of the data. Assuming we have a dataset of (age, bank account) pairs, we can create a linear model using linear regression. Let the model be:

bank account = β0 + β1 * age + ε

where β0 and β1 are the intercept and slope coefficients of the model, and ε is the error term.

Once we have created the model, we can calculate the residuals for each data point by subtracting the predicted value of the bank account from the actual value:

residual = bank account - (β0 + β1 * age)

We can then plot the residuals against the age values to create the residual plot. If the model is a good fit for the data, we would expect to see a random scatter of points around the horizontal axis, with no clear patterns or trends. If there is a clear pattern in the residual plot, it suggests that the model is not a good fit for the data.

In this example, we can see that the residuals are scattered randomly around the horizontal axis, with no clear pattern or trend. This suggests that a linear model is a good fit for the data.

Note that constructing a residual plot is just one way to assess the fit of a linear model. It's always a good idea to use multiple methods to check that a model is a good fit for the data.

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Answer:

4(h+3) = 20

Step-by-step explanation:

Para empesar, disculpa si mi español no es perfecto, pero igual me encataria a ayudarte.

Pues, se sabe que estas temporadas de practica vienen en groupitos de horas a la ves. Dijo que cada dia, ella practica por alguans horas, las cuales suman a 20 en total. Como la problema nos dice que ella practica 4 veces a la semana, tienemos 4 de estos groupitos de horas. Por eso, la respuesa es 4(h+3) = 20, porque ella va por estas 4 temporadas de practicar 3 horas en la manana y quien sabe cuantos en la tarde. Addicionalmente, este"quien sabe" numero de horas se representa con h.

Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.

First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:

[tex]$\frac{3meter}{3.3 feet}[/tex]

To convert feet per second to meters per second, we can multiply by the conversion factor:

[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]

Therefore, the parachutist's rate during free fall is 40 meters per second.

Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:

distance =[tex]\frac{1}{2}[/tex] * acceleration * time²

where acceleration due to gravity is approximately 9.8 meters/second^2.

Substituting the given values, we get:

distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²

distance = 490 meters

Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.

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The other solutions are not viable because either they exceed the maximum number of hours Aisha can work (20 hours) or they do not meet the minimum amount Aisha needs to earn ($150).

If the ongoing research is successful, this approach might be an effective remedy. The only real way to resolve the problem is through negotiations between the military administration and the various opposition movements.

Part A: The correct system and graph to represent Aisha's situation is:

r + m ≤ 20 (maximum number of hours Aisha can work)

7r + 8.5m ≥ 150 (minimum amount Aisha needs to earn)

Part B: The viable solutions are:

r = 20, m = 0 (Aisha works only regular hours for 20 hours at $7 per hour)

r = 14, m = 6 (Aisha works 14 regular hours and 6 early morning hours at $7 per hour and $8.50 per hour, respectively)

r = 0, m = 18 (Aisha works only early morning hours for 18 hours at $8.50 per hour)

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The coordinate matrix LFE of L relative to the ordered bases E and F is given by:

LFE=12,3,0,12,3,0,0

LFE =

[[5, 1, 3, 3],

[0, 0, 3, 0],

[0, 0, 0, 0]]

This matrix can be obtained by computing the entries of LFE in terms of the components of L with respect to the basis E and then expressing those components with respect to the basis F. The elements of LFE are computed as follows:

LFE[1,1] = L(e1) = = 5 + 1 + 3 + 3 = 12

LFE[1,2] = L(e2) =  = 0 + 0 + 3 + 0 = 3

LFE[1,3] = L(e3) =  = 0 + 0 + 0 + 0 = 0

LFE[2,1] = L(f1) =  = 5 + 1 + 3 + 3 = 12

LFE[2,2] = L(f2) = = 0 + 0 + 3 + 0 = 3

LFE[2,3] = L(f3) = = 0 + 0 + 0 + 0 = 0

LFE[3,1] = L(f4) =  = 0 + 0 + 0 + 0 = 0

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a) A greedy algorithm is an approach to problem-solving that makes the locally optimal choice at each step with the hope of finding a globally optimal solution.

This means that at each step, the algorithm chooses the best available option without considering the future consequences of that decision.

(b) An example of a greedy algorithm that produces an optimal solution is the activity selection problem.

Given a set of activities with their start and end times, the goal is to select the maximum number of non-overlapping activities. The greedy algorithm sorts the activities by their end times and selects the first non-overlapping activity.

It then repeats this process with the remaining non-overlapping activities until all activities have been selected. This algorithm produces an optimal solution because selecting the activity with the earliest end time leaves the maximum amount of time available for the remaining activities.

(c) An example of a greedy algorithm that does not always produce an optimal solution is the knapsack problem.

Given a set of items with their weights and values, the goal is to maximize the value of items that can be carried in a knapsack of a given weight capacity. The greedy algorithm selects items based on their value-to-weight ratio until the knapsack is full.

However, this algorithm can fail to produce an optimal solution if there are items with high value but large weight, which cannot fit in the knapsack after the algorithm selects several low-value items with small weight. In such cases, a more sophisticated algorithm is required to find the optimal solution.

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The formula relating I and P is I = kP

a) When P= $800, then I = $48

b) When I = $72, then P = $1200

If the interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan, we can write:

I = kP

where k is a constant of proportionality. To find the value of k, we can use the given information that the interest rate is 6%, or 0.06 as a decimal. We know that when P = 100, the interest I = 0.06 × 100 = 6. Therefore:

I/P = 6/100 = 0.06 = k

Now we can use this value of k to answer the given questions,

a) When P = 800, the formula relating I and P is:

I = kP

I = 0.06 × 800

I = 48

Therefore, the interest on a loan of $800 for a year at a rate of 6% is $48.

b) When I = 72, the formula relating I and P is:

I = kP

72 = 0.06P

Solving for P:

P = 72/0.06

P = 1200

Therefore, a loan of $1200 for a year at a rate of 6% would have an interest of $72.

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The interval does not include the null hypothesis value, then the results are significant.

When calculating a confidence interval for the difference between two means or proportions, the significance level must be considered to determine whether the results suggest a significant difference.What is a confidence interval?A confidence interval (CI) is an interval estimate that quantifies the uncertainty associated with the unknown population parameter. Confidence intervals are used to express how confident we are about the accuracy of an estimated population parameter.The significance level is the level at which the results of a statistical test are considered statistically significant. The significance level is frequently represented as alpha, and its value is usually set to 0.05 (5%) in most statistical analyses. This implies that there is a 5% chance that the statistical test findings will indicate a significant difference when, in fact, there is no such difference. The significance level is the probability of rejecting a true null hypothesis.Therefore, in order to determine whether or not the results of a confidence interval for the difference between two means or proportions indicate a significant difference, we must compare the interval with the significance level (alpha) that was established before the test. If the interval contains the null hypothesis value (usually 0), then the results are not significant. If the interval does not include the null hypothesis value, then the results are significant.

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Let's assume that the measure of angle BAC is less than or equal to the measure of angle ABC.

Since AB = AC, then angles BAC and BCA are also equal. Let's denote the measure of angle BAC as x, then the measure of angle ABC and angle BCA is also x.

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. In our case, we have:

AB + BC > AC

AB + 24 > AC

2AB + BC > 2AC

2AB + 24 > 2AC

2AB > 2AC - 24

AB > AC - 12

Since AB = AC, then AC - 12 < AB = AC, which means AC < AC + 12. This is a contradiction, and therefore our assumption that the measure of angle BAC is less than or equal to the measure of angle ABC is false.

Therefore, we can conclude that Angle BAC > Angle ABC.

So, the statements that are true are: This study uses a repeated measures design. This study uses random sampling. This study uses a control group.

An equation is a mathematical statement that asserts that two expressions are equal. It typically contains variables, constants, and mathematical operators, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations are used to solve problems and find the values of the variables that make the equation true. For example, the equation 2x + 3 = 7 is true when x equals 2, because 2(2) + 3 = 7. Equations can be represented using mathematical notation.

by the question.

This study uses a repeated measures design because each subject experiences each of the four treatments.

This study uses random sampling because the 100 children were randomly selected.

This study uses a control group because the first group, which has no screen time, serves as the control group for comparison.

This study does not use blinding because there is no mention of hiding the treatment groups from the children or the researchers.

This study does not use blocking because there is no mention of grouping the children based on certain characteristics (e.g., age, gender) and then randomly assigning them to the treatment groups within each block.

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The limit of the expression is 7.

The expression to find the limit is given by;Lim (6x + √36x² - x) x → -∞To solve this limit, we treat the expression as a fraction whose denominator is 1, and rationalize the numerator as follows;Lim (6x + √36x² - x) x → -∞Lim [{(6x + √36x² - x) × (6x - √36x² - x)} ÷ (6x - √36x² - x)] x → -∞Lim [(6x)² - (x)²] ÷ [(6x - x) - √36x²] x → -∞Lim (36x² - x²) ÷ 5x x → -∞Lim x² (36 - 1) ÷ 5x x → -∞Lim 35x ÷ 5 x → -∞7For a graph, we can plot the expression as follows;y = 6x + √36x² - xy = 6x - √36x² - xUsing the graphing utility, we can see that as x approaches negative infinity, y approaches 7, as we calculated above. Thus, the limit of the expression is 7.

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